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Circumscription (logic)
Circumscription is a non-monotonic logic created by John McCarthy to formalize the common sense assumption that things are as expected unless otherwise specified. Circumscription was later used by McCarthy in an attempt to solve the frame problem. To implement circumscription in its initial formulation, McCarthy augmented first-order logic to allow the minimization of the extension of some predicates, where the extension of a predicate is the set of tuples of values the predicate is true on. This minimization is similar to the closed-world assumption that what is not known to be true is false. The original problem considered by McCarthy was that of missionaries and cannibals: there are three missionaries and three cannibals on one bank of a river; they have to cross the river using a boat that can only take two, with the additional constraint that cannibals must never outnumber the missionaries on either bank (as otherwise the missionaries would be killed and, presumably, eaten) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-monotonic Logic
A non-monotonic logic is a formal logic whose conclusion relation is not monotonic. In other words, non-monotonic logics are devised to capture and represent defeasible inferences (cf. defeasible reasoning), i.e., a kind of inference in which reasoners draw tentative conclusions, enabling reasoners to retract their conclusion(s) based on further evidence. Most studied formal logics have a monotonic entailment relation, meaning that adding a formula to a theory never produces a pruning of its set of conclusions. Intuitively, monotonicity indicates that learning a new piece of knowledge cannot reduce the set of what is known. A monotonic logic cannot handle various reasoning tasks such as reasoning by default (conclusions may be derived only because of lack of evidence of the contrary), abductive reasoning (conclusions are only deduced as most likely explanations), some important approaches to reasoning about knowledge (the ignorance of a conclusion must be retracted when the concl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propositional Variable
In mathematical logic, a propositional variable (also called a sentential variable or sentential letter) is an input variable (that can either be true or false) of a truth function. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher-order logics. Uses Formulas in logic are typically built up recursively from some propositional variables, some number of logical connectives, and some logical quantifiers. Propositional variables are the atomic formulas of propositional logic, and are often denoted using capital roman letters such as P, Q and R. ;Example In a given propositional logic, a formula can be defined as follows: * Every propositional variable is a formula. * Given a formula ''X'', the negation ''¬X'' is a formula. * Given two formulas ''X'' and ''Y'', and a binary connective ''b'' (such as the logical conjunction ∧),the expression ''(X b Y)'' is a formula. (Note the parentheses.) Through this const ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yuri Gurevich
Yuri Gurevich, Professor Emeritus at the University of Michigan, is an American computer scientist and mathematician and the inventor of abstract state machines. Gurevich was born and educated in the Soviet Union. He taught mathematics there and then in Israel before moving to the United States in 1982. The best-known work of his Soviet period is on the ''classical decision problem''. In Israel, Gurevich worked with Saharon Shelah on monadic second-order theories. The ''Forgetful Determinacy Theorem'' of Gurevich– Harrington is of that period as well. From 1982 to 1998, Gurevich taught computer science at the University of Michigan, where he started to work on various aspects of computational complexity theory including average case complexity. He became one of the founders of the emerging field of finite model theory. Most importantly, he became interested in the problem of what an algorithm is. This led him to the theory of abstract state machines (ASMs). The ASM Thesis s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Georg Gottlob
Georg Gottlob FRS is an Austrian computer scientist who works in the areas of database theory, logic, and artificial intelligence and is Professor of Informatics at the University of Oxford. Education Gottlob obtained his undergraduate and PhD degrees in computer science at Vienna University of Technology in 1981. Career and research Gottlob is currently a chaired professor of computing science at the Oxford University Department of Computer Science, where he helped establish the information systems research group. He is also a Fellow of St John's College, Oxford. Previously, he was a professor of computer science at Vienna University of Technology, where he still maintains an adjunct position. He was elected a member of the Royal Society in May 2010. He is a founding member of the Oxford-Man Institute. He has published more than 250 scientific articles in the areas of computational logic, database theory, and artificial intelligence, and one textbook on logic programming and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Eiter
Thomas may refer to: People * List of people with given name Thomas * Thomas (name) * Thomas (surname) * Saint Thomas (other) * Thomas Aquinas (1225–1274) Italian Dominican friar, philosopher, and Doctor of the Church * Thomas the Apostle * Thomas (bishop of the East Angles) (fl. 640s–650s), medieval Bishop of the East Angles * Thomas (Archdeacon of Barnstaple) (fl. 1203), Archdeacon of Barnstaple * Thomas, Count of Perche (1195–1217), Count of Perche * Thomas (bishop of Finland) (1248), first known Bishop of Finland * Thomas, Earl of Mar (1330–1377), 14th-century Earl, Aberdeen, Scotland Geography Places in the United States * Thomas, Illinois * Thomas, Indiana * Thomas, Oklahoma * Thomas, Oregon * Thomas, South Dakota * Thomas, Virginia * Thomas, Washington * Thomas, West Virginia * Thomas County (other) * Thomas Township (other) Elsewhere * Thomas Glacier (Greenland) Arts, entertainment, and media * ''Thomas'' (Burton novel) 1969 novel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raymond Reiter
Raymond Reiter (; June 12, 1939 – September 16, 2002) was a Canadian computer scientist and logician. He was one of the founders of the field of non-monotonic reasoning with his work on default logic, model-based diagnosis, closed world reasoning, and truth maintenance systems. He also contributed to the situation calculus. Awards and honors He was a Fellow of the Association for Computing Machinery (ACM), an AAAI Fellow, and a Fellow of the Royal Society of Canada. He won the IJCAI Award for Research Excellence in 1993. Publications * R. Reiter (1978). On closed world data bases. In H. Gallaire and J. Minker, editors, ''Logic and Data Bases'', pages 119–140. Plenum., New York. * R. Reiter (1980). A logic for default reasoning. ''Artificial Intelligence'', 13:81-132. * R. Reiter (1987). A theory of diagnosis from first principles. ''Artificial Intelligence'', 32:57-95. * R. Reiter (1991). The frame problem in the situation calculus: a simple solution (sometimes) and a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Domain Of Discourse
In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range. Overview The domain of discourse is usually identified in the preliminaries, so that there is no need in the further treatment to specify each time the range of the relevant variables. Many logicians distinguish, sometimes only tacitly, between the ''domain of a science'' and the ''universe of discourse of a formalization of the science''.José Miguel Sagüillo, Domains of sciences, universe of discourse, and omega arguments, History and philosophy of logic, vol. 20 (1999), pp. 267–280. Examples For example, in an interpretation of first-order logic, the domain of discourse is the set of individuals over which the quantifiers range. A proposition such as is ambiguous, if no domain of discourse has been identified. In one interpretation, the domain of di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predicate (logic)
In logic, a predicate is a symbol which represents a property or a relation. For instance, in the first order formula P(a), the symbol P is a predicate which applies to the individual constant a. Similarly, in the formula R(a,b), R is a predicate which applies to the individual constants a and b. In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the formula R(a,b) would be true on an interpretation if the entities denoted by a and b stand in the relation denoted by R. Since predicates are non-logical symbols, they can denote different relations depending on the interpretation used to interpret them. While first-order logic only includes predicates which apply to individual constants, other logics may allow predicates which apply to other predicates. Predicates in different systems * In propositional logic, atomic formulas are sometimes regarded as zero-place predicates In a sense, these are nullar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Lifschitz
Vladimir Lifschitz (born 30 May 1947) is the Gottesman Family Centennial Professor in Computer Sciences at the University of Texas at Austin. He received a degree in mathematics from the Steklov Institute of Mathematics in Russia in 1971 and emigrated to the United States in 1976. Lifschitz's research interests are in the areas of computational logic and knowledge representation. He is a Fellow of the Association for the Advancement of Artificial Intelligence, the Editor-in-Chief of the ACM Transactions on Computational Logic, and an Editorial Advisor of the journal ''Theory and Practice of Logic Programming''. He, together with Michael Gelfond, defined stable model semantics for logic programs, which later became the theoretical foundation for Answer Set Programming,Victor Marek and Miroslaw Truszczynski. Stable models and an alternative logic programming paradigm. In The Logic Programming Paradigm: a 25-Year Perspective, pages 375-398. Springer Verlag, 1999 a new declarative pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory (logic)
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios, a deductive system is first understood from context, after which an element \phi\in T of a deductively closed theory T is then called a theorem of the theory. In many deductive systems there is usually a subset \Sigma \subseteq T that is called "the set of axioms" of the theory T, in which case the deductive system is also called an "axiomatic system". By definition, every axiom is automatically a theorem. A first-order theory is a set of first-order sentences (theorems) recursively obtained by the inference rules of the system applied to the set of axioms. General theories (as expressed in formal language) When defining theories for foundational purposes, additional care must be taken, as normal set-theoretic language may not be appropriate. The construction of a theory begins by specifying a definite non-empty ''conceptual class'' \mathcal, the element ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structure (mathematical Logic)
In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it. Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used for structures with no relation symbols. Model theory has a different scope that encompasses more arbitrary theories, including foundational structures such as models of set theory. From the model-theoretic point of view, structures are the objects used to define the semantics of first-order logic. For a given theory in model theory, a structure is called a model if it satisfies the defining axioms of that theory, although it is sometimes disambiguated as a ''semantic model'' when one discusses the notion in the more general setting of mathematical models. Logicians sometimes refer to structures as " interpretations", whereas the term "interpretation" generally has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John McCarthy (computer Scientist)
John McCarthy (September 4, 1927 – October 24, 2011) was an American computer scientist and cognitive scientist. He was one of the founders of the discipline of artificial intelligence. He co-authored the document that coined the term "artificial intelligence" (AI), developed the programming language family Lisp, significantly influenced the design of the language ALGOL, popularized time-sharing, and invented garbage collection. McCarthy spent most of his career at Stanford University. He received many accolades and honors, such as the 1971 Turing Award for his contributions to the topic of AI, the United States National Medal of Science, and the Kyoto Prize. Early life and education John McCarthy was born in Boston, Massachusetts, on September 4, 1927, to an Irish immigrant father and a Lithuanian Jewish immigrant mother, John Patrick and Ida (Glatt) McCarthy. The family was obliged to relocate frequently during the Great Depression, until McCarthy's father found work as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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