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Anti-unification
Anti-unification is the process of constructing a generalization common to two given symbolic expressions. As in unification, several frameworks are distinguished depending on which expressions (also called terms) are allowed, and which expressions are considered equal. If variables representing functions are allowed in an expression, the process is called "higher-order anti-unification", otherwise "first-order anti-unification". If the generalization is required to have an instance literally equal to each input expression, the process is called "syntactical anti-unification", otherwise "E-anti-unification", or "anti-unification modulo theory". An anti-unification algorithm should compute for given expressions a complete and minimal generalization set, that is, a set covering all generalizations and containing no redundant members, respectively. Depending on the framework, a complete and minimal generalization set may have one, finitely many, or possibly infinitely many members, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unification (computer Science)
In logic and computer science, specifically automated reasoning, unification is an algorithmic process of solving equations between symbolic expression (mathematics), expressions, each of the form ''Left-hand side = Right-hand side''. For example, using ''x'',''y'',''z'' as variables, and taking ''f'' to be an uninterpreted function, the Singleton (mathematics), singleton equation set is a syntactic first-order unification problem that has the substitution as its only solution. Conventions differ on what values variables may assume and which expressions are considered equivalent. In first-order syntactic unification, variables range over first-order terms and equivalence is syntactic. This version of unification has a unique "best" answer and is used in logic programming and programming language type system implementation, especially in Hindley–Milner based type inference algorithms. In higher-order unification, possibly restricted to higher-order pattern unification, terms may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dis-unification (computer Science)
Dis-unification, in computer science and logic, is an algorithmic process of solving inequations between symbolic expression (mathematics), expressions. Publications on dis-unification * * "Anti-Unification" here refers to inequation-solving, a naming which nowadays has become quite unusual, cf. Anti-unification (computer science). * * * * * Comon shows that the first-order logic theory of equality and sort membership is decidable, that is, each first-order logic formula built from arbitrary function symbols, "=" and "∈", but no other predicates, can effectively be proven or disproven. Using the logical negation (¬), non-equality (≠) can be expressed in formulas, but order relations (<) cannot. As an application, he proves sufficient completeness of Term_rewriting#Term_rewriting_systems, term rewriting systems. * * See also * Unification (computer science): solving equations between symbolic expressions * Constraint logic programming: incorporating ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inductive Logic Programming
Inductive logic programming (ILP) is a subfield of symbolic artificial intelligence which uses logic programming as a uniform representation for examples, background knowledge and hypotheses. The term "''inductive''" here refers to philosophical (i.e. suggesting a theory to explain observed facts) rather than mathematical (i.e. proving a property for all members of a well-ordered set) induction. Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesised logic program which entails all the positive and none of the negative examples. * Schema: ''positive examples'' + ''negative examples'' + ''background knowledge'' ⇒ ''hypothesis''. Inductive logic programming is particularly useful in bioinformatics and natural language processing. History Building on earlier work on Inductive inference, Gordon Plotkin was the first to formalise induction in a clausal setting around 1970, ad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Injective Mapping
In mathematics, an injective function (also known as injection, or one-to-one function ) is a function that maps distinct elements of its domain to distinct elements of its codomain; that is, implies (equivalently by contraposition, implies ). In other words, every element of the function's codomain is the image of one element of its domain. The term must not be confused with that refers to bijective functions, which are functions such that each element in the codomain is an image of exactly one element in the domain. A homomorphism between algebraic structures is a function that is compatible with the operations of the structures. For all common algebraic structures, and, in particular for vector spaces, an is also called a . However, in the more general context of category theory, the definition of a monomorphism differs from that of an injective homomorphism. This is thus a theorem that they are equivalent for algebraic structures; see for more details. A functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automated Theorem Proving
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major motivating factor for the development of computer science. Logical foundations While the roots of formalized Logicism, logic go back to Aristotelian logic, Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalized mathematics. Gottlob Frege, Frege's ''Begriffsschrift'' (1879) introduced both a complete propositional logic, propositional calculus and what is essentially modern predicate logic. His ''The Foundations of Arithmetic, Foundations of Arithmetic'', published in 1884, expressed (parts of) mathematics in formal logic. This approach was continued by Bertrand Russell, Russell and Alfred North Whitehead, Whitehead in their influential ''Principia Mathematica'', first published 1910� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ACM Transactions On Programming Languages And Systems
The ''ACM Transactions on Programming Languages and Systems'' (''TOPLAS'') is a bimonthly, open access, peer-reviewed scientific journal on the topic of programming languages published by the Association for Computing Machinery. Background Published since 1979, the journal's scope includes programming language design, implementation, and semantics of programming languages, compilers and interpreters, run-time systems, storage allocation and garbage collection, and formal specification, testing, and verification of software. It is indexed in Scopus and SCImago. The editor-in-chief is Andrew Myers (Cornell University). According to the ''Journal Citation Reports'', the journal had a 2020 impact factor of 0.410. References External links * TOPLASat ACM Digital Library TOPLASat DBLP DBLP is a computer science bibliography website. Starting in 1993 at Universität Trier in Germany, it grew from a small collection of HTML files and became an organization hosting a datab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SRI International
SRI International (SRI) is a nonprofit organization, nonprofit scientific research, scientific research institute and organization headquartered in Menlo Park, California, United States. It was established in 1946 by trustees of Stanford University to serve as a center of innovation to support economic development in the region. The organization was founded as the Stanford Research Institute. SRI formally separated from Stanford University in 1970 and became known as SRI International in 1977. SRI performs client-sponsored research and development for government agencies, commercial businesses, and private foundations. It also licenses its technologies, forms strategic partnerships, sells products, and creates Research spin-off, spin-off companies. SRI's headquarters are located near the Stanford University campus. SRI's annual revenue in 2014 was approximately $540 million, which tripled from 1998 under the leadership of Curtis Carlson. In 1998, the organization was on the ver ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equational Theories
Equational may refer to: * Equative (other), a construction in linguistics * something pertaining to equations, in mathematics * something pertaining to equality Equality generally refers to the fact of being equal, of having the same value. In specific contexts, equality may refer to: Society * Egalitarianism, a trend of thought that favors equality for all people ** Political egalitarianism, in which ..., in logic See also * * Equation (other) * Equality (other) {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Golem (ILP)
Golem is an inductive logic programming algorithm developed by Stephen Muggleton and Cao Feng in 1990. It uses the technique of Inductive logic programming#Least general generalisation, relative least general generalisation proposed by Gordon Plotkin, leading to a bottom-up search through the theta-subsumption, subsumption lattice. In 1992, shortly after its introduction, Golem was considered the only inductive logic programming system capable of scaling to tens of thousands of examples. Description Golem takes as input a Definite clause, definite program as background knowledge together with sets of positive and negative examples, denoted E^ and E^ respectively. The overall idea is to construct the least general generalisation of E^ with respect to the background knowledge. However, if is not merely a finite set of Ground expression, ground Atomic formula, atoms, then this relative least general generalisation may not exist. Therefore, rather than using directly, Golem uses t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
