A Gorn address (Gorn, 1967) is a method of identifying and addressing any node within a tree data structure. This notation is often used for identifying nodes in a parse tree defined by phrase structure rules. The Gorn address is a sequence of zero or more integers conventionally separated by dots, e.g., 0 or 1.0.1. The root which Gorn calls can be regarded as the empty sequence. And the j {\displaystyle j} -th child of the i {\displaystyle i} -th child has an address i . j {\displaystyle i.j} , counting from 0. It is named after American computer scientist Saul Gorn.
Recursive transition network
A recursive transition network ("RTN") is a graph theoretical schematic used to represent the rules of a context-free grammar. RTNs have application to programming languages, natural language and lexical analysis. Any sentence that is constructed according to the rules of an RTN is said to be "well-formed". The structural elements of a well-formed sentence may also be well-formed sentences by themselves, or they may be simpler structures. This is why RTNs are described as recursive. == Notes and references ==
Karen Hao
Karen Hao (born in the United States c. 1993) is an American journalist and author. Currently a freelancer for publications like The Atlantic and previously a foreign correspondent based in Hong Kong for The Wall Street Journal and senior artificial intelligence editor at the MIT Technology Review, she is best known for her coverage on AI research, technology ethics and the social impact of AI. Hao also co-produced the podcast In Machines We Trust and wrote the newsletter The Algorithm. Previously, she worked at Quartz as a tech reporter and data scientist and was an application engineer at the first startup to spin out of X Development. Hao's writing has also appeared in Mother Jones, Sierra Magazine, The New Republic, and other publications. == Early life and education == Hao is the daughter of Chinese immigrant parents, and grew up in New Jersey. She is a native speaker of both English and Mandarin Chinese. She graduated from The Lawrenceville School in 2011. She then studied at the Massachusetts Institute of Technology (MIT), graduating with a B.S. in mechanical engineering and a minor in energy studies in 2015. == Career == Hao is known in the technology world for her coverage of new AI research findings and their societal and ethical impacts. Her writing has spanned research and issues regarding big tech data privacy, misinformation, deepfakes, facial recognition, and AI healthcare tools. In March 2021, Hao published a piece that uncovered previously unknown information about how attempts to combat misinformation by different teams at Facebook using machine learning were impeded and constantly at odds with Facebook's drive to grow user engagement. Upon its release, leaders at Facebook including Mike Schroepfer and Yann LeCun immediately criticized the piece through Twitter responses. AI researchers and AI ethics experts Timnit Gebru and Margaret Mitchell responded in support of Hao's writing and advocated for more change and improvement for all. Hao also co-produced the podcast In Machines We Trust, which discusses the rise of AI with people developing, researching, and using AI technologies. The podcast won the 2020 Front Page Award in investigative reporting. Hao has occasionally created data visualizations that have been featured in her work at the MIT Technology Review and elsewhere. In 2018, her "What is AI?" flowchart visualization was exhibited as an installation at the Museum of Applied Arts in Vienna. She has been an invited speaker at TEDxGateway, the United Nations Foundation, EmTech, WNPR, and many other conferences and podcasts. Her TEDx talk discussed the importance of democratizing how AI is built. In March 2022, she was hired by The Wall Street Journal to cover China technology and society, while being based in Hong Kong. She left the WSJ in 2023. In May 2025, Hao released the book Empire of AI: Dreams and Nightmares in Sam Altman's OpenAI. The book became a New York Times Bestseller and was named a Book of the Year by the Financial Times. In December 2025, after criticism from readers, Hao issued a correction to her book where she had previously overestimated the water consumption of a data center in Chile compared to the community's water consumption by factor of 1,000, due to an error in a government document. In April 2026 the book won the New York Public Library's Helen Bernstein Book Award for Excellence in Journalism. === Selected awards and honors === 2019 Webby Award nominee for best newsletter, as a writer of The Algorithm 2021 Front Page Award in investigative reporting, as a co-producer for In Machines We Trust 2021 Ambies Award nominee for best knowledge and science podcast, as a co-producer for In Machines We Trust 2021 Webby Award nominee for best technology podcast, as a co-producer for In Machines We Trust 2024 American Humanist Media Award 2025 TIME100 AI, named by TIME magazine as one of the 100 most influential people in artificial intelligence 2026 New York Public Library's Helen Bernstein Book Award for Excellence in Journalism 2026 Whiting Award in Non-fiction
Defeasible logic
Defeasible logic is a non-monotonic logic proposed by Donald Nute to formalize defeasible reasoning. In defeasible logic, there are three different types of propositions: strict rules specify that a fact is always a consequence of another; defeasible rules specify that a fact is typically a consequence of another; undercutting defeaters specify exceptions to defeasible rules. A priority ordering over the defeasible rules and the defeaters can be given. During the process of deduction, the strict rules are always applied, while a defeasible rule can be applied only if no defeater of a higher priority specifies that it should not.
Daniel Wolfe
Daniel Wolfe (born 1960) is an American activist, advocate, and writer whose work advances health programs and policy that balance scientific research and community expertise. His career has focused on support for community health movements, particularly among groups often regarded as criminal or socially suspect, including gay men and people who use illicit drugs. == Early life == Wolfe was raised between Arizona—including time on Rancho Linda Vista, a commune outside of Tucson—and East Hampton, NY. He received his undergraduate degree in Near Eastern Studies from Princeton University, and following time studying Arabic in Egypt, worked as the junior ghostwriter on the autobiographies of First Lady of Egypt Jehan Sadat and Pakistani Prime Minister Benazir Bhutto. Upon return to New York, he was an assistant at the Council on Foreign Relations to Richard W. Murphy, former US Assistant Secretary of State for Near Eastern and South Asian Affairs. Disagreement with US killing of Iraqi civilians during the 1990 Gulf War—and the rising toll of HIV in NY—moved Wolfe to leave Middle East studies and work full-time on AIDS in 1990. == Education == Wolfe was Community Scholar at the Columbia University Mailman School of Public Healthwhere he received his Masters in Public Health in 2004. He holds a Masters of Philosophy (in history) from Columbia University, and a BA in Near Eastern Studies from Princeton University. He was the recipient of a Charles H. Revson Foundation fellowship for urban leaders who have made a substantial contribution to New York City, and a fellow at the Center for Arabic Studies Abroad in Cairo, Egypt. == AIDS and gay activism == Wolfe was part of the media committee for ACT UP’s 1998 action to seize control of the FDA, and helped organize ACT UP NY’s challenge to Governor Cuomo to do better on the AIDS response and other actions.Wolfe also joined ACT UP colleagues Gregg Bordowitz, David Barr, Richard Elovich, Jean Carlomusto and others to work at Gay Men’s Health Crisis (GMHC), the nation’s first AIDS organization, where he served as director of communications and spokesperson on issues including opposition to NY State cuts to the AIDS budget, the disclosure that Olympic Champion Greg Louganis had HIV, reports of the FBI spying on AIDS activists, and GMHC’s move to offer HIV testing and targeted support to those who were HIV-negative. Wolfe also continued cultural work, making art, performance and video as a member of the gay and lesbian collective GANG with artists and ACT UP members including Zoe Leonard, Suzanne Wright, Loring McAlpin, Wellington Love, Adam Rolston and others, and writing a biography of Lawrence of Arabia for a series for young adults on famous gay men and lesbians in history edited by Martin Duberman. Controversy followed, with North Carolina Senator Jesse Helms waving a GANG piece in an issue of the Movement Research Performance Journal on the floor of Congress to show the "rottenness" of publicly funded art, and a number of schools banning the biography series for young adults from their libraries. Wolfe and others challenged the move as continuing the longstanding and homophobic demand that notable gay men and lesbians stay silent about essential details of their private lives even while being celebrated for their professional achievements. == Gay health == The approval of antiretroviral therapy for HIV in 1996 opened up new space for discussions of gay health beyond HIV, and new directions for Wolfe. Working from hundreds of interviews, surveys, workshops, and with a team of writers, Wolfe was the author of Men Like Us, the Our Bodies, Ourselves-inspired GMHC Complete Guide to Gay Men’s Sexual, Physical, and Emotional Well-being, covering issues from spirituality to sexual health to aging. The move to frame gay health beyond condoms and pills—and to offer a guide to health that “did not need to be translated from the original heterosexual”—was part of a larger gay health movement encompassing wellness and pleasure, and focused less on health disparity than on individual and community resilience. Wolfe was a keynote speaker and workshop leader, along with Eric Rofes, Chris Bartlett, and other organizers, at the first National Gay Men’s Health Summit held in Boulder, Colorado in 2002. Awarded a Charles H. Revson Fellowship for urban leaders in the City of New York, Wolfe became a community scholar at Columbia University’s Center of History and Ethics of Public Health, where he received his MPH in 2003, and was a contributor to Searching Eyes: Privacy, the State, and Disease Surveillance in America. == International harm reduction == Wolfe was Director of International Harm Reduction Development at the Open Society Foundations (2005-2021) where he led grantmaking and advocacy to protect the health and rights of people who use drugs in Eastern Europe, Asia, Africa and the Americas. Wolfe challenged approaches that conditioned support on abstinence or that sought to treat people who use illegal drugs like drugs themselves, as something to be controlled or contained. As with the gay health movement, he advocated a focus on community resilience and strengths, and on supporting individuals and communities to negotiate the balance between risk and pleasure of activities integral to life. Noting what he called the “antisocial behavior of health systems,” Wolfe’s analysis elevated issues such as forced labor and harsh punishment delivered in the name of addiction treatment and rehabilitation, the role of criminalization, imprisonment and stigma in interrupting or impeding HIV treatment, and the bias toward coercive approaches in studying and delivering addiction treatments. He also pointed to defects in national and international drug control policies and human rights violations as a root cause of HIV, hepatitis, and other health challenges faced by people who used drugs. Concrete advocacy supported by Open Society’s International Harm Reduction Development program under his direction included rebuffing US government efforts to force the UN to remove all references to harm reduction in its materials, addition of the addiction treatment medicines methadone and buprenorphine to the World Health Organization’s essential medicines list, and WHO endorsement of lay distribution of the opioid overdose antidote naloxone. Wolfe and OSF colleagues also advocated for new approaches to intellectual property and data sharing in research and development of medicines and vaccines to lower price and improve access to medicines globally to those in need. == AI and patient rights == Reports of patients denied opioid prescriptions based on an algorithm purporting to calculate their risk of overdose led Wolfe to work on AI, first as a resident at the Rockefeller Foundation Bellagio Center, and then as Executive Director of a new UCSF UC Berkeley program pioneering efforts to join AI, clinical and public health practice, and equity. In keeping with his earlier (analog) work on HIV, Wolfe has highlighted concerns about health systems using algorithms to gauge the merit of treatments for those regarded as socially suspect, the importance of moving beyond proprietary, black box algorithms toward an architecture of health data as a public good, and the need to maximize benefit for patients and communities, as well health systems, in the use of large language models.
Machine translation software usability
The sections below give objective criteria for evaluating the usability of machine translation software output. == Stationarity or canonical form == Do repeated translations converge on a single expression in both languages? I.e. does the translation method show stationarity or produce a canonical form? Does the translation become stationary without losing the original meaning? This metric has been criticized as not being well correlated with BLEU (BiLingual Evaluation Understudy) scores. == Adaptive to colloquialism, argot or slang == Is the system adaptive to colloquialism, argot or slang? The French language has many rules for creating words in the speech and writing of popular culture. Two such rules are: (a) The reverse spelling of words such as femme to meuf. (This is called verlan.) (b) The attachment of the suffix -ard to a noun or verb to form a proper noun. For example, the noun faluche means "student hat". The word faluchard formed from faluche colloquially can mean, depending on context, "a group of students", "a gathering of students" and "behavior typical of a student". The Google translator as of 28 December 2006 doesn't derive the constructed words as for example from rule (b), as shown here: Il y a une chorale falucharde mercredi, venez nombreux, les faluchards chantent des paillardes! ==> There is a choral society falucharde Wednesday, come many, the faluchards sing loose-living women! French argot has three levels of usage: familier or friendly, acceptable among friends, family and peers but not at work grossier or swear words, acceptable among friends and peers but not at work or in family verlan or ghetto slang, acceptable among lower classes but not among middle or upper classes The United States National Institute of Standards and Technology conducts annual evaluations [1] Archived 2009-03-22 at the Wayback Machine of machine translation systems based on the BLEU-4 criterion [2]. A combined method called IQmt which incorporates BLEU and additional metrics NIST, GTM, ROUGE and METEOR has been implemented by Gimenez and Amigo [3]. == Well-formed output == Is the output grammatical or well-formed in the target language? Using an interlingua should be helpful in this regard, because with a fixed interlingua one should be able to write a grammatical mapping to the target language from the interlingua. Consider the following Arabic language input and English language translation result from the Google translator as of 27 December 2006 [4]. This Google translator output doesn't parse using a reasonable English grammar: وعن حوادث التدافع عند شعيرة رمي الجمرات -التي كثيرا ما يسقط فيها العديد من الضحايا- أشار الأمير نايف إلى إدخال "تحسينات كثيرة في جسر الجمرات ستمنع بإذن الله حدوث أي تزاحم". ==> And incidents at the push Carbuncles-throwing ritual, which often fall where many of the victims - Prince Nayef pointed to the introduction of "many improvements in bridge Carbuncles God would stop the occurrence of any competing." == Semantics preservation == Do repeated re-translations preserve the semantics of the original sentence? For example, consider the following English input passed multiple times into and out of French using the Google translator as of 27 December 2006: Better a day earlier than a day late. ==> Améliorer un jour plus tôt qu'un jour tard. ==> To improve one day earlier than a day late. ==> Pour améliorer un jour plus tôt qu'un jour tard. ==> To improve one day earlier than a day late. As noted above and in, this kind of round-trip translation is a very unreliable method of evaluation. == Trustworthiness and security == An interesting peculiarity of Google Translate as of 24 January 2008 (corrected as of 25 January 2008) is the following result when translating from English to Spanish, which shows an embedded joke in the English-Spanish dictionary which has some added poignancy given recent events: Heath Ledger is dead ==> Tom Cruise está muerto This raises the issue of trustworthiness when relying on a machine translation system embedded in a Life-critical system in which the translation system has input to a Safety Critical Decision Making process. Conjointly it raises the issue of whether in a given use the software of the machine translation system is safe from hackers. It is not known whether this feature of Google Translate was the result of a joke/hack or perhaps an unintended consequence of the use of a method such as statistical machine translation. Reporters from CNET Networks asked Google for an explanation on January 24, 2008; Google said only that it was an "internal issue with Google Translate". The mistranslation was the subject of much hilarity and speculation on the Internet. If it is an unintended consequence of the use of a method such as statistical machine translation, and not a joke/hack, then this event is a demonstration of a potential source of critical unreliability in the statistical machine translation method. In human translations, in particular on the part of interpreters, selectivity on the part of the translator in performing a translation is often commented on when one of the two parties being served by the interpreter knows both languages. This leads to the issue of whether a particular translation could be considered verifiable. In this case, a converging round-trip translation would be a kind of verification.
Ontology components
Contemporary ontologies share many structural similarities, regardless of the ontology language in which they are expressed. Most ontologies describe individuals (instances), classes (concepts), attributes, and relations. == List == Common components of ontologies include: Individuals instances or objects (the basic or "ground level" objects; the tokens). Classes sets, collections, concepts, types of objects, or kinds of things. Attributes aspects, properties, features, characteristics, or parameters that individuals (and classes and relations) can have. Relations ways in which classes and individuals can be related to one another. Relations can carry attributes that specify the relation further. Function terms complex structures formed from certain relations that can be used in place of an individual term in a statement. Restrictions formally stated descriptions of what must be true in order for some assertion to be accepted as input. Rules statements in the form of an if-then (antecedent-consequent) sentence that describe the logical inferences that can be drawn from an assertion in a particular form. Axioms assertions (including rules) in a logical form that together comprise the overall theory that the ontology describes in its domain of application. This definition differs from that of "axioms" in generative grammar and formal logic. In these disciplines, axioms include only statements asserted as a priori knowledge. As used here, "axioms" also include the theory derived from axiomatic statements. Events the changing of attributes or relations. Actions types of events. Ontologies are commonly encoded using ontology languages. == Individuals == Individuals (instances) are the basic, "ground level" components of an ontology. The individuals in an ontology may include concrete objects such as people, animals, tables, automobiles, molecules, and planets, as well as abstract individuals such as numbers and words (although there are differences of opinion as to whether numbers and words are classes or individuals). Strictly speaking, an ontology need not include any individuals, but one of the general purposes of an ontology is to provide a means of classifying individuals, even if those individuals are not explicitly part of the ontology. In formal extensional ontologies, only the utterances of words and numbers are considered individuals – the numbers and names themselves are classes. In a 4D ontology, an individual is identified by its spatio-temporal extent. Examples of formal extensional ontologies are BORO, ISO 15926 and the model in development by the IDEAS Group. == Classes == == Attributes == Objects in an ontology can be described by relating them to other things, typically aspects or parts. These related things are often called attributes, although they may be independent things. Each attribute can be a class or an individual. The kind of object and the kind of attribute determine the kind of relation between them. A relation between an object and an attribute express a fact that is specific to the object to which it is related. For example, the Ford Explorer object has attributes such as: ⟨has as name⟩ Ford Explorer ⟨as by definition as part⟩ 6-speed transmission ⟨as by definition as part⟩ door (with as minimum and maximum cardinality: 4) ⟨as by definition as part one of⟩ {4.0L engine, 4.6L engine} The value of an attribute can be a complex data type; in this example, the related engine can only be one of a list of subtypes of engines, not just a single thing. Ontologies are only true ontologies if concepts are related to other concepts (the concepts do have attributes). If that is not the case, then you would have either a taxonomy (if hyponym relationships exist between concepts) or a controlled vocabulary. These are useful, but are not considered true ontologies. == Relations == Relations (also known as relationships) between objects in an ontology specify how objects are related to other objects. Typically a relation is of a particular type (or class) that specifies in what sense the object is related to the other object in the ontology. For example, in the ontology that contains the concept Ford Explorer and the concept Ford Bronco might be related by a relation of type ⟨is defined as a successor of⟩. The full expression of that fact then becomes: Ford Explorer is defined as a successor of : Ford Bronco This tells us that the Explorer is the model that replaced the Bronco. This example also illustrates that the relation has a direction of expression. The inverse expression expresses the same fact, but with a reverse phrase in natural language. Much of the power of ontologies comes from the ability to describe relations. Together, the set of relations describes the semantics of the domain: that is, its various semantic relations, such as synonymy, hyponymy and hypernymy, coordinate relation, and others. The set of used relation types (classes of relations) and their subsumption hierarchy describe the expression power of the language in which the ontology is expressed. An important type of relation is the subsumption relation (is-a-superclass-of, the converse of is-a, is-a-subtype-of or is-a-subclass-of). This defines which objects are classified by which class. For example, we have already seen that the class Ford Explorer is-a-subclass-of 4-Wheel Drive Car, which in turn is-a-subclass-of Car. The addition of the is-a-subclass-of relationships creates a taxonomy; a tree-like structure (or, more generally, a partially ordered set) that clearly depicts how objects relate to one another. In such a structure, each object is the 'child' of a 'parent class' (Some languages restrict the is-a-subclass-of relationship to one parent for all nodes, but many do not). Another common type of relations is the mereology relation, written as part-of, that represents how objects combine to form composite objects. For example, if we extended our example ontology to include concepts like Steering Wheel, we would say that a "Steering Wheel is-by-definition-a-part-of-a Ford Explorer" since a steering wheel is always one of the components of a Ford Explorer. If we introduce meronymy relationships to our ontology, the hierarchy that emerges is no longer able to be held in a simple tree-like structure since now members can appear under more than one parent or branch. Instead this new structure that emerges is known as a directed acyclic graph. As well as the standard is-a-subclass-of and is-by-definition-a-part-of-a relations, ontologies often include additional types of relations that further refine the semantics they model. Ontologies might distinguish between different categories of relation types. For example: relation types for relations between classes relation types for relations between individuals relation types for relations between an individual and a class relation types for relations between a single object and a collection relation types for relations between collections Relation types are sometimes domain-specific and are then used to store specific kinds of facts or to answer particular types of questions. If the definitions of the relation types are included in an ontology, then the ontology defines its own ontology definition language. An example of an ontology that defines its own relation types and distinguishes between various categories of relation types is the Gellish ontology. For example, in the domain of automobiles, we might need a made-in type relationship which tells us where each car is built. So the Ford Explorer is made-in Louisville. The ontology may also know that Louisville is-located-in Kentucky and Kentucky is-classified-as-a state and is-a-part-of the U.S. Software using this ontology could now answer a question like "which cars are made in the U.S.?"