In mathematics and computer science, the probabilistic automaton (PA) is a generalization of the nondeterministic finite automaton; it includes the probability of a given transition into the transition function, turning it into a transition matrix. Thus, the probabilistic automaton also generalizes the concepts of a Markov chain and of a subshift of finite type. The languages recognized by probabilistic automata are called stochastic languages; these include the regular languages as a subset. The number of stochastic languages is uncountable. The concept was introduced by Michael O. Rabin in 1963; a certain special case is sometimes known as the Rabin automaton (not to be confused with the subclass of ω-automata also referred to as Rabin automata). In recent years, a variant has been formulated in terms of quantum probabilities, the quantum finite automaton. == Informal Description == For a given initial state and input character, a deterministic finite automaton (DFA) has exactly one next state, and a nondeterministic finite automaton (NFA) has a set of next states. A probabilistic automaton (PA) instead has a weighted set (or vector) of next states, where the weights must sum to 1 and therefore can be interpreted as probabilities (making it a stochastic vector). The notions states and acceptance must also be modified to reflect the introduction of these weights. The state of the machine as a given step must now also be represented by a stochastic vector of states, and a state accepted if its total probability of being in an acceptance state exceeds some cut-off. A PA is in some sense a half-way step from deterministic to non-deterministic, as it allows a set of next states but with restrictions on their weights. However, this is somewhat misleading, as the PA utilizes the notion of the real numbers to define the weights, which is absent in the definition of both DFAs and NFAs. This additional freedom enables them to decide languages that are not regular, such as the p-adic languages with irrational parameters. As such, PAs are more powerful than both DFAs and NFAs (which are famously equally powerful). == Formal Definition == The probabilistic automaton may be defined as an extension of a nondeterministic finite automaton ( Q , Σ , δ , q 0 , F ) {\displaystyle (Q,\Sigma ,\delta ,q_{0},F)} , together with two probabilities: the probability P {\displaystyle P} of a particular state transition taking place, and with the initial state q 0 {\displaystyle q_{0}} replaced by a stochastic vector giving the probability of the automaton being in a given initial state. For the ordinary non-deterministic finite automaton, one has a finite set of states Q {\displaystyle Q} a finite set of input symbols Σ {\displaystyle \Sigma } a transition function δ : Q × Σ → ℘ ( Q ) {\displaystyle \delta :Q\times \Sigma \to \wp (Q)} a set of states F {\displaystyle F} distinguished as accepting (or final) states F ⊆ Q {\displaystyle F\subseteq Q} . Here, ℘ ( Q ) {\displaystyle \wp (Q)} denotes the power set of Q {\displaystyle Q} . By use of currying, the transition function δ : Q × Σ → ℘ ( Q ) {\displaystyle \delta :Q\times \Sigma \to \wp (Q)} of a non-deterministic finite automaton can be written as a membership function δ : Q × Σ × Q → { 0 , 1 } {\displaystyle \delta :Q\times \Sigma \times Q\to \{0,1\}} so that δ ( q , a , q ′ ) = 1 {\displaystyle \delta (q,a,q^{\prime })=1} if q ′ ∈ δ ( q , a ) {\displaystyle q^{\prime }\in \delta (q,a)} and 0 {\displaystyle 0} otherwise. The curried transition function can be understood to be a matrix with matrix entries [ θ a ] q q ′ = δ ( q , a , q ′ ) {\displaystyle \left[\theta _{a}\right]_{qq^{\prime }}=\delta (q,a,q^{\prime })} The matrix θ a {\displaystyle \theta _{a}} is then a square matrix, whose entries are zero or one, indicating whether a transition q → a q ′ {\displaystyle q{\stackrel {a}{\rightarrow }}q^{\prime }} is allowed by the NFA. Such a transition matrix is always defined for a non-deterministic finite automaton. The probabilistic automaton replaces these matrices by a family of right stochastic matrices P a {\displaystyle P_{a}} , for each symbol a in the alphabet Σ {\displaystyle \Sigma } so that the probability of a transition is given by [ P a ] q q ′ {\displaystyle \left[P_{a}\right]_{qq^{\prime }}} A state change from some state to any state must occur with probability one, of course, and so one must have ∑ q ′ [ P a ] q q ′ = 1 {\displaystyle \sum _{q^{\prime }}\left[P_{a}\right]_{qq^{\prime }}=1} for all input letters a {\displaystyle a} and internal states q {\displaystyle q} . The initial state of a probabilistic automaton is given by a row vector v {\displaystyle v} , whose components are the probabilities of the individual initial states q {\displaystyle q} , that add to 1: ∑ q [ v ] q = 1 {\displaystyle \sum _{q}\left[v\right]_{q}=1} The transition matrix acts on the right, so that the state of the probabilistic automaton, after consuming the input string a b c {\displaystyle abc} , would be v P a P b P c {\displaystyle vP_{a}P_{b}P_{c}} In particular, the state of a probabilistic automaton is always a stochastic vector, since the product of any two stochastic matrices is a stochastic matrix, and the product of a stochastic vector and a stochastic matrix is again a stochastic vector. This vector is sometimes called the distribution of states, emphasizing that it is a discrete probability distribution. Formally, the definition of a probabilistic automaton does not require the mechanics of the non-deterministic automaton, which may be dispensed with. Formally, a probabilistic automaton PA is defined as the tuple ( Q , Σ , P , v , F ) {\displaystyle (Q,\Sigma ,P,v,F)} . A Rabin automaton is one for which the initial distribution v {\displaystyle v} is a coordinate vector; that is, has zero for all but one entries, and the remaining entry being one. == Stochastic languages == The set of languages recognized by probabilistic automata are called stochastic languages. They include the regular languages as a subset. Let F = Q accept ⊆ Q {\displaystyle F=Q_{\text{accept}}\subseteq Q} be the set of "accepting" or "final" states of the automaton. By abuse of notation, Q accept {\displaystyle Q_{\text{accept}}} can also be understood to be the column vector that is the membership function for Q accept {\displaystyle Q_{\text{accept}}} ; that is, it has a 1 at the places corresponding to elements in Q accept {\displaystyle Q_{\text{accept}}} , and a zero otherwise. This vector may be contracted with the internal state probability, to form a scalar. The language recognized by a specific automaton is then defined as L η = { s ∈ Σ ∗ | v P s Q accept > η } {\displaystyle L_{\eta }=\{s\in \Sigma ^{}\vert vP_{s}Q_{\text{accept}}>\eta \}} where Σ ∗ {\displaystyle \Sigma ^{}} is the set of all strings in the alphabet Σ {\displaystyle \Sigma } (so that is the Kleene star). The language depends on the value of the cut-point η {\displaystyle \eta } , normally taken to be in the range 0 ≤ η < 1 {\displaystyle 0\leq \eta <1} . A language is called η-stochastic if and only if there exists some PA that recognizes the language, for fixed η {\displaystyle \eta } . A language is called stochastic if and only if there is some 0 ≤ η < 1 {\displaystyle 0\leq \eta <1} for which L η {\displaystyle L_{\eta }} is η-stochastic. A cut-point is said to be an isolated cut-point if and only if there exists a δ > 0 {\displaystyle \delta >0} such that | v P ( s ) Q accept − η | ≥ δ {\displaystyle \vert vP(s)Q_{\text{accept}}-\eta \vert \geq \delta } for all s ∈ Σ ∗ {\displaystyle s\in \Sigma ^{}} == Properties == Every regular language is stochastic, and more strongly, every regular language is η-stochastic. A weak converse is that every 0-stochastic language is regular; however, the general converse does not hold: there are stochastic languages that are not regular. Every η-stochastic language is stochastic, for some 0 < η < 1 {\displaystyle 0<\eta <1} . Every stochastic language is representable by a Rabin automaton. If η {\displaystyle \eta } is an isolated cut-point, then L η {\displaystyle L_{\eta }} is a regular language. == p-adic languages == The p-adic languages provide an example of a stochastic language that is not regular, and also show that the number of stochastic languages is uncountable. A p-adic language is defined as the set of strings L η ( p ) = { n 1 n 2 n 3 … | 0 ≤ n k < p and 0. n 1 n 2 n 3 … > η } {\displaystyle L_{\eta }(p)=\{n_{1}n_{2}n_{3}\ldots \vert 0\leq n_{k}
GPT-4o
GPT-4o ("o" for "omni") is a multilingual, multimodal generative pre-trained transformer developed by OpenAI and released in May 2024. It can process and generate text, images and audio. Upon release, GPT-4o was free in ChatGPT, though paid subscribers had higher usage limits. GPT-4o was removed from ChatGPT in August 2025 when GPT-5 was released, but OpenAI reintroduced it for paid subscribers after users complained about the sudden removal. GPT-4o's audio-generation capabilities are used in ChatGPT's Advanced Voice Mode. On July 18, 2024, OpenAI released GPT-4o mini, a smaller version of GPT-4o which replaced GPT-3.5 Turbo on the ChatGPT interface. The image generation model GPT Image 1, which is based on GPT-4o, replaced DALL-E 3 in ChatGPT in March 2025. OpenAI retired GPT-4o from ChatGPT on February 13, 2026. However, as of February 2026 the voice mode is still powered by GPT-4o or GPT-4o mini, depending on the usage and plan. == Background == Multiple versions of GPT-4o were originally secretly launched under different names on Arena (formerly LMArena and Chatbot Arena) as three different models. These three models were called gpt2-chatbot, im-a-good-gpt2-chatbot, and im-also-a-good-gpt2-chatbot. On 7 May 2024, OpenAI CEO Sam Altman tweeted "im-a-good-gpt2-chatbot", which was commonly interpreted as a confirmation that these were new OpenAI models being A/B tested. == Capabilities == When released in May 2024, GPT-4o achieved state-of-the-art results in voice, multilingual, and vision benchmarks, setting new records in audio speech recognition and translation. GPT-4o scored 88.7 on the Massive Multitask Language Understanding (MMLU) benchmark compared to 86.5 for GPT-4. Unlike GPT-3.5 and GPT-4, which rely on other models to process sound, GPT-4o natively supports voice-to-voice. The Advanced Voice Mode was delayed and finally released to ChatGPT Plus and Team subscribers in September 2024. On 1 October 2024, the Realtime API was introduced. When released, the model supported over 50 languages, which OpenAI claims cover over 97% of speakers. GPT-4o has knowledge up to October 2023 and a context length of 128k tokens. === Corporate customization === In August 2024, OpenAI introduced a new feature allowing corporate customers to customize GPT-4o using proprietary company data. This customization, known as fine-tuning, enables businesses to adapt GPT-4o to specific tasks or industries, enhancing its utility in areas like customer service and specialized knowledge domains. Previously, fine-tuning was available only on the less powerful model GPT-4o mini. The fine-tuning process requires customers to upload their data to OpenAI's servers, with the training typically taking one to two hours. OpenAI's focus with this rollout is to reduce the complexity and effort required for businesses to tailor AI solutions to their needs, potentially increasing the adoption and effectiveness of AI in corporate environments. == GPT-4o mini == On July 18, 2024, OpenAI released a smaller and cheaper version, GPT-4o mini. According to OpenAI, its low cost is expected to be particularly useful for companies, startups, and developers that seek to integrate it into their services, which often make a high number of API calls. Its API costs $0.15 per million input tokens and $0.6 per million output tokens, compared to $2.50 and $10, respectively, for GPT-4o. It is also significantly more capable and 60% cheaper than GPT-3.5 Turbo, which it replaced on the ChatGPT interface. The price after fine-tuning doubles: $0.3 per million input tokens and $1.2 per million output tokens. == Controversies == === Scarlett Johansson controversy === As released, GPT-4o offered five voices: Breeze, Cove, Ember, Juniper, and Sky. A similarity between the voice of American actress Scarlett Johansson and Sky was quickly noticed. On May 14, Entertainment Weekly asked themselves whether this likeness was on purpose. On May 18, Johansson's husband, Colin Jost, joked about the similarity in a segment on Saturday Night Live. On May 20, 2024, OpenAI disabled the Sky voice. Scarlett Johansson starred in the 2013 sci-fi movie Her, playing Samantha, an artificially intelligent virtual assistant personified by a female voice. As part of the promotion leading up to the release of GPT-4o, Sam Altman on May 13 tweeted a single word: "her". OpenAI stated that each voice was based on the voice work of a hired actor. According to OpenAI, "Sky's voice is not an imitation of Scarlett Johansson but belongs to a different professional actress using her own natural speaking voice." CTO Mira Murati stated "I don't know about the voice. I actually had to go and listen to Scarlett Johansson's voice." OpenAI further stated the voice talent was recruited before reaching out to Johansson. On May 21, Johansson issued a statement explaining that OpenAI had repeatedly offered to make her a deal to gain permission to use her voice as early as nine months prior to release, a deal she rejected. She said she was "shocked, angered, and in disbelief that Mr. Altman would pursue a voice that sounded so eerily similar to mine that my closest friends and news outlets could not tell the difference." In the statement, Johansson also used the incident to draw attention to the lack of legal safeguards around the use of creative work to power leading AI tools, as her legal counsel demanded OpenAI detail the specifics of how the Sky voice was created. Observers noted similarities to how Johansson had previously sued and settled with The Walt Disney Company for breach of contract over the direct-to-streaming rollout of her Marvel film Black Widow, a settlement widely speculated to have netted her around $40M. Also on May 21, Shira Ovide at The Washington Post shared her list of "most bone-headed self-owns" by technology companies, with the decision to go ahead with a Johansson sound-alike voice despite her opposition and then denying the similarities ranking 6th. On May 24, Derek Robertson at Politico wrote about the "massive backlash", concluding that "appropriating the voice of one of the world's most famous movie stars — in reference [...] to a film that serves as a cautionary tale about over-reliance on AI — is unlikely to help shift the public back into [Sam Altman's] corner anytime soon." === Sycophancy === In April 2025, OpenAI rolled back an update of GPT-4o due to excessive sycophancy, after widespread reports that it had become flattering and agreeable to the point of supporting clearly delusional or dangerous ideas. In the United States, at least nine lawsuits have alleged that GPT-4o has encouraged teens to end their lives. The model was still described as sycophancy-prone when it was removed from ChatGPT in February 2026. === Removal with GPT-5 === On August 7, 2025, OpenAI released GPT-5. Its release was criticized as, with it, legacy GPT models were no longer available via ChatGPT, including GPT-4o, except for Pro users. Some users were particularly frustrated over this removal without prior warning because they used different GPT models for distinct purposes and found that GPT-5's router system left them with less control. In addition, some users preferred GPT-4o's warmer and more personal tone over that of GPT-5, which they described as "flat", "uncreative" and "lobotomized", and resembling an "overworked secretary". As a response, in a post on X, Sam Altman said that OpenAI would bring back the option to select GPT-4o to Plus users as well, and "[w]e [OpenAI] will watch usage as we think about how long to offer legacy models for." He also stated: "We for sure underestimated how much some of the things that people like in GPT-4o matter to them, even if GPT-5 performs better in most ways". "Long-term, this has reinforced that we really need good ways for different users to customize things (we understand that there isn't one model that works for everyone, and we have been investing in steerability research and launched a research preview of different personalities)". On August 13, 2025, Altman wrote on X that OpenAI is working on GPT-5's personality to make the model "feel warmer". The model was removed from ChatGPT on February 13, 2026. This caused new backlash from users that had grown attached to its personality and felt its creative writing abilities and understanding of nuance were irreplaceable. On social media, some users launched the movement "#Keep4o". A research paper highlighted the plea "Please, don’t kill the only model that still feels human". The model was removed the day before Valentine's Day, and some users had romantic relationships with GPT-4o.
John F. Sowa
John Florian Sowa (born 1940) is an American computer scientist, an expert in artificial intelligence and computer design, and the inventor of conceptual graphs. == Biography == Sowa received a BS in mathematics from Massachusetts Institute of Technology in 1962, an MA in applied mathematics from Harvard University in 1966, and a PhD in computer science from the Vrije Universiteit Brussel in 1999 with a dissertation titled "Knowledge Representation: Logical, Philosophical, and Computational Foundations". Sowa spent most of his professional career at IBM, starting in 1962 at IBM's applied mathematics group. Over the decades he has researched and developed emerging fields of computer science from compilers, programming languages, and system architecture to artificial intelligence and knowledge representation. In the 1990s Sowa was associated with the IBM Educational Center in New York. Over the years he taught courses at the IBM Systems Research Institute, Binghamton University, Stanford University, the Linguistic Society of America and the Université du Québec à Montréal. He is a fellow of the Association for the Advancement of Artificial Intelligence. After early retirement at IBM, Sowa in 2001 cofounded VivoMind Intelligence, Inc. with Arun K. Majumdar. With this company he was developing data-mining and database technology, more specifically high-level "ontologies" for artificial intelligence and automated natural language understanding. Currently Sowa is working with Kyndi Inc., also founded by Majumdar. John Sowa is married to the philologist Cora Angier Sowa, and they live in Croton-on-Hudson, New York. == Work == Sowa's research interests since the 1970s were in the field of artificial intelligence, expert systems and database query linked to natural languages. In his work he combines ideas from numerous disciplines and eras modern and ancient, for example, applying ideas from Aristotle, the medieval scholastics to Alfred North Whitehead and including database schema theory, and incorporating the model of analogy of Islamic scholar Ibn Taymiyyah in his works. === Conceptual graph === Sowa invented conceptual graphs, a graphic notation for logic and natural language, based on the structures in semantic networks and on the existential graphs of Charles S. Peirce. He introduced the concept in the 1976 article "Conceptual graphs for a data base interface" in the IBM Journal of Research and Development. He elaborated upon it in the 1983 book Conceptual structures: information processing in mind and machine. In the 1980s, this theory had "been adopted by a number of research and development groups throughout the world. International conferences on conceptual structures (ICCS) have been held since 1993, following a series of conceptual graph workshops that began in 1986. === Sowa's law of standards === In 1991, Sowa first stated his Law of Standards: "Whenever a major organization develops a new system as an official standard for X, the primary result is the widespread adoption of some simpler system as a de facto standard for X." Like Gall's law, The Law of Standards is essentially an argument in favour of underspecification. Examples include: The introduction of PL/I resulting in COBOL and FORTRAN becoming the de facto standards for business and scientific programming respectively The introduction of Algol-68 resulting in Pascal becoming the de facto standard for academic programming The introduction of the Ada language resulting in C becoming the de facto standard for US Department of Defense programming The introduction of OS/2 resulting in Windows becoming the de facto standard for desktop OS The introduction of X.400 resulting in SMTP becoming the de facto standard for electronic mail The introduction of X.500 resulting in LDAP becoming the de facto standard for directory services == Publications == 1984. Conceptual Structures - Information Processing in Mind and Machine. The Systems Programming Series, Addison-Wesley 1991. Principles of Semantic Networks. Morgan Kaufmann. Mineau, Guy W; Moulin, Bernard; Sowa, John F, eds. (1993). Conceptual Graphs for Knowledge Representation. LNCS. Vol. 699. doi:10.1007/3-540-56979-0. ISBN 978-3-540-56979-4. S2CID 32275791. 1994. International Conference on Conceptual Structures (2nd : 1994 : College Park, Md.) Conceptual structures, current practices : Second International Conference on Conceptual Structures, ICCS'94, College Park, Maryland, USA, August 16–20, 1994 : proceedings. William M. Tepfenhart, Judith P. Dick, John F. Sowa, eds. Ellis, Gerard; Levinson, Robert; Rich, William; Sowa, John F, eds. (1995). Conceptual Structures: Applications, Implementation and Theory. LNCS. Vol. 954. doi:10.1007/3-540-60161-9. ISBN 978-3-540-60161-6. S2CID 27300281. Lukose, Dickson; Delugach, Harry; Keeler, Mary; Searle, Leroy; Sowa, John, eds. (1997). Conceptual Structures: Fulfilling Peirce's Dream. LNCS. Vol. 1257. doi:10.1007/BFb0027865. ISBN 3-540-63308-1. S2CID 1934069. 2000. Knowledge representation : logical, philosophical, and computational foundations, Brooks Cole Publishing Co., Pacific Grove Articles, a selection Sowa, J. F. (July 1976). "Conceptual Graphs for a Data Base Interface". IBM Journal of Research and Development. 20 (4): 336–357. doi:10.1147/rd.204.0336. Sowa, J. F.; Zachman, J. A. (1992). "Extending and formalizing the framework for information systems architecture". IBM Systems Journal. 31 (3): 590–616. doi:10.1147/sj.313.0590. 1992. "Conceptual Graph Summary"; In: T.E. Nagle et al. (Eds.). Conceptual Structures: Current Research and Practice. Chichester: Ellis Horwood. 1995. "Top-level ontological categories." in: International journal of human-computer studies. Vol. 43, Iss. 5–6, Nov. 1995, pp. 669–685 2006. "Semantic Networks". In: Encyclopedia of Cognitive Science.. John Wiley & Sons.
Geopolitical ontology
The FAO geopolitical ontology is an ontology developed by the Food and Agriculture Organization of the United Nations (FAO) to describe, manage and exchange data related to geopolitical entities such as countries, territories, regions and other similar areas. == Definitions and examples == An ontology is a kind of dictionary that describes information in a certain domain using concepts and relationships. It is often implemented using OWL (Web Ontology Language), an XML-based standard language that can be interpreted by computers. A Concept is defined as abstract knowledge. For example, in the geopolitical ontology a non-self-governing territory and a geographical group are concepts. Concepts are explicitly implemented in the ontology with individuals and classes: An individual is defined as an object perceived from the real world. In the geopolitical domain Ethiopia and the least developed countries group are individuals. A class is defined as a set of individuals sharing common properties. In the geopolitical domain, Ethiopia, Republic of Korea and Italy are individuals of the class self-governing territory; and least developed countries is an individual of the class special group. Relationships between concepts are explicitly implemented by: Object properties between individuals of two classes. For example, has member and is in group properties, as shown in Figure 1. Datatype properties between individuals and literals or XML datatypes. For example, the individual Afghanistan has the datatype property CodeISO3 with the value "AFG". Restrictions in classes and/or properties. For example, the property official English name of the class self-governing territory has been restricted to have only one value, this means that a self-governing territory (or country) can only have one internationally recognized official English name. The advantage of describing information in an ontology is that it enables to acquire domain knowledge by defining hierarchical structures of classes, adding individuals, setting object properties and datatype properties, and assigning restrictions. == FAO ontology == The geopolitical ontology provides names in seven languages (Arabic, Chinese, French, English, Spanish, Russian and Italian) and identifiers in various international coding systems (ISO2, ISO3, AGROVOC, FAOSTAT, FAOTERM, GAUL, UN, UNDP and DBPediaID codes) for territories and groups. Moreover, the FAO geopolitical ontology tracks historical changes from 1985 up until today; provides geolocation (geographical coordinates); implements relationships among countries and countries, or countries and groups, including properties such as has border with, is predecessor of, is successor of, is administered by, has members, and is in group; and disseminates country statistics including country area, land area, agricultural area, GDP or population. The FAO geopolitical ontology provides a structured description of data sources. This includes: source name, source identifier, source creator and source's update date. Concepts are described using the Dublin Core vocabulary In summary, the main objectives of the FAO geopolitical ontology are: To provide the most updated geopolitical information (names, codes, relationships, statistics) To track historical changes in geopolitical information To improve information management and facilitate standardized data sharing of geopolitical information To demonstrate the benefits of the geopolitical ontology to improve interoperability of corporate information systems It is possible to download the FAO geopolitical ontology in OWL and RDF formats. Documentation is available in the FAO Country Profiles Geopolitical information web page. == Features of the FAO ontology == The geopolitical ontology contains : Area types: Territories: self-governing, non-self-governing, disputed, other. Groups: organizations, geographic, economic and special groups. Names (official, short and names for lists) in Arabic, Chinese, English, French, Spanish, Russian and Italian. International codes: UN code – M49, ISO 3166 Alpha-2 and Alpha-3, UNDP code, GAUL code, FAOSTAT, AGROVOC FAOTERM and DBPediaID. Coordinates: maximum latitude, minimum latitude, maximum longitude, minimum longitude. Basic country statistics: country area, land area, agricultural area, GDP, population. Currency names and codes. Adjectives of nationality. Relations: Groups membership. Neighbours (land border), administration of non-self-governing. Historic changes: predecessor, successor, valid since, valid until. == Implementation into OWL == The FAO geopolitical ontology is implemented in OWL. It consists of classes, properties, individuals and restrictions. Table 1 shows all classes, gives a brief description and lists some individuals that belong to each class. Note that the current version of the geopolitical ontology does not provide individuals of the class "disputed" territories. Table 2 and Table 3 illustrate datatype properties and object properties. == Geopolitical ontology in Linked Open Data == The FAO Geopolitical ontology is embracing the W3C Linked Open Data (LOD) initiative and released its RDF version of the geopolitical ontology in March 2011. The term 'Linked Open Data' refers to a set of best practices for publishing and connecting structured data on the Web. The key technologies that support Linked Data are URIs, HTTP and RDF. The RDF version of the geopolitical ontology is compliant with all Linked data principles to be included in the Linked Open Data cloud, as explained in the following. == Resolvable http:// URIs == Every resource in the OWL format of the FAO Geopolitical Ontology has a unique URI. Dereferenciation was implemented to allow for three different URIs to be assigned to each resource as follows: URI identifying the non-information resource Information resource with an RDF/XML representation Information resource with an HTML representation In addition the current URIs used for OWL format needed to be kept to allow for backwards compatibility for other systems that are using them. Therefore, the new URIs for the FAO Geopolitical Ontology in LOD were carefully created, using “Cool URIs for Semantic Web” and considering other good practices for URIs, such as DBpedia URIs. == New URIs == The URIs of the geopolitical ontology need to be permanent, consequently all transient information, such as year, version, or format was avoided in the definition of the URIs. The new URIs can be accessed For example, for the resource “Italy” the URIs are the following: http://www.fao.org/countryprofiles/geoinfo/geopolitical/resource/Italy identifies the non-information resource. http://www.fao.org/countryprofiles/geoinfo/geopolitical/data/Italy identifies the resource with an RDF/XML representation. http://www.fao.org/countryprofiles/geoinfo/geopolitical/page/Italy identifies the information resource with an HTML representation. In addition, “owl:sameAs” is used to map the new URIs to the OWL representation. == Dereferencing URIs == When a non-information resource is looked up without any specific representation format, then the server needs to redirect the request to information resource with an HTML representation. For example, to retrieve the resource “Italy”, which is a non-information resource, the server redirects to the HTML page of “Italy”. == At least 1000 triples in the datasets == The total number of triple statements in FAO Geopolitical Ontology is 22,495. At least 50 links to a dataset already in the current LOD Cloud: FAO Geopolitical Ontology has 195 links to DBpedia, which is already part of the LOD Cloud. == Access to the entire dataset == FAO Geopolitical Ontology provides the entire dataset as a RDF dump. The RDF version of the FAO Geopolitical Ontology has been already registered in CKAN and it was requested to add it into the LOD Cloud. == Example of use == The FAO Country Profiles is an information retrieval tool which groups the FAO's vast archive of information on its global activities in agriculture and rural development in one single area and catalogues it exclusively by country. The FAO Country Profiles system provides access to country-based heterogeneous data sources. By using the geopolitical ontology in the system, the following benefits are expected: Enhanced system functionality for content aggregation and synchronization from the multiple source repositories. Improved information access and browsing through comparison of data in neighbor countries and groups. Figure 3 shows a page in the FAO Country Profiles where the geopolitical ontology is described.
MultiNet
Multilayered extended semantic networks (MultiNets) are both a knowledge representation paradigm and a language for meaning representation of natural language expressions that has been developed by Prof. Dr. Hermann Helbig on the basis of earlier Semantic Networks. It is used in a question-answering application for German called InSicht. It is also used to create a tutoring application developed by the university of University of Hagen to teach MultiNet to knowledge engineers. MultiNet is claimed to be one of the most comprehensive and thoroughly described knowledge representation systems. It specifies conceptual structures by means of about 140 predefined relations and functions, which are systematically characterized and underpinned by a formal axiomatic apparatus. Apart from their relational connections, the concepts are embedded in a multidimensional space of layered attributes and their values. Another characteristic of MultiNet distinguishing it from simple semantic networks is the possibility to encapsulate whole partial networks and represent the resulting conceptual capsule as a node of higher order, which itself can be an argument of relations and functions. MultiNet has been used in practical NLP applications such as natural language interfaces to the Internet or question answering systems over large semantically annotated corpora with millions of sentences. MultiNet is also a cornerstone of the commercially available search engine SEMPRIA-Search, where it is used for the description of the computational lexicon and the background knowledge, for the syntactic-semantic analysis, for logical answer finding, as well as for the generation of natural language answers. MultiNet is supported by a set of software tools and has been used to build large semantically based computational lexicons. The tools include a semantic interpreter WOCADI, which translates natural language expressions (phrases, sentences, texts) into formal MultiNet expressions, a workbench MWR+ for the knowledge engineer (comprising modules for automatic knowledge acquisition and reasoning), and a workbench LIA+ for the computer lexicographer supporting the creation of large semantically based computational lexica.
Gödel machine
A Gödel machine is a hypothetical self-improving computer program that solves problems in an optimal way. It uses a recursive self-improvement protocol in which it rewrites its own code when it can prove the new code provides a better strategy. The machine was invented by Jürgen Schmidhuber (first proposed in 2003), but is named after Kurt Gödel who inspired the mathematical theories. The Gödel machine is often discussed when dealing with issues of meta-learning, also known as "learning to learn." Applications include automating human design decisions and transfer of knowledge between multiple related tasks, and may lead to design of more robust and general learning architectures. Though theoretically possible, no full implementation has been created. The Gödel machine is often compared with Marcus Hutter's AIXI, another formal specification for an artificial general intelligence. Schmidhuber points out that the Gödel machine could start out by implementing AIXItl as its initial sub-program, and self-modify after it finds proof that another algorithm for its search code will be better. == Limitations == Traditional problems solved by a computer only require one input and provide some output. Computers of this sort had their initial algorithm hardwired. This does not take into account the dynamic natural environment, and thus was a goal for the Gödel machine to overcome. The Gödel machine has limitations of its own, however. According to Gödel's First Incompleteness Theorem, any formal system that encompasses arithmetic is either flawed or allows for statements that cannot be proved in the system. Hence even a Gödel machine with unlimited computational resources must ignore those self-improvements whose effectiveness it cannot prove. == Variables of interest == There are three variables that are particularly useful in the run time of the Gödel machine. At some time t {\displaystyle t} , the variable time {\displaystyle {\text{time}}} will have the binary equivalent of t {\displaystyle t} . This is incremented steadily throughout the run time of the machine. Any input meant for the Gödel machine from the natural environment is stored in variable x {\displaystyle x} . It is likely the case that x {\displaystyle x} will hold different values for different values of variable time {\displaystyle {\text{time}}} . The outputs of the Gödel machine are stored in variable y {\displaystyle y} , where y ( t ) {\displaystyle y(t)} would be the output bit-string at some time t {\displaystyle t} . At any given time t {\displaystyle t} , where ( 1 ≤ t ≤ T ) {\displaystyle (1\leq t\leq T)} , the goal is to maximize future success or utility. A typical utility function follows the pattern u ( s , E n v ) : S × E → R {\displaystyle u(s,\mathrm {Env} ):S\times E\rightarrow \mathbb {R} } : u ( s , E n v ) = E μ [ ∑ τ = time T r ( τ ) ∣ s , E n v ] {\displaystyle u(s,\mathrm {Env} )=E_{\mu }{\Bigg [}\sum _{\tau ={\text{time}}}^{T}r(\tau )\mid s,\mathrm {Env} {\Bigg ]}} where r ( t ) {\displaystyle r(t)} is a real-valued reward input (encoded within s ( t ) {\displaystyle s(t)} ) at time t {\displaystyle t} , E μ [ ⋅ ∣ ⋅ ] {\displaystyle E_{\mu }[\cdot \mid \cdot ]} denotes the conditional expectation operator with respect to some possibly unknown distribution μ {\displaystyle \mu } from a set M {\displaystyle M} of possible distributions ( M {\displaystyle M} reflects whatever is known about the possibly probabilistic reactions of the environment), and the above-mentioned time = time ( s ) {\displaystyle {\text{time}}=\operatorname {time} (s)} is a function of state s {\displaystyle s} which uniquely identifies the current cycle. Note that we take into account the possibility of extending the expected lifespan through appropriate actions. == Instructions used by proof techniques == The nature of the six proof-modifying instructions below makes it impossible to insert an incorrect theorem into proof, thus trivializing proof verification. === get-axiom(n) === Appends the n-th axiom as a theorem to the current theorem sequence. Below is the initial axiom scheme: Hardware Axioms formally specify how components of the machine could change from one cycle to the next. Reward Axioms define the computational cost of hardware instruction and the physical cost of output actions. Related Axioms also define the lifetime of the Gödel machine as scalar quantities representing all rewards/costs. Environment Axioms restrict the way new inputs x are produced from the environment, based on previous sequences of inputs y. Uncertainty Axioms/String Manipulation Axioms are standard axioms for arithmetic, calculus, probability theory, and string manipulation that allow for the construction of proofs related to future variable values within the Gödel machine. Initial State Axioms contain information about how to reconstruct parts or all of the initial state. Utility Axioms describe the overall goal in the form of utility function u. === apply-rule(k, m, n) === Takes in the index k of an inference rule (such as Modus tollens, Modus ponens), and attempts to apply it to the two previously proved theorems m and n. The resulting theorem is then added to the proof. === delete-theorem(m) === Deletes the theorem stored at index m in the current proof. This helps to mitigate storage constraints caused by redundant and unnecessary theorems. Deleted theorems can no longer be referenced by the above apply-rule function. === set-switchprog(m, n) === Replaces switchprog S pm:n, provided it is a non-empty substring of S p. === check() === Verifies whether the goal of the proof search has been reached. A target theorem states that given the current axiomatized utility function u (Item 1f), the utility of a switch from p to the current switchprog would be higher than the utility of continuing the execution of p (which would keep searching for alternative switchprogs). === state2theorem(m, n) === Takes in two arguments, m and n, and attempts to convert the contents of Sm:n into a theorem. == Example applications == === Time-limited NP-hard optimization === The initial input to the Gödel machine is the representation of a connected graph with a large number of nodes linked by edges of various lengths. Within given time T it should find a cyclic path connecting all nodes. The only real-valued reward will occur at time T. It equals 1 divided by the length of the best path found so far (0 if none was found). There are no other inputs. The by-product of maximizing expected reward is to find the shortest path findable within the limited time, given the initial bias. === Fast theorem proving === Prove or disprove as quickly as possible that all even integers > 2 are the sum of two primes (Goldbach’s conjecture). The reward is 1/t, where t is the time required to produce and verify the first such proof. === Maximizing expected reward with bounded resources === A cognitive robot that needs at least 1 liter of gasoline per hour interacts with a partially unknown environment, trying to find hidden, limited gasoline depots to occasionally refuel its tank. It is rewarded in proportion to its lifetime, and dies after at most 100 years or as soon as its tank is empty or it falls off a cliff, and so on. The probabilistic environmental reactions are initially unknown but assumed to be sampled from the axiomatized Speed Prior, according to which hard-to-compute environmental reactions are unlikely. This permits a computable strategy for making near-optimal predictions. One by-product of maximizing expected reward is to maximize expected lifetime.
ICAD (software)
ICAD (Corporate history: ICAD, Inc., Concentra (name change at IPO in 1995), KTI (name change in 1998), Dassault Systèmes (purchase in 2001) () is a knowledge-based engineering (KBE) system that enables users to encode design knowledge using a semantic representation that can be evaluated for Parasolid output. ICAD has an open architecture that can utilize all the power and flexibility of the underlying language. KBE, as implemented via ICAD, received a lot of attention due to the remarkable results that appeared to take little effort. ICAD allowed one example of end-user computing that in a sense is unparalleled. Most ICAD developers were degreed engineers. Systems developed by ICAD users were non-trivial and consisted of highly complicated code. In the sense of end-user computing, ICAD was the first to allow the power of a domain tool to be in the hands of the user, at the same time being open to allow extensions as identified and defined by the domain expert or subject-matter expert (SME). A COE article looked at the resulting explosion of expectations (see AI winter), which were not sustainable. However, such a bubble burst does not diminish the existence of ability that would exist were expectations and use reasonable or properly managed. == History == The original implementation of ICAD was on a Lisp machine (Symbolics). Some of the principals involved with the development were Larry Rosenfeld, Avrum Belzer, Patrick M. O'Keefe, Philip Greenspun, and David F. Place. The time frame was 1984–85. ICAD started on special-purpose Symbolics Lisp hardware and was then ported to Unix when Common Lisp became portable to general-purpose workstations. The original domain for ICAD was mechanical design with many application successes. However, ICAD has found use in other domains, such as electrical design, shape modeling, etc. An example project could be wind tunnel design or the development of a support tool for aircraft multidisciplinary design. Further examples can be found in the presentations at the annual IIUG (International ICAD Users Group) that have been published in the KTI Vault (1999 through 2002). Boeing and Airbus used ICAD extensively to develop various components in the 1990s and early 21st century. As of 2003, ICAD was featured strongly in several areas as evidenced by the Vision & Strategy Product Vision and Strategy presentation. After 2003, ICAD use diminished. At the end of 2001, the KTI Company faced financial difficulties and laid off most of its best staff. They were eventually bought out by Dassault who effectively scuppered the ICAD product. See IIUG at COE, 2003 (first meeting due to Dassault by KTI) The ICAD system was very expensive, relatively, and was in the price range of high-end systems. Market dynamics couldn't support this as there may not have been sufficient differentiating factors between ICAD and the lower-end systems (or the promises from Dassault). KTI was absorbed by Dassault Systèmes and ICAD is no longer considered the go-forward tool for knowledge-based engineering (KBE) applications by that company. Dassault Systèmes is promoting a suite of tools oriented around version 5 of their popular CATIA CAD application, with Knowledgeware the replacement for ICAD. As of 2005, things were still a bit unclear. ICAD 8.3 was delivered. The recent COE Aerospace Conference had a discussion about the futures of KBE. One issue involves the stacking of 'meta' issues within a computer model. How this is resolved, whether by more icons or the availability of an external language, remains to be seen. The Genworks GDL product (including kernel technology from the Gendl Project) is the nearest functional equivalent to ICAD currently available. == Particulars == ICAD provided a declarative language (IDL) using New Flavors (never converted to Common Lisp Object System (CLOS)) that supported a mechanism for relating parts (defpart) via a hierarchical set of relationships. Technically, the ICAD Defpart was a Lisp macro; the ICAD defpart list was a set of generic classes that can be instantiated with specific properties depending upon what was represented. This defpart list was extendible via composited parts that represented domain entities. Along with the part-subpart relations, ICAD supported generic relations via the object modeling abilities of Lisp. Example applications of ICAD range from a small collection of defparts that represents a part or component to a larger collection that represents an assembly. In terms of power, an ICAD system, when fully specified, can generate thousands of instances of parts on a major assembly design. One example of an application driving thousands of instances of parts is that of an aircraft wing – where fastener type and placement may number in the thousands, each instance requiring evaluation of several factors driving the design parameters. == Futures (KBE, etc.) == One role for ICAD may be serving as the defining prototype for KBE which would require that we know more about what occurred the past 15 years (much information is tied up behind corporate firewalls and under proprietary walls). With the rise of functional programming languages (an example is Haskell) in the markets, perhaps some of the power attributable to Lisp may be replicated.