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Critical Pair (logic)
A critical pair arises in a term rewriting system when two rewrite rules overlap to yield two different terms. In more detail, (''t''1, ''t''2) is a critical pair if there is a term ''t'' for which two different applications of a rewrite rule (either the same rule applied differently, or two different rules) yield the terms ''t''1 and ''t''2. Definitions The actual definition of a critical pair is slightly more involved as it excludes pairs that can be obtained from critical pairs by substitution and orients the pair based on the overlap. Specifically, for a pair of overlapping rules \rho_0 : l_0 \to r_0 and \rho_1 : l_1 \to r_1, with the overlap being that l_0 = D /math> for some non-empty context D ;/math>, and the term s (that is not a variable) matches l_1 under some substitutions s \sigma = l_1 \tau that are most general, the critical pair is (D \sigma _1 \tau r_0 \sigma). When both sides of the critical pair can reduce to the same term, the critical pair is called ''con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Term Rewriting System
In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems (also known as rewrite systems, rewrite engines, or reduction systems). In their most basic form, they consist of a set of objects, plus relations on how to transform those objects. Rewriting can be non-deterministic. One rule to rewrite a term could be applied in many different ways to that term, or more than one rule could be applicable. Rewriting systems then do not provide an algorithm for changing one term to another, but a set of possible rule applications. When combined with an appropriate algorithm, however, rewrite systems can be viewed as computer programs, and several theorem provers and declarative programming languages are based on term rewriting. Example cases Logic In logic, the procedure for obtaining the conjunctive normal form (CNF) of a formula can be implemented as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Context (term Rewriting)
In mathematical logic, a term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of a formula. This is analogous to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact. A first-order term is recursively constructed from constant symbols, variables and function symbols. An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation. For example, is a term built from the constant 1, the variable , and the binary function symbols and ; it is part of the atomic formula which evaluates to true for each real-numbered value of . Besides in logic, terms play important roles in universal algebra, and rewriting systems. Formal definition Given a set ''V'' of variable symbols, a set ''C'' of constant symbols and sets ''F''''n'' of ''n''-ary fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Confluence (term Rewriting)
In computer science, confluence is a property of rewriting systems, describing which terms in such a system can be rewritten in more than one way, to yield the same result. This article describes the properties in the most abstract setting of an abstract rewriting system. Motivating examples The usual rules of elementary arithmetic form an abstract rewriting system. For example, the expression (11 + 9) × (2 + 4) can be evaluated starting either at the left or at the right parentheses; however, in both cases the same result is eventually obtained. If every arithmetic expression evaluates to the same result regardless of reduction strategy, the arithmetic rewriting system is said to be ground-confluent. Arithmetic rewriting systems may be confluent or only ground-confluent depending on details of the rewriting system. A second, more abstract example is obtained from the following proof of each group element equalling the inverse of its inverse: This proof starts fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Confluence (term Rewriting)
In computer science, confluence is a property of rewriting systems, describing which terms in such a system can be rewritten in more than one way, to yield the same result. This article describes the properties in the most abstract setting of an abstract rewriting system. Motivating examples The usual rules of elementary arithmetic form an abstract rewriting system. For example, the expression (11 + 9) × (2 + 4) can be evaluated starting either at the left or at the right parentheses; however, in both cases the same result is eventually obtained. If every arithmetic expression evaluates to the same result regardless of reduction strategy, the arithmetic rewriting system is said to be ground-confluent. Arithmetic rewriting systems may be confluent or only ground-confluent depending on details of the rewriting system. A second, more abstract example is obtained from the following proof of each group element equalling the inverse of its inverse: This proof starts fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rewriting
In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a well-formed formula, formula with other terms. Such methods may be achieved by rewriting systems (also known as rewrite systems, rewrite engines, or reduction systems). In their most basic form, they consist of a set of objects, plus relations on how to transform those objects. Rewriting can be non-deterministic algorithm, non-deterministic. One rule to rewrite a term could be applied in many different ways to that term, or more than one rule could be applicable. Rewriting systems then do not provide an algorithm for changing one term to another, but a set of possible rule applications. When combined with an appropriate algorithm, however, rewrite systems can be viewed as computer programs, and several automated theorem proving, theorem provers and declarative programming languages are based on term rewriting. Example cases Logic In logic, the procedure for obtaini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Franz Baader
Franz Baader (15 June 1959, Spalt) is a German computer scientist at Dresden University of Technology. He received his PhD in Computer Science in 1989 from the University of Erlangen-Nuremberg, Germany, where he was a teaching and research assistant for 4 years. In 1989, he went to the German Research Centre for Artificial Intelligence (DFKI) as a senior researcher and project leader. In 1993 he became associate professor for computer science at RWTH Aachen, and in 2002 full professor for computer science at TU Dresden. He received the Herbrand Award The Herbrand Award for Distinguished Contributions to Automated Reasoning is an award given by the Conference on Automated Deduction (CADE), Inc., (although it predates the formal incorporation of CADE) to honour persons or groups for important cont ... for the year 2020 "in recognition of his significant contributions to unification theory, combinations of theories and reasoning in description logics". Works * * * * References ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tobias Nipkow
Tobias Nipkow (born 1958) is a German computer scientist. Career Nipkow received his Diplom (MSc) in computer science from the Department of Computer Science of the Technische Hochschule Darmstadt in 1982, and his Ph.D. from the University of Manchester in 1987. He worked at MIT from 1987, changed to Cambridge University in 1989, and to Technical University Munich in 1992, where he was appointed professor for programming theory. He is chair of the Logic and Verification group since 2011. He is known for his work in interactive and automatic theorem proving, in particular for the Isabelle proof assistant; he was the editor of the '' Journal of Automated Reasoning'' up to January 1, 2021. Moreover, he focuses on programming language semantics, type systems and functional programming In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
