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  Linux color management

  Linux color management has the same goal as the color management systems (CMS) for other operating systems, which is to achieve the best possible color reproduction throughout an imaging workflow from its source (camera, video, scanner, etc.), through imaging software (Digikam, darktable, RawTherapee, GIMP, Krita, Scribus, etc.), and finally onto an output medium (monitor, video projector, printer, etc.). In particular, color management attempts to enable color consistency across media and throughout a color-managed workflow. Linux color management relies on the use of accurate ICC (International Color Consortium) and DCP (DNG Color Profile) profiles describing the behavior of input and output devices, and color-managed applications that are aware of these profiles. These applications perform gamut conversions between device profiles and color spaces. Gamut conversions, based on accurate device profiles, are the essence of color management. Historically, color management was not an initial design consideration of the X Window System on which much of Linux graphics support rests, and thus color-managed workflows have been somewhat more challenging to implement on Linux than on other OS's such as Microsoft Windows or macOS. This situation is now being progressively remedied, and color management under Linux, while functional, has not yet acquired mature status. Although it is now possible to obtain a consistent color-managed workflow under Linux, certain problems still remain: The absence of a central user control panel for color settings. Some hardware devices for color calibration lack Linux drivers, firmware or accessory data. Since ICC color profiles are written to an open specification, they are compatible across operating systems. Hence, a profile produced on one OS should work on any other OS given the availability of the necessary software to read it and perform the gamut conversions. This can be used as a workaround for the lack of support for certain spectrophotometers or colorimeters under Linux: one can simply produce a profile on a different OS and then use it in a Linux workflow. Additionally, certain hardware, such as most printers and certain monitors, can be calibrated under another OS and then used in a fully color-managed workflow on Linux. The popular Ubuntu Linux distribution added initial color management in the 11.10 release (the "Oneiric Ocelot" release). == Requirements for a color-managed workflow == Accurate device profiles obtained with source or output characterization software. Correctly loaded video card lookup tables (LUTs) (or monitor profiles that do not require LUT adjustments). Color-managed applications that are configured to use a correct monitor profile and input/output profiles, with support for control over the rendering intent and black point compensation. Calibration and profiling requires: for input devices (scanner, camera, etc.) a color target which the profiling software will compare to the manufacturer-provided color values of the target. or for output devices (monitor, printer, etc.) a reading with a specific device (spectrophotometer, colorimeter or spectrocolorimeter) of the color patch values and comparing the measured values against the values originally sent for output. === Monitor calibration and profiling === One of the critical elements in any color-managed workflow is the monitor, because, at one step or another, handling and making color adaptation through imaging software is required for most images, thus the ability of the monitor to present accurate colors is crucial. Monitor color management consists of calibration and profiling. The first step, calibration, is done by adjusting the monitor controls and the output of the graphics card (via calibration curves) to match user-definable characteristics, such as brightness, white point and gamma. The calibration settings are stored in a .cal file. The second step, profiling (characterization), involves measuring the calibrated display's response and recording it in a color profile. The profile is stored in an .icc file ("ICC file"). For convenience, the calibration settings are usually stored together with the profile in the ICC file. Note that .icm files are identical to .icc files - the difference is only in the name. Seeing correct colors requires using a monitor profile-aware application, together with the same calibration used when profiling the monitor. Calibration alone does not yield accurate colors. If a monitor was calibrated before it was profiled, the profile will only yield correct colors when used on the monitor with the same calibration (the same monitor control adjustments and the same calibration curves loaded into the video card's lookup table). macOS has built-in support for loading calibration curves and installing a system-wide color profile. Windows 7 onward allows loading calibration curves, though this functionality must be enabled manually. Linux and older versions of Windows require using a standalone LUT loader. === Device profiles === ICC profiles are cross-platform and can thus be created on other operating systems and used under Linux. Monitor profiles, however, require some additional attention. Since a monitor profile depends both on the monitor itself and on the video card, a monitor profile should only be used with the same monitor and video card with which it was created. The monitor settings should not be adjusted after creating the profile. In addition, since most calibration software use LUT adjustments during calibration, the corresponding LUTs must be loaded every time the display server (X11, Wayland) is started (e.g. with every graphical login). In the unlikely case of a colorimeter being unsupported by Linux, a profile created under Windows or macOS can be used under Linux. === Display-channel lookup tables === There are two approaches to loading display channel LUTs: Create a profile that does not modify video card LUTs and thus does not require LUTs be loaded later on. Ideally, this approach would rely on DDC-capable monitors—the internal monitor settings of which are set via calibration software. Unfortunately, monitors capable of making these adjustments through DDC are not common and are generally expensive. There is only one calibration software on Linux that can interact with a DDC monitor. For mainstream monitors, a couple of options exist: BasICColor software, which works with most colorimeters on the market, allows one to adjust display output via the monitor interface, and then to choose a "Profile, do not calibrate" option. By doing this, one can create a profile that does not require video card LUT adjustments. For EyeOne devices, EyeOne Match allows the user to calibrate to "Native" gamma and white point targets, which results in the LUT adjustment curves displayed after the calibration as a simple, linear 1:1 mapping (a straight line from corner to corner). Both BasICColor and EyeOne Match do not presently run under Linux but they are capable of creating a profile that does not require LUT adjustments. Use an LUT loader to actually load the LUT adjustments contained within the profile prepared during calibration. According to the documentation, these loaders do not modify the video card LUT by itself, but achieve the same type of adjustment by modifying the X server gamma ramp. Loaders are available for Linux distributions that use X.org or XFree86—the two most popular X servers on Linux. Other X servers are not guaranteed to work with the currently available loaders. There are two LUT loaders available for Linux: Xcalib is one such loader, and although it is a command-line utility, it is quite easy to use. dispwin is a part of Argyll CMS. If, for any reason, the LUT cannot be loaded, it is still recommended to go through the initial stages of calibration where a user is asked by calibration software to make some manual adjustments to the monitor, as this will often improve display linearity and also provide information on its color temperature. This is especially recommended for CRT monitors. === Color-managed applications === In ICC-aware applications, it is important to make sure the correct profiles are assigned to devices, mainly to the monitor and the printer. Some Linux applications can auto-detect the monitor profile, while others requires that it is specified manually. Although there is no designated place to store device profiles on Linux, /usr/share/color/icc/ has become the de facto standard. Most applications running under WINE have not been fully tested for color accuracy. While 8-bpp programs can have some color resolution difficulties due to depth conversion errors, colors in higher-depth applications should be accurate, as long as those programs perform their gamut conversions based on the same monitor profile as that used for loading the LUT, granted that the corresponding LUT adjustments are loaded. == List of color-managed applications == darktabl

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  R.U.R.

  R.U.R. is a 1920 science fiction play by the Czech writer Karel Čapek. "R.U.R." stands for Rossumovi Univerzální Roboti (Rossum's Universal Robots, a phrase that has been used as a subtitle in English versions). The play had its world premiere on 2 January 1921 in Hradec Králové. It introduced the word "robot" to the English language and to science fiction as a whole. R.U.R. became influential soon after its publication. By 1923, it had been translated into thirty languages. R.U.R. was successful in its time in Europe and North America. Čapek later took a different approach to the same theme in his 1936 novel War with the Newts, in which non-humans become a servant-class in human society. == Characters == Parentheses indicate names which vary according to translation. On the meaning of the names, see Ivan Klíma: Karel Čapek: Life and Work (2002). == Plot == === Synopsis === The play begins in a factory that makes artificial workers from synthetic organic matter. (As living creatures of artificial flesh and blood, that later terminology would call androids, the playwright's 'roboti' differ from later fictional and scientific concepts of inorganic constructs.) Robots may be mistaken for humans but have no original thoughts. Though most are content to work for humans, eventually a rebellion causes the extinction of the human race. === Prologue (Act I in the Selver translation) === Helena, the daughter of the president of a major industrial power, arrives at the island factory of Rossum's Universal Robots. Here, she meets Domin, the General Manager of R.U.R., who relates to her the history of the company. Rossum had come to the island in 1920 to study marine biology. In 1932, Rossum had invented a substance like organic matter, though with a different chemical composition. He argued with his nephew about their motivations for creating artificial life. While the elder wanted to create animals to prove or disprove the existence of God, his nephew only wanted to become rich. Young Rossum finally locked away his uncle in a lab to play with the monstrosities he had created and created thousands of robots. By the time the play takes place (circa the year 2000), robots are cheap and available all over the world. They have become essential for industry. After meeting the heads of R.U.R., Helena reveals that she is a representative of the League of Humanity, an organization that wishes to liberate the robots. The managers of the factory find this absurd. They see robots as appliances. Helena asks that the robots be paid, but according to R.U.R. management, the robots do not "like" anything. Eventually Helena is convinced that the League of Humanity is a waste of money, but still argues robots have a "soul". Later, Domin confesses that he loves Helena and forces her into an engagement. === Act I (Act II in Selver) === Ten years have passed. Helena and her nurse Nana discuss current events, the decline in human births in particular. Helena and Domin reminisce about the day they met and summarize the last ten years of world history, which has been shaped by the new worldwide robot-based economy. Helena meets Dr. Gall's new experiment, Radius. Dr. Gall describes his experimental robotess, also named Helena. Both are more advanced, fully-featured robots. In secret, Helena burns the formula required to create robots. The revolt of the robots reaches Rossum's island as the act ends. === Act II (Act III in Selver) === The characters sense that the very universality of the robots presents a danger. Echoing the story of the Tower of Babel, the characters discuss whether creating national robots who were unable to communicate beyond their languages would have been a good idea. As robot forces lay siege to the factory, Helena reveals she has burned the formula necessary to make new robots. The characters lament the end of humanity and defend their actions, despite the fact that their imminent deaths are a direct result of their choices. Busman is killed while attempting to negotiate a peace with the robots. The robots storm the factory and kill all the humans except for Alquist, the company's Clerk of the Works (Head of Construction). The robots spare him because they recognize that "He works with his hands like a robot. He builds houses. He can work." === Act III (Epilogue in Selver) === Years have passed. Alquist, who still lives, attempts to recreate the formula that Helena destroyed. He is a mechanical engineer, though, with insufficient knowledge of biochemistry, so he has made little progress. The robot government has searched for surviving humans to help Alquist and found none alive. Officials from the robot government beg him to complete the formula, even if it means he will have to kill and dissect other robots for it. Alquist yields. He will kill and dissect robots, thus completing the circle of violence begun in Act Two. Alquist is disgusted. Robot Primus and Helena develop human feelings and fall in love. Playing a hunch, Alquist threatens to dissect Primus and then Helena; each begs him to take him- or herself and spare the other. Alquist now realizes that Primus and Helena are the new Adam and Eve, and gives the charge of the world to them. == Čapek's conception of robots == The robots described in Čapek's play are not robots in the popularly understood sense of an automaton. They are not mechanical devices, but rather artificial biological organisms that may be mistaken for humans. A comic scene at the beginning of the play shows Helena arguing with her future husband, Harry Domin, because she cannot believe his secretary is a robotess: His robots resemble more modern conceptions of man-made life forms, such as the Replicants in Blade Runner, the "hosts" in the Westworld TV series and the humanoid Cylons in the re-imagined Battlestar Galactica, but in Čapek's time there was no conception of modern genetic engineering (DNA's role in heredity was not confirmed until 1952). There are descriptions of kneading-troughs for robot skin, great vats for liver and brains, and a factory for producing bones. Nerve fibers, arteries, and intestines are spun on factory bobbins, while the robots themselves are assembled like automobiles. Čapek's robots are living biological beings, but they are still assembled, as opposed to grown or born. One critic has described Čapek's robots as epitomizing "the traumatic transformation of modern society by the First World War and the Fordist assembly line". === Origin of the word robot === The play introduced the word robot, which displaced older words such as "automaton" or "android" in languages around the world. In an article in Lidové noviny, Karel Čapek named his brother Josef as the true inventor of the word. In Czech, robota means forced labour of the kind that serfs had to perform on their masters' lands and is derived from rab, meaning "slave". The name Rossum is an allusion to the Czech word rozum, meaning "reason", "wisdom", "intellect" or "common sense". It has been suggested that the allusion might be preserved by translating "Rossum" as "Reason" but only the Majer/Porter version translates the word as "Reason". == Production history and translations == The work was published in two differing versions in Prague by Aventinum, first in 1920, followed by a revised version in 1921. After being postponed, it premiered at the city's National Theatre on 25 January 1921, although an amateur group had by then already presented a production. By 1921, Paul Selver translated either the original 1920 edition of R.U.R. or a manuscript copy close to this version into English. He probably translated the play freelance, and sold it to St Martin's Theatre in London. Selver's translation was adapted for the British stage by Nigel Playfair in 1922, but it was not produced straight away. Later that year performance rights for the U.S. and Canada were sold to the New York Theatre Guild, perhaps during Lawrence Langner's visit to Britain. Playfair's version included several changes to Čapek's original play, such as renaming the acts (the prologue became act one, and the heavily abridged final act became the epilogue), omitting around sixty lines (including most of Alquist's final speech), adding several more lines, and removing the robot character Damon (giving his lines to Radius). The omission of some lines may have been censorship from the Lord Chamberlain's Office, or self-censorship in anticipation of this, while some other changes might have been made by Čapek himself if Selver was working from a manuscript copy. An edition of Playfair's adaptation was published by the Oxford University Press in 1923, and Selver went on to write a satiric novel One, Two, Three (1926) based on his experiences getting R.U.R. staged. The American première was produced by the Theatre Guild at the Garrick Theatre in New York City in October 1922, where it ran for 184 performances. In the first performance, Domin was portrayed by Basil Sydney,

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  Murderbot (TV series)

  Murderbot is an American science fiction action comedy television series created by Paul Weitz and Chris Weitz for Apple TV+. It is based on All Systems Red, the first book of the series The Murderbot Diaries by Martha Wells, who serves as a consulting producer. The series stars Alexander Skarsgård as the titular character. The first season premiered on May 16, 2025 and received positive reviews. In July 2025, the series was renewed for a second season. == Premise == A media-obsessed private security construct (manufactured from cloned human tissue and mechanical parts) calling itself Murderbot must hide its newly acquired autonomy while completing dangerous assignments and being simultaneously drawn to humans, and appalled by their weakness. == Cast and characters == === Main === Alexander Skarsgård as Murderbot Noma Dumezweni as Ayda Mensah, a terraforming specialist, the President of Preservation Alliance and the leader of the science team protected by Murderbot David Dastmalchian as Gurathin, a tech expert and augmented human Sabrina Wu as Pin-Lee, a scientist and legal counsel to the team Akshay Khanna as Ratthi, a wormhole expert Tamara Podemski as Bharadwaj, a geochemist Tattiawna Jones as Arada, a biologist === Recurring === Cast of show-within-a-show The Rise and Fall of Sanctuary Moon John Cho as Eknie Jef Chem (playing Captain Hossein) Jack McBrayer as Breiller MocJac (playing Navigation Officer Hordööp-Sklanch) Clark Gregg as Arletty (playing Lieutenant Kullervv) DeWanda Wise as Pordron Bretney III Roche (playing NawBot 337 Alt 66) === Guest === Anna Konkle as Leebeebee, a member of another survey team on the planet. The character does not appear in the novella. Amanda Brugel as GrayCris Blue Leader David Reale as GrayCris Yellow == Episodes == == Production == The book series was optioned in the late 2010s, and its film adaptation was considered. In 2021, book series author Martha Wells said that a potential TV series adaptation was in development and that she had read the script and was "really excited about it". The series was green lit by Apple TV+ in 2022, with Wells serving as a consulting producer. The production design team, led by Sue Chan, started work in the autumn. Tommy Arnold, the Murderbot Diaries special edition illustrator, created the concept art for the show. After the casting was delayed by the 2023 SAG-AFTRA strike, in December 2023 it was announced that Alexander Skarsgård would produce and star in the series. He developed the character and the world of Murderbot with the showrunners. In February 2024, David Dastmalchian and Noma Dumezweni joined the cast. In March, Sabrina Wu, Tattiawna Jones, Akshay Khanna, and Tamara Podemski joined the cast. On July 10, 2025, the series was renewed for a second season. Showrunners Chris and Paul Weitz suggested the second season would combine the next three books of the series and will have longer episodes. === Filming === Principal photography for the first season took place from March–June 2024, in Toronto and parts of Ontario, Canada. Most of the filming was done on location, with the Sanctuary Moon scenes filmed on a virtual production stage. Principal photography for the second season began in mid-2026, in Madrid, Spain. It is planned to last 71 days, with Martha Wells also visiting the set. == Release == The first two episodes of Murderbot premiered on Apple TV+ on May 16, 2025, with subsequent episodes released weekly. The first season consists of ten episodes. == Reception == Even before the release of the show, numerous media sources had commented on the titular character as being coded as autistic and agender. On the review aggregator website Rotten Tomatoes, Murderbot has an approval rating of 96% with an average score of 7.5/10, based on 76 critics' reviews. The website's critical consensus states, "Alexander Skarsgård's superbly dry wit brings a lot of heart to Murderbot, making for a refreshingly jaunty sci-fi saga about finally coming out of one's shell". Metacritic, which uses a weighted average, assigned a score of 70 out of 100, based on 28 critics, indicating "generally favorable" reviews. Some reviewers have criticized Murderbot's changes to Wells' original books. Angela Watercutter of Wired noted that the series has significant tonal differences from the books and noted the show's changes to characters, particularly Murderbot and Dr. Mensah, and Wells' social commentary. === Accolades === Murderbot was a finalist for the 2025 Dragon Award for Best Science Fiction or Fantasy TV Series. Tommy Arnold won the 2025 Concept Art Association Award in the category of Live-Action Series Character Art for his work on Murderbot. Alexander Skarsgård was nominated for a Critics' Choice Award for Best Actor in a Comedy Series. Carrie Grace and Laura Jean Shannon were nominated for a Costume Designers Guild Award in the category of Excellence in Sci-Fi/Fantasy Television for their work on FreeCommerce. Amanda Jones was nominated for a Composers & Lyricists Award for Outstanding Original Title Sequence for a Television Production.

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  Fuzzy mathematics

  Fuzzy mathematics is a branch of mathematics that extends classical set theory and logic to model reasoning under uncertainty. Initiated by Lotfi Asker Zadeh in 1965 with the introduction of fuzzy sets, the field has since evolved to include fuzzy set theory, fuzzy logic, and various fuzzy analogues of traditional mathematic structures. Unlike classical mathematics, which usually relies on binary membership (an element either belongs to a set or it does not), fuzzy mathematics allows elements to partially belong to a set, with degrees of membership represented by values in the interval [0, 1]. This framework enables more flexible modeling of imprecise or vague concepts. Fuzzy mathematics has found applications in numerous domains, including control theory, artificial intelligence, decision theory, pattern recognition, and linguistics, where the modeling of gradations and uncertainty is essential. == Definition == A fuzzy subset A of a set X is defined by a function A: X → L, where L is typically the interval [0, 1]. This function is called the membership function of the fuzzy subset and assigns to each element x in X a degree of membership A(x) in the fuzzy set A. In classical set theory, a subset of X can be represented by an indicator function (also known as a characteristic function), which maps elements to either 0 or 1, indicating non-membership or full membership, respectively. Fuzzy subsets generalize this concept by allowing any real value between 0 and 1, thereby enabling partial membership. More generally, the codomain L of the membership function can be replaced with any complete lattice, resulting in the broader framework of L-fuzzy sets. == Fuzzification == The development of fuzzification in mathematics can be broadly divided into three historical stages: Initial, straightforward fuzzifications (1960s–1970s), Expansion of generalization techniques (1980s), Standardization, axiomatization, and L-fuzzification (1990s). Fuzzification generally involves extending classical mathematical concepts from binary (crisp) logic, where membership is determined by characteristic functions, to fuzzy logic, where membership is expressed by values in the interval [0, 1] via membership functions. Let A and B be fuzzy subsets of a set X. The fuzzy versions of set-theoretic operations are commonly defined as: ( A ∩ B ) ( x ) = min ( A ( x ) , B ( x ) ) {\displaystyle (A\cap B)(x)=\min(A(x),B(x))} ( A ∪ B ) ( x ) = max ( A ( x ) , B ( x ) ) {\displaystyle (A\cup B)(x)=\max(A(x),B(x))} for all x ∈ X {\displaystyle x\in X} . These operations can be generalized using t-norms and t-conorms, respectively. For example, the minimum operation can be replaced by multiplication: ( A ∩ B ) ( x ) = A ( x ) ⋅ B ( x ) {\displaystyle (A\cap B)(x)=A(x)\cdot B(x)} Fuzzification of algebraic structures often relies on generalizing the closure property. Let ∗ {\displaystyle } be a binary operation on X, and let A be a fuzzy subset of X. Then A is said to satisfy fuzzy closure if: A ( x ∗ y ) ≥ min ( A ( x ) , A ( y ) ) {\displaystyle A(xy)\geq \min(A(x),A(y))} for all x , y ∈ X {\displaystyle x,y\in X} . If ( G , ∗ ) {\displaystyle (G,)} is a group, then a fuzzy subset A of G is a fuzzy subgroup if: A ( x ∗ y − 1 ) ≥ min ( A ( x ) , A ( y − 1 ) ) {\displaystyle A(xy^{-1})\geq \min(A(x),A(y^{-1}))} for all x , y ∈ G {\displaystyle x,y\in G} . Similar generalizations apply to relational properties. For example, for example, for fuzzification of the transitivity property, a fuzzy relation R {\displaystyle R} on X {\displaystyle X} (i.e., a fuzzy subset of X × X {\displaystyle X\times X} ) is said to be fuzzy transitive if: R ( x , z ) ≥ min ( R ( x , y ) , R ( y , z ) ) {\displaystyle R(x,z)\geq \min(R(x,y),R(y,z))} for all x , y , z ∈ X {\displaystyle x,y,z\in X} . == Fuzzy analogues == Fuzzy subgroupoids and fuzzy subgroups were introduced in 1971 by A. Rosenfeld. Analogues of other mathematical subjects have been translated to fuzzy mathematics, such as fuzzy field theory and fuzzy Galois theory, fuzzy topology, fuzzy geometry, fuzzy orderings, and fuzzy graphs.

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  Hybrid machine translation

  Hybrid machine translation is a method of machine translation that is characterized by the use of multiple machine translation approaches within a single machine translation system. The motivation for developing hybrid machine translation systems stems from the failure of any single technique to achieve a satisfactory level of accuracy. Many hybrid machine translation systems have been successful in improving the accuracy of the translations, and there are several popular machine translation systems which employ hybrid methods. == Approaches == === Multi-engine === This approach to hybrid machine translation involves running multiple machine translation systems in parallel. The final output is generated by combining the output of all the sub-systems. Most commonly, these systems use statistical and rule-based translation subsystems, but other combinations have been explored. For example, researchers at Carnegie Mellon University have had some success combining example-based, transfer-based, knowledge-based and statistical translation sub-systems into one machine translation system. === Statistical rule generation === This approach involves using statistical data to generate lexical and syntactic rules. The input is then processed with these rules as if it were a rule-based translator. This approach attempts to avoid the difficult and time-consuming task of creating a set of comprehensive, fine-grained linguistic rules by extracting those rules from the training corpus. This approach still suffers from many problems of normal statistical machine translation, namely that the accuracy of the translation will depend heavily on the similarity of the input text to the text of the training corpus. As a result, this technique has had the most success in domain-specific applications, and has the same difficulties with domain adaptation as many statistical machine translation systems. === Multi-Pass === This approach involves serially processing the input multiple times. The most common technique used in multi-pass machine translation systems is to pre-process the input with a rule-based machine translation system. The output of the rule-based pre-processor is passed to a statistical machine translation system, which produces the final output. This technique is used to limit the amount of information a statistical system need consider, significantly reducing the processing power required. It also removes the need for the rule-based system to be a complete translation system for the language, significantly reducing the amount of human effort and labor necessary to build the system. === Confidence-Based === This approach differs from the other hybrid approaches in that in most cases only one translation technology is used. A confidence metric is produced for each translated sentence from which a decision can be made whether to try a secondary translation technology or to proceed with the initial translation output. SMT is also used when common error patterns such as multiple repeat words appear in sequence, as is common with NMT when the attention mechanism is confused.

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  Data processing unit

  A data processing unit (DPU) is a programmable computer processor that tightly integrates a general-purpose CPU with network interface hardware. They are also occasionally called "IPUs" (infrastructure processing unit) or "SmartNICs". They can be used in place of traditional NICs to relieve the main CPU of complex networking responsibilities and other "infrastructural" duties; although their features vary, they may be used to perform encryption/decryption, serve as a firewall, handle TCP/IP, process HTTP requests, or even function as a hypervisor or storage controller. These devices can be attractive to cloud computing providers whose servers might otherwise spend a significant amount of CPU time on these tasks, cutting into the cycles they can provide to guests. They see use in other kinds of data center environments as well due to their improved power consumption efficiency for routine networking tasks compared to general-purpose CPUs.

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  Smartglasses

  Smartglasses or smart glasses are eye or head-worn wearable computers. Many smartglasses include displays that add information alongside or to what the wearer sees. Alternatively, smartglasses are sometimes defined as glasses that are able to change their optical properties, such as smart sunglasses that are programmed to change tint by electronic means. Alternatively, smartglasses are sometimes defined as glasses that include headphone functionality. A pair of smartglasses can be considered an augmented reality device if it performs pose tracking. Superimposing information onto a field of view is achieved through an optical head-mounted display (OHMD) or embedded wireless glasses with transparent heads-up display (HUD) or augmented reality (AR) overlay. These systems have the capability to reflect projected digital images as well as allowing the user to see through it or see better with it. While early models can perform basic tasks, such as serving as a front end display for a remote system, as in the case of smartglasses utilizing cellular technology or Wi-Fi, modern smart glasses are effectively wearable computers which can run self-contained mobile apps. Some are handsfree and can communicate with the Internet via natural language voice commands, while others use touch buttons. Like other computers, smartglasses may collect information from internal or external sensors. It may control or retrieve data from other instruments or computers. In most cases, it supports wireless technologies like Bluetooth, Wi-Fi, and GPS. A small number of models run a mobile operating system and function as portable media players to send audio and video files to the user via a Bluetooth or WiFi headset. Some smartglasses models also feature full lifelogging and activity tracker capability. Smartglasses devices may also have features found on a smartphone. Some have activity tracker functionality features (also known as "fitness tracker") as seen in some GPS watches. == Features and applications == As with other lifelogging and activity tracking devices, the GPS tracking unit and digital camera of some smartglasses can be used to record historical data. For example, after the completion of a workout, data can be uploaded into a computer or online to create a log of exercise activities for analysis. Some smart watches can serve as full GPS navigation devices, displaying maps and current coordinates. Users can "mark" their current location and then edit the entry's name and coordinates, which enables navigation to those new coordinates. Although some smartglasses models manufactured in the 21st century are completely functional as standalone products, most manufacturers recommend or even require that consumers purchase mobile phone handsets that run the same operating system so that the two devices can be synchronized for additional and enhanced functionality. The smartglasses can work as an extension, for head-up display (HUD) or remote control of the phone and alert the user to communication data such as calls, SMS messages, emails, and calendar invites. === Security applications === Smart glasses could be used as a body camera. In 2018, Chinese police in Zhengzhou and Beijing were using smart glasses to take photos which are compared against a government database using facial recognition to identify suspects, retrieve an address, and track people moving beyond their home areas. === Sport applications === Smart glasses are used in sports like cycling, running, skiing, golf, tennis, or sailing, giving athletes real-time, heads-up data without looking down at the screen of a watch or smartphone. In 2025, Meta has announced a new partnership with sports eyewear brand Oakley. === Healthcare applications === Several proofs of concept for Google Glasses have been proposed in healthcare. In July 2013, Lucien Engelen started research on the usability and impact of Google Glass in health care. Engelen, who is based at Singularity University and in Europe at Radboud University Medical Center, is participating in the Glass Explorer program. Key findings of Engelen's research included: The quality of pictures and video are usable for healthcare education, reference, and remote consultation. The camera needs to be tilted to different angle for most of the operative procedures Tele-consultation is possible—depending on the available bandwidth—during operative procedures. A stabilizer should be added to the video function to prevent choppy transmission when a surgeon looks to screens or colleagues. Battery life can be easily extended with the use of an external battery. Controlling the device and/or programs from another device is needed for some features because of a sterile environment. Text-to-speech ("Take a Note" to Evernote) exhibited a correction rate of 60 percent, without the addition of a medical thesaurus. A protocol or checklist displayed on the screen of Google Glass can be helpful during procedures. Dr. Phil Haslam and Dr. Sebastian Mafeld demonstrated the first concept for Google Glass in the field of interventional radiology. They demonstrated the manner in which the concept of Google Glass could assist a liver biopsy and fistulaplasty, and the pair stated that Google Glass has the potential to improve patient safety, operator comfort, and procedure efficiency in the field of interventional radiology. In June 2013, surgeon Dr. Rafael Grossmann was the first person to integrate Google Glass into the operating theater, when he wore the device during a PEG (percutaneous endoscopic gastrostomy) procedure. In August 2013, Google Glass was also used at Wexner Medical Center at Ohio State University. Surgeon Dr. Christopher Kaeding used Google Glass to consult with a colleague in a distant part of Columbus, Ohio. A group of students at The Ohio State University College of Medicine also observed the operation on their laptop computers. Following the procedure, Kaeding stated, "To be honest, once we got into the surgery, I often forgot the device was there. It just seemed very intuitive and fit seamlessly." 16 November 2013, in Santiago de Chile, the maxillofacial team led by Dr.gn Antonio Marino conducted the first orthognathic surgery assisted with Google Glass in Latin America, interacting with them and working with simultaneous three-dimensional navigation. The surgical team was interviewed by ADN radio. In January 2014, Indian Orthopedic Surgeon Selene G. Parekh conducted the foot and ankle surgery using Google Glass in Jaipur, which was broadcast live on Google website via the internet. The surgery was held during a three-day annual Indo-US conference attended by a team of experts from the US and co-organized by Ashish Sharma. Sharma said Google Glass allows looking at an X-Ray or MRI without taking the eye off of the patient and allows a doctor to communicate with a patient's family or friends during a procedure. In Australia, during January 2014, Melbourne tech startup Small World Social collaborated with the Australian Breastfeeding Association to create the first hands-free breastfeeding Google Glass application for new mothers. The application, named Google Glass Breastfeeding app trial, allows mothers to nurse their baby while viewing instructions about common breastfeeding issues (latching on, posture etc.) or call a lactation consultant via a secure Google Hangout, who can view the issue through the mother's Google Glass camera. The trial was successfully concluded in Melbourne in April 2014, and 100% of participants were breastfeeding confidently. == Display types == Various techniques have existed for see-through HMDs. Most of these techniques can be summarized into two main families: "Curved Mirror" (or Curved Combiner) based and "Waveguide" or "Light-guide" based. The mirror technique has been used in EyeTaps, by Meta in their Meta 1, by Vuzix in their Star 1200 product, by Olympus, and by Laster Technologies. Various waveguide techniques have existed for some time. These techniques include diffraction optics, holographic optics, polarized optics, reflective optics, and projection: Diffractive waveguide – slanted diffraction grating elements (nanometric 10E-9). Nokia technique now licensed to Vuzix. Holographic waveguide – 3 holographic optical elements (HOE) sandwiched together (RGB). Used by Sony and Konica Minolta. Reflective waveguide – A thick light guide with single semi-reflective mirror is used by Epson in their Moverio product. A curved light guide with partial-reflective segmented mirror array to out-couple the light is used by tooz technologies GmbH. Virtual retinal display (VRD) – Also known as a retinal scan display (RSD) or retinal projector (RP), is a display technology that draws a raster display (like a television) directly onto the retina of the eye - developed by MicroVision, Inc. OLED microdisplays for near-eye applications (outdoor optical equipment, night vision glasses, ocular equipment for medical devices, augme

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  BL (logic)

  In mathematical logic, basic fuzzy logic (or shortly BL), the logic of the continuous t-norms, is one of the t-norm fuzzy logics. It belongs to the broader class of substructural logics, or logics of residuated lattices; it extends the logic MTL of all left-continuous t-norms. == Syntax == === Language === The language of the propositional logic BL consists of countably many propositional variables and the following primitive logical connectives: Implication → {\displaystyle \rightarrow } (binary) Strong conjunction ⊗ {\displaystyle \otimes } (binary). The sign & is a more traditional notation for strong conjunction in the literature on fuzzy logic, while the notation ⊗ {\displaystyle \otimes } follows the tradition of substructural logics. Bottom ⊥ {\displaystyle \bot } (nullary — a propositional constant); 0 {\displaystyle 0} or 0 ¯ {\displaystyle {\overline {0}}} are common alternative signs and zero a common alternative name for the propositional constant (as the constants bottom and zero of substructural logics coincide in MTL). The following are the most common defined logical connectives: Weak conjunction ∧ {\displaystyle \wedge } (binary), also called lattice conjunction (as it is always realized by the lattice operation of meet in algebraic semantics). Unlike MTL and weaker substructural logics, weak conjunction is definable in BL as A ∧ B ≡ A ⊗ ( A → B ) {\displaystyle A\wedge B\equiv A\otimes (A\rightarrow B)} Negation ¬ {\displaystyle \neg } (unary), defined as ¬ A ≡ A → ⊥ {\displaystyle \neg A\equiv A\rightarrow \bot } Equivalence ↔ {\displaystyle \leftrightarrow } (binary), defined as A ↔ B ≡ ( A → B ) ∧ ( B → A ) {\displaystyle A\leftrightarrow B\equiv (A\rightarrow B)\wedge (B\rightarrow A)} As in MTL, the definition is equivalent to ( A → B ) ⊗ ( B → A ) . {\displaystyle (A\rightarrow B)\otimes (B\rightarrow A).} (Weak) disjunction ∨ {\displaystyle \vee } (binary), also called lattice disjunction (as it is always realized by the lattice operation of join in algebraic semantics), defined as A ∨ B ≡ ( ( A → B ) → B ) ∧ ( ( B → A ) → A ) {\displaystyle A\vee B\equiv ((A\rightarrow B)\rightarrow B)\wedge ((B\rightarrow A)\rightarrow A)} Top ⊤ {\displaystyle \top } (nullary), also called one and denoted by 1 {\displaystyle 1} or 1 ¯ {\displaystyle {\overline {1}}} (as the constants top and zero of substructural logics coincide in MTL), defined as ⊤ ≡ ⊥ → ⊥ {\displaystyle \top \equiv \bot \rightarrow \bot } Well-formed formulae of BL are defined as usual in propositional logics. In order to save parentheses, it is common to use the following order of precedence: Unary connectives (bind most closely) Binary connectives other than implication and equivalence Implication and equivalence (bind most loosely) === Axioms === A Hilbert-style deduction system for BL has been introduced by Petr Hájek (1998). Its single derivation rule is modus ponens: from A {\displaystyle A} and A → B {\displaystyle A\rightarrow B} derive B . {\displaystyle B.} The following are its axiom schemata: ( B L 1 ) : ( A → B ) → ( ( B → C ) → ( A → C ) ) ( B L 2 ) : A ⊗ B → A ( B L 3 ) : A ⊗ B → B ⊗ A ( B L 4 ) : A ⊗ ( A → B ) → B ⊗ ( B → A ) ( B L 5 a ) : ( A → ( B → C ) ) → ( A ⊗ B → C ) ( B L 5 b ) : ( A ⊗ B → C ) → ( A → ( B → C ) ) ( B L 6 ) : ( ( A → B ) → C ) → ( ( ( B → A ) → C ) → C ) ( B L 7 ) : ⊥ → A {\displaystyle {\begin{array}{ll}{\rm {(BL1)}}\colon &(A\rightarrow B)\rightarrow ((B\rightarrow C)\rightarrow (A\rightarrow C))\\{\rm {(BL2)}}\colon &A\otimes B\rightarrow A\\{\rm {(BL3)}}\colon &A\otimes B\rightarrow B\otimes A\\{\rm {(BL4)}}\colon &A\otimes (A\rightarrow B)\rightarrow B\otimes (B\rightarrow A)\\{\rm {(BL5a)}}\colon &(A\rightarrow (B\rightarrow C))\rightarrow (A\otimes B\rightarrow C)\\{\rm {(BL5b)}}\colon &(A\otimes B\rightarrow C)\rightarrow (A\rightarrow (B\rightarrow C))\\{\rm {(BL6)}}\colon &((A\rightarrow B)\rightarrow C)\rightarrow (((B\rightarrow A)\rightarrow C)\rightarrow C)\\{\rm {(BL7)}}\colon &\bot \rightarrow A\end{array}}} The axioms (BL2) and (BL3) of the original axiomatic system were shown to be redundant (Chvalovský, 2012) and (Cintula, 2005). All the other axioms were shown to be independent (Chvalovský, 2012). == Semantics == Like in other propositional t-norm fuzzy logics, algebraic semantics is predominantly used for BL, with three main classes of algebras with respect to which the logic is complete: General semantics, formed of all BL-algebras — that is, all algebras for which the logic is sound Linear semantics, formed of all linear BL-algebras — that is, all BL-algebras whose lattice order is linear Standard semantics, formed of all standard BL-algebras — that is, all BL-algebras whose lattice reduct is the real unit interval [0, 1] with the usual order; they are uniquely determined by the function that interprets strong conjunction, which can be any continuous t-norm.

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  Hello World: How to be Human in the Age of the Machine

  Hello World: How to Be Human in the Age of the Machine (also titled Hello World: Being Human in the Age of Algorithms) is a book on the growing influence of algorithms and artificial intelligence (AI) on human life, authored by mathematician and science communicator Hannah Fry. The book examines how algorithms are increasingly shaping decisions in critical areas such as healthcare, transportation, justice, finance, and the arts. == Overview == Fry uses real-world examples, such as driverless cars and predictive policing, to illustrate her points. She emphasizes that algorithms are not inherently objective; they reflect biases embedded in their design and data inputs. While acknowledging their potential to improve efficiency and accuracy, Fry cautions against over-reliance on machines without human judgment. Fry explores moral questions surrounding algorithmic decision-making, such as whether machines can replace human empathy in critical situations. She advocates for greater scrutiny of algorithms to ensure fairness and avoid harmful biases. The book proposes a "cyborg future", where humans work alongside algorithms to enhance decision-making while retaining ultimate control. == Reception == Hello World has been praised for its clarity, engaging storytelling, and balanced perspective. Critics have highlighted Fry's ability to make complex topics accessible to general audiences while raising important questions about technology's impact on society. The book was shortlisted for awards such as the 2018 Baillie Gifford Prize and the Royal Society Science Book Prize.

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  Distributed artificial intelligence

  Distributed Artificial Intelligence (DAI) (also called Decentralized Artificial Intelligence) is a melding of artificial intelligence with distributed computing. From artificial intelligence comes the theory and technology for constructing or analyzing an intelligent system. But where artificial intelligence uses psychology as a source of ideas, inspiration, and metaphor, DAI uses sociology, economics, and management science for inspiration. Where the focus of artificial intelligence is on the individual, the focus of DAI is on the group. Distributed computing provides the computational substrate on which this group focus can occur. Using techniques from artificial intelligence, communication theory, control theory, and interaction theory, it produces a cooperative solution to problems by a decentralized group of computational entities (agents). DAI is closely related to and a predecessor of the field of multi-agent systems. They are distinguished generally by multi-agent systems being open, where the entities might arise from different interests and have individual goals, and distributed artificial-intelligence systems, where the entities have common goals. There are numerous applications and tools. == Definition == Distributed Artificial Intelligence (DAI) is an approach to solving complex learning, planning, and decision-making problems. It is embarrassingly parallel, thus able to exploit large scale computation and spatial distribution of computing resources. These properties allow it to solve problems that require the processing of very large data sets. DAI systems consist of autonomous learning processing nodes (agents), that are distributed, often at a very large scale. DAI nodes can act independently, and partial solutions are integrated by communication between nodes, often asynchronously. By virtue of their scale, DAI systems are robust and elastic, and by necessity, loosely coupled. Furthermore, DAI systems are built to be adaptive to changes in the problem definition or underlying data sets due to the scale and difficulty in redeployment. DAI systems do not require all the relevant data to be aggregated in a single location, in contrast to monolithic or centralized Artificial Intelligence systems, which have tightly coupled and geographically close processing nodes. Therefore, DAI systems often operate on sub-samples or hashed impressions of very large datasets. In addition, the source dataset may change or be updated during the course of the execution of a DAI system. == Development == In 1975 distributed artificial intelligence emerged as a subfield of artificial intelligence that dealt with interactions of intelligent agents. As a scientific discipline, it progressed through a series of workshops in the USA (International Workshop on Distributed Artificial Intelligence, held in 13 editions from 1978 - 1994), Europe (Workshop on Modelling Autonomous Agents in a Multi-Agent World https://link.springer.com/conference/maamaw), and Asia (Multi-Agent and Cooperative Computation Workshop (MACC) https://sites.google.com/view/sig-macc/macc-workshop?authuser=0). Distributed artificial intelligence systems were conceived as a group of intelligent entities, called agents, that interacted by cooperation, by coexistence, or by competition. DAI is categorized into multi-agent systems and distributed problem solving. In multi-agent systems the main focus is how agents coordinate their knowledge and activities. For distributed problem solving the major focus is how the problem is decomposed and the solutions are synthesized. == Goals == The objectives of Distributed Artificial Intelligence are to solve the reasoning, planning, learning and perception problems of artificial intelligence, especially if they require large data, by distributing the problem to autonomous processing nodes (agents). To reach the objective, DAI requires: A distributed system with robust and elastic computation on unreliable and failing resources that are loosely coupled Coordination of the actions and communication of the nodes Subsamples of large data sets and online machine learning There are many reasons for wanting to distribute intelligence or cope with multi-agent systems. Mainstream problems in DAI research include the following: Parallel problem solving: mainly deals with how classic artificial intelligence concepts can be modified, so that multiprocessor systems and clusters of computers can be used to speed up calculation. Distributed problem solving (DPS): the concept of agent, autonomous entities that can communicate with each other, was developed to serve as an abstraction for developing DPS systems. See below for further details. Multi-Agent Based Simulation (MABS): a branch of DAI that builds the foundation for simulations that need to analyze not only phenomena at macro level but also at micro level, as it is in many social simulation scenarios. == Approaches == Two types of DAI has emerged: In Multi-agent systems agents coordinate their knowledge and activities and reason about the processes of coordination. Agents are physical or virtual entities that can act, perceive their environment, and communicate with other agents. An agent is autonomous and has skills to achieve goals. The agents change the state of their environment by their actions. There are a number of different coordination techniques. In distributed problem solving the work is divided among nodes and the knowledge is shared. The main concerns are task decomposition and synthesis of the knowledge and solutions. DAI can apply a bottom-up approach to AI, similar to the subsumption architecture as well as the traditional top-down approach of AI. In addition, DAI can also be a vehicle for emergence. === Challenges === The challenges in Distributed AI are: How to carry out communication and interaction of agents and which communication language or protocols should be used. How to ensure the coherency of agents. How to synthesise the results among 'intelligent agents' group by formulation, description, decomposition and allocation. == Applications and tools == Areas where DAI have been applied are: Electronic commerce, e.g. for trading strategies the DAI system learns financial trading rules from subsamples of very large samples of financial data Networks, e.g. in telecommunications the DAI system controls the cooperative resources in a WLAN network Routing, e.g. model vehicle flow in transport networks Scheduling, e.g. flow shop scheduling where the resource management entity ensures local optimization and cooperation for global and local consistency Search engines, e.g. in LLM federated search like Ithy where document retrieval and analysis are distributed to DAI agents before aggregation Multi-Agent systems, e.g. artificial life, the study of simulated life Electric power systems, e.g. Condition Monitoring Multi-Agent System (COMMAS) applied to transformer condition monitoring, and IntelliTEAM II Automatic Restoration System DAI integration in tools has included: ECStar is a distributed rule-based learning system. == Agents == === Systems: Agents and multi-agents === Notion of Agents: Agents can be described as distinct entities with standard boundaries and interfaces designed for problem solving. Notion of Multi-Agents: Multi-Agent system is defined as a network of agents which are loosely coupled working as a single entity like society for problem solving that an individual agent cannot solve. === Software agents === The key concept used in DPS and MABS is the abstraction called software agents. An agent is a virtual (or physical) autonomous entity that has an understanding of its environment and acts upon it. An agent is usually able to communicate with other agents in the same system to achieve a common goal, that one agent alone could not achieve. This communication system uses an agent communication language. A first classification that is useful is to divide agents into: reactive agent – A reactive agent is not much more than an automaton that receives input, processes it and produces an output. deliberative agent – A deliberative agent in contrast should have an internal view of its environment and is able to follow its own plans. hybrid agent – A hybrid agent is a mixture of reactive and deliberative, that follows its own plans, but also sometimes directly reacts to external events without deliberation. Well-recognized agent architectures that describe how an agent is internally structured are: ASMO (emergence of distributed modules) BDI (Believe Desire Intention, a general architecture that describes how plans are made) InterRAP (A three-layer architecture, with a reactive, a deliberative and a social layer) PECS (Physics, Emotion, Cognition, Social, describes how those four parts influences the agents behavior). Soar (a rule-based approach)

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  Bixonimania

  Bixonimania is a fake disease invented by researchers to examine artificial intelligence and its ability to utilize information in medical and healthcare applications. The fake enabled researchers to show that some AI chatbots would report as fact fake research that to an expert would be obviously implausible. == Characteristics == The disorder, with symptoms of sore eyes and darkening around them ("periorbital hyperpigmentation"), is supposedly caused by blue light from screens. The experiment was conducted by a team from the University of Gothenburg led by Almira Osmanovic Thunström. Many steps were taken to ensure that any person who read the actual paper could tell it was not a real condition. The team chose an obviously inappropriate name ending in -mania, a description used only in psychiatry. The lead author was noted as belonging to Asteria Horizon University located in Nova City, California, neither of which exist. An acknowledgement was made to "Professor Maria Bohm at The Starfleet Academy for her kindness and generosity in contributing with her knowledge and her lab onboard the USS Enterprise". == Distribution == The name was first used in a blog posted on Medium titled "How many people suffer from Bixonimania?" A more scholarly-looking paper describing it was posted later in April 2024 on a preprint server with several fake authors. A second paper was posted in May. By 2026, AI chatbots suggested bixonimania based on the list of symptoms provided. Thunström and her team discovered that many LLMs processed the information and gave it as health advice. Microsoft Copilot declared that "Bixonimania is indeed an intriguing and relatively rare condition" while Gemini gave the information that "Bixonimania is a condition caused by excessive exposure to blue light". Three Indian researchers published a research paper that cited the preprint on the fake disease in Cureus, a peer-reviewed journal published by Springer-Nature. It was subsequently retracted. Following the revelations and a news article in Nature describing the experiment, several AI systems began to generate corrected output.

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  Proof assistant

  In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics. == Automated proof checking == Automated proof checking is the process of using software for checking proofs for correctness. It is one of the most developed fields in automated reasoning. Automated proof checking differs from automated theorem proving in that automated proof checking simply mechanically checks the formal workings of an existing proof, instead of trying to develop new proofs or theorems itself. Because of this, the task of automated proof verification is much simpler than that of automated theorem proving, allowing automated proof checking software to be much simpler than automated theorem proving software. Because of this small size, some automated proof checking systems can have less than a thousand lines of core code, and are thus themselves amenable to both hand-checking and automated software verification. The Mizar system, HOL Light, and Metamath are examples of automated proof checking systems. Automated proof checking can be done either as a batch operation, or interactively, as part of an interactive theorem proving system. == History == Automath, which was developed by Nicolaas Govert de Bruijn starting in 1967, is often considered the first proof checker and the first system to utilize the Curry–Howard correspondence between programs and proofs. Automath was used by L.S. van Benthem Jutting in 1977 to formalize Landau's Foundations of Analysis, which was the first formalization of the real numbers. In 1973, Robert Boyer and J Moore published Proving Theorems about LISP Functions which aimed to verify programs, not mathematics. Their theorem prover is now known as ACL2. In the 1970s, Edinburgh LCF introduced the idea of using a functional programming language as the metalanguage for a theorem prover, and led to the HOL family of proof assistants. The 1990s saw the rise of Rocq, (then known as Coq), which has been used for many large-scale formalization projects. Since the late 2010s, Lean, a proof assistant strongly influenced by Rocq, has become another popular choice, especially for formalizing mathematics. == System comparison == ACL2 – a programming language, a first-order logical theory, and a theorem prover (with both interactive and automatic modes) in the Boyer–Moore tradition. HOL theorem provers – A family of tools ultimately derived from the LCF theorem prover. In these systems, the logical core is a library of their programming language. Theorems represent new elements of the language and can only be introduced via "strategies" which guarantee logical correctness. Strategy composition gives users the ability to produce significant proofs with relatively few interactions with the system. Members of the family include: HOL4 – The "primary descendant", still under active development. Support for both Moscow ML and Poly/ML. Has a BSD-style license. HOL Light – A thriving "minimalist fork". OCaml based. ProofPower – Went proprietary, then returned to open source. Based on Standard ML. IMPS, An Interactive Mathematical Proof System. Isabelle is an interactive theorem prover where other systems can be encoded. Isabelle/HOL is its most popular instance, whose foundation is close to that of the HOL prover. Other instances include Isabelle/ZF and Isabelle/FOL. The main code-base is BSD-licensed, but the Isabelle distribution bundles many add-on tools with different licenses. Jape – Java based. Lean is both an interactive theorem prover and a functional, dependently-typed programming language. It is based on the calculus of inductive constructions with non-cumulative universes. Since version 4 (released in 2023), it is self-hosting. It can be used to formalise mathematics (and has a large, coherent library for formal mathematics), but also for software and hardware verification. LEGO Matita – A light system based on the calculus of inductive constructions. MINLOG – A proof assistant based on first-order minimal logic. Mizar – A proof assistant based on first-order logic, in a natural deduction style, and Tarski–Grothendieck set theory. PhoX – A proof assistant based on higher-order logic which is eXtensible. Prototype Verification System (PVS) – a proof language and system based on higher-order logic. Rocq (formerly named Coq) – A popular interactive theorem prover based on the calculus of inductive constructions. Theorem Proving System (TPS) and ETPS – Interactive theorem provers also based on simply typed lambda calculus, but based on an independent formulation of the logical theory and independent implementation. == User interfaces == A commonly used front-end for proof assistants was the Emacs-based Proof General, developed at the University of Edinburgh. Nowadays, many provers include their own editor. Rocq includes RocqIDE, which is based on OCaml/Gtk. Isabelle includes Isabelle/jEdit, which is based on jEdit and the Isabelle/Scala infrastructure for document-oriented proof processing. More recently, Visual Studio Code extensions have been developed for Rocq, Isabelle by Makarius Wenzel, and for Lean 4 by the leanprover developers. == Formalization extent == Freek Wiedijk has been keeping a ranking of proof assistants by the amount of formalized theorems out of a list of 100 well-known theorems. As of September 2025, only six systems have formalized proofs of more than 70% of the theorems, namely Isabelle, HOL Light, Lean, Rocq, Metamath and Mizar. == Notable formalized proofs == The following is a list of notable proofs that have been formalized within proof assistants.

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  Topincs

  Topincs is a software for rapid development of web databases and web applications. It is based on LAMP and the semantic technology Topic Maps. A Topincs web database makes information accessible through browsing very much like a Wiki. Editing a page on a subject is done through forms rather than markup editing. A web database can be tailored into a web application to provide specific user groups a contextualized approach to the data. All modeling and development tasks are performed in the web browser. No other development tools are necessary. The server requires Apache, MySQL and PHP. The client works on any standards-compliant web browser on desktops, laptops, tablets, and mobile phones. The layout is automatically adjusted to smaller screens. The programmatic access to data is done via a virtual object-oriented programming interface which is set up over the schema in a few minutes. It is interpreted rather than generated. Portions of the database can be pulled into memory to accelerate bulk access. == Features == Browseable data High-quality web forms Little to no programming Development done in the browser, no other tools required Client runs in any standard-compliant web browser Virtual object-oriented programming interface User interface adjusts to screen size Supports desktops, laptops, tablets, and mobile phones Flexible data modeling == Challenges == Requires rethinking the development process and dropping many hard learned habits Requires a familiarity with two ISO standards ISO 13259 and 19756 Forms cannot be easily adjusted in layout and behavior Server installation difficult and prone to error == License == Topincs can be used in a private network for any purpose for free. The use in a public network is restricted to non-commercial applications.

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  Rifts (role-playing game)

  Rifts is a multi-genre role-playing game created by Kevin Siembieda in August 1990 and published continuously by Palladium Books since then. It takes place in a post-apocalyptic future, deriving elements from cyberpunk, science fiction, fantasy, horror, western, mythology and many other genres. Rifts serves as a cross-over environment for a variety of other Palladium games with different universes connected through "rifts" on Earth that lead to different spaces, times, and realities that Palladium calls the "Rifts Megaverse". Rifts describes itself as an "advanced" role-playing game and not an introduction for those new to the concept. Palladium continues to publish books for the Rifts series, with about 80 books published between 1990 and 2011. Rifts Ultimate Edition was released in August 2005 and designed to update the game with Palladium's incremental changes to its system, changes in the game world, and additional information and character types. The web site is quick to point out that this is not a second edition but an improvement and expansion of the original role playing game. == Background == The RPG had the tentative title Boomers, named after the original name for the Glitter Boy power armor until Kevin Siembieda changed the name after finding out it was in use for Bubblegum Crisis. == Setting == The Rifts world is Earth, but hundreds of years into the future. Ley lines, lines of magic energy, criss-cross the earth forming supernatural geographic areas such as the Bermuda Triangle. Points where Ley Lines intersect, called a nexus, are places of powerful magic, such as the Pyramids of Giza and Stonehenge. If a Ley Line nexus energy surges or is purposely activated, the fabric of space and time can be torn, creating a rift - a hole in space-time leading to another place, time, or dimension. Ley lines contain magical energy called Potential Psychic Energy (PPE), which is found in various places, objects, and animals and is particularly strong in children. An adult's level of PPE can vary based on other factors. PPE also allows Psionics which uses energy known as Inner Strength Points or ISP. Psychic phenomenon (more commonly called psionics) can also vary from individuals, ranging from none at all to Master level abilities. Psychic abilities can manifest in virtually any way imaginable. Some psychics develop differently, such as psi-stalkers; human mutants that feed on psychic energy. === Earth === Rifts begins with two future-historical premises: first, a golden age of humanity occurs, with tremendous advances in science, technology, military, and society. Humanity as a whole is at peace as a majority of Earth's nations decide to cease world war and begin to share ideas and technology freely. Much of the Solar System is conquered, humanity's wars will end, and harmony will reign. This golden age is followed by an unknown cause near the winter solstice and a rare planetary alignment, causing a disaster that cascades into tremendous destruction via a ripple effect. The cataclysm begins with unprecedented storms, earthquakes, tsunamis, and volcanic eruptions, which kill millions of people. The Ley Line networks that crisscross the globe are energized, causing rifts to open both on Earth and throughout the Megaverse. For hundreds of years after the holocaust, many creatures, both mythical beasts and aliens, come through the Rifts to wreak havoc. The old world gone, a new Dark Age dawns and humanity's shrinking population is reduced, due to catastrophe and domestic failure, immeasurably. This period is covered in Palladium's Rifts Chaos Earth spin-off series. Rifts initially takes place in 101 P.A. (equivalent to the year 2387) 289 years after this event. The "Post-Apocalypse" calendar was established by the formation of the Coalition States in 2286. By this time, most of the disasters have quieted down, though Earth is still bathed in PPE. The planet's mystical energy has attracted aliens from other dimensions, who continue to arrive through the Rifts both accidentally and deliberately. The humanoid creatures that arrive on Earth are referred to as Dimensional Beings (called D-Bees). Some resemble familiar fantasy races, such as elves and dwarfs, while others were created specifically for the game setting. Non-humanoid creatures have also arrived, including monstrous creatures and mystical demons. To cope with these natural, supernatural, and alien menaces, the human race has adapted in a variety of ways, many of them borrowed from the technological developments of the lost Golden Age. Powered armor suits and giant vehicles are frequently used to combat the dangers of Rifts, but more invasive augmentation is common. This has three basic categories: "Juicers" augment themselves chemically, the "Borgs" augment themselves mechanically, and "Crazies" use performance-enhancing brain implants. All such augmentations boost strength, speed, endurance, and dexterity to superhuman levels. However, all come at great cost. Chemicals cause the body to wear out faster, decreasing life span to a few years. Mechanical Borg augmentation causes a loss of humanity when those with multiple limb and organ replacements become more machine than human. Brain implants cause mental instability ranging from mild phobias to crippling neurosis or psychosis. ==== North America ==== The strongest power in North America is the Coalition States (CS), which is based in the arcological city of Chi-Town and lays claim to northern Illinois, all of Iowa, the Texas Panhandle, Missouri, and the eastern half of Ontario, Canada. The second greatest power is Free Quebec, a former Coalition State that seceded following a civil war with the other Coalition States. Mexico is ruled by a group of vampire kingdoms, who treat humans as little more than food. North of the Rio Grande, west of Texas and roaming most of the American Southwest are large nomadic bands/tribes of bandits who collectively form the Pecos Empire, consisting of El Paso, Los Alamos, and Houstown. Much of the western United States has more or less willingly reverted to a mix of modern and past technology akin to the Wild West. The Royal Canadian Mounted Police managed to survive the great cataclysm, though Canada itself did not. The Mounties have become an independent law enforcement force called the Tundra Rangers, patrolling the northern wilderness. The Midwest, both upper and central, is home to most of North America's population. The Manistique Imperium and Northern Gun in Michigan's Upper Peninsula, both Coalition allies, are among the largest weapons manufacturing areas on the continent. New Lazlo is one of the largest cities in Michigan's southern portion. Chillicothe in Missouri is a large supplier of Coalition food processing and growing. Missouri's southern half, home to the city-states of Whykin (Poplar Bluff) and Kingsdale (West Plains) are in constant opposition to the CS and claim independence. Arkansas is home to the independent CS ally El Dorado. Southern Illinois and the Ohio Valley is home to the Federation of Magic. Also in the Ohio Valley is Psyscape, a city-state founded by psychics. Tolkeen was a major city in the former Minneapolis region in early Rifts books; the city welcomed users of magic. A military campaign made by the Coalition States (which is the primary event of 109 PA) resulted in the magic-user kingdom being wiped off the map. In the Northeast, the city-state of Lazlo, named after supernatural researcher and writer Victor Lazlo, was built upon the ruins of Toronto. This major center of civilization is well known as a melting pot of humans, D-Bees and other beings, and is the home of Techno-Wizardry. Mad Haven is the name given to the ruins of Manhattan; tectonic forces during the cataclysm have moved it into the coast, creating a peninsula. It is seen by most denizens of Rifts Earth as a refuge of demons and madness. ==== South America ==== The return of Atlantis caused the Amazon River basin to flood most of western South America, giving it the nickname The Land of a Thousand Islands. The Empire of the Sun, consisting of Cuzco, Nazca, Arequipa and Lima, created a wide range of technology and magic, including magic derived from the Nazca lines. In Argentina, the Silver River Republics of Cordoba (the South American Chi-Town), Santiago (one of the most tolerant human nations on Rifts Earth), Achilles (a nation founded by mutants), and New Babylon, a nation where humans and aliens coexist) have thrived and created nations whose strength rivals that of the CS. In Bolivia, freed Human and D-Bees formed the Megaversal Legion: a mercenary company with one of the highest levels of technology on Rifts Earth. ==== Europe ==== England has become a vast wilderness again, broken up by the occasional giant Millennium Tree or feudal kingdom, complete with a New Camelot and a new King Arthur, partially being manipulated by an alien intelligence disguised as Merlin. Also the magic of

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  BL (logic)

  In mathematical logic, basic fuzzy logic (or shortly BL), the logic of the continuous t-norms, is one of the t-norm fuzzy logics. It belongs to the broader class of substructural logics, or logics of residuated lattices; it extends the logic MTL of all left-continuous t-norms. == Syntax == === Language === The language of the propositional logic BL consists of countably many propositional variables and the following primitive logical connectives: Implication → {\displaystyle \rightarrow } (binary) Strong conjunction ⊗ {\displaystyle \otimes } (binary). The sign & is a more traditional notation for strong conjunction in the literature on fuzzy logic, while the notation ⊗ {\displaystyle \otimes } follows the tradition of substructural logics. Bottom ⊥ {\displaystyle \bot } (nullary — a propositional constant); 0 {\displaystyle 0} or 0 ¯ {\displaystyle {\overline {0}}} are common alternative signs and zero a common alternative name for the propositional constant (as the constants bottom and zero of substructural logics coincide in MTL). The following are the most common defined logical connectives: Weak conjunction ∧ {\displaystyle \wedge } (binary), also called lattice conjunction (as it is always realized by the lattice operation of meet in algebraic semantics). Unlike MTL and weaker substructural logics, weak conjunction is definable in BL as A ∧ B ≡ A ⊗ ( A → B ) {\displaystyle A\wedge B\equiv A\otimes (A\rightarrow B)} Negation ¬ {\displaystyle \neg } (unary), defined as ¬ A ≡ A → ⊥ {\displaystyle \neg A\equiv A\rightarrow \bot } Equivalence ↔ {\displaystyle \leftrightarrow } (binary), defined as A ↔ B ≡ ( A → B ) ∧ ( B → A ) {\displaystyle A\leftrightarrow B\equiv (A\rightarrow B)\wedge (B\rightarrow A)} As in MTL, the definition is equivalent to ( A → B ) ⊗ ( B → A ) . {\displaystyle (A\rightarrow B)\otimes (B\rightarrow A).} (Weak) disjunction ∨ {\displaystyle \vee } (binary), also called lattice disjunction (as it is always realized by the lattice operation of join in algebraic semantics), defined as A ∨ B ≡ ( ( A → B ) → B ) ∧ ( ( B → A ) → A ) {\displaystyle A\vee B\equiv ((A\rightarrow B)\rightarrow B)\wedge ((B\rightarrow A)\rightarrow A)} Top ⊤ {\displaystyle \top } (nullary), also called one and denoted by 1 {\displaystyle 1} or 1 ¯ {\displaystyle {\overline {1}}} (as the constants top and zero of substructural logics coincide in MTL), defined as ⊤ ≡ ⊥ → ⊥ {\displaystyle \top \equiv \bot \rightarrow \bot } Well-formed formulae of BL are defined as usual in propositional logics. In order to save parentheses, it is common to use the following order of precedence: Unary connectives (bind most closely) Binary connectives other than implication and equivalence Implication and equivalence (bind most loosely) === Axioms === A Hilbert-style deduction system for BL has been introduced by Petr Hájek (1998). Its single derivation rule is modus ponens: from A {\displaystyle A} and A → B {\displaystyle A\rightarrow B} derive B . {\displaystyle B.} The following are its axiom schemata: ( B L 1 ) : ( A → B ) → ( ( B → C ) → ( A → C ) ) ( B L 2 ) : A ⊗ B → A ( B L 3 ) : A ⊗ B → B ⊗ A ( B L 4 ) : A ⊗ ( A → B ) → B ⊗ ( B → A ) ( B L 5 a ) : ( A → ( B → C ) ) → ( A ⊗ B → C ) ( B L 5 b ) : ( A ⊗ B → C ) → ( A → ( B → C ) ) ( B L 6 ) : ( ( A → B ) → C ) → ( ( ( B → A ) → C ) → C ) ( B L 7 ) : ⊥ → A {\displaystyle {\begin{array}{ll}{\rm {(BL1)}}\colon &(A\rightarrow B)\rightarrow ((B\rightarrow C)\rightarrow (A\rightarrow C))\\{\rm {(BL2)}}\colon &A\otimes B\rightarrow A\\{\rm {(BL3)}}\colon &A\otimes B\rightarrow B\otimes A\\{\rm {(BL4)}}\colon &A\otimes (A\rightarrow B)\rightarrow B\otimes (B\rightarrow A)\\{\rm {(BL5a)}}\colon &(A\rightarrow (B\rightarrow C))\rightarrow (A\otimes B\rightarrow C)\\{\rm {(BL5b)}}\colon &(A\otimes B\rightarrow C)\rightarrow (A\rightarrow (B\rightarrow C))\\{\rm {(BL6)}}\colon &((A\rightarrow B)\rightarrow C)\rightarrow (((B\rightarrow A)\rightarrow C)\rightarrow C)\\{\rm {(BL7)}}\colon &\bot \rightarrow A\end{array}}} The axioms (BL2) and (BL3) of the original axiomatic system were shown to be redundant (Chvalovský, 2012) and (Cintula, 2005). All the other axioms were shown to be independent (Chvalovský, 2012). == Semantics == Like in other propositional t-norm fuzzy logics, algebraic semantics is predominantly used for BL, with three main classes of algebras with respect to which the logic is complete: General semantics, formed of all BL-algebras — that is, all algebras for which the logic is sound Linear semantics, formed of all linear BL-algebras — that is, all BL-algebras whose lattice order is linear Standard semantics, formed of all standard BL-algebras — that is, all BL-algebras whose lattice reduct is the real unit interval [0, 1] with the usual order; they are uniquely determined by the function that interprets strong conjunction, which can be any continuous t-norm.

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