Topic

# Computational logic

About: Computational logic is a(n) research topic. Over the lifetime, 4185 publication(s) have been published within this topic receiving 135716 citation(s).

##### Papers

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01 Jan 1984-

TL;DR: This is the second edition of an account of the mathematical foundations of logic programming, which collects, in a unified and comprehensive manner, the basic theoretical results of the field, which have previously only been available in widely scattered research papers.

Abstract: This is the second edition of an account of the mathematical foundations of logic programming. Its purpose is to collect, in a unified and comprehensive manner, the basic theoretical results of the field, which have previously only been available in widely scattered research papers. In addition to presenting the technical results, the book also contains many illustrative examples and problems. The text is intended to be self-contained, the only prerequisites being some familiarity with PROLOG and knowledge of some basic undergraduate mathematics. The material is suitable either as a reference book for researchers or as a textbook for a graduate course on the theoretical aspects of logic programming and deductive database systems.

4,496 citations

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01 Jan 1972-

TL;DR: A comparison of first- and second-order logic in the case of SETs shows that the former is more likely to be correct and the latter is less likely.

Abstract: USEFUL FACTS ABOUT SETS. SENTENTIAL LOGIC. FIRST-ORDER LOGIC. UNDECIDABILITY. SECOND-ORDER LOGIC.

2,134 citations

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TL;DR: This paper is primarily concerned with a special case of one of the leading problems of mathematical logic, the problem of finding a regular procedure to determine the truth or falsity of any given logical formula.

Abstract: This paper is primarily concerned with a special case of one of the leading problems of mathematical logic, the problem of finding a regular procedure to determine the truth or falsity of any given logical formula*. But in the course of this investigation it is necessary to use certain theorems on combinations which have an independent interest and are most conveniently set out by themselves beforehand.

2,030 citations

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01 Jan 1964-

TL;DR: This long-established text continues to expose students to natural proofs and set-theoretic methods and offers enough material for either a one- or two-semester course on mathematical logic.

Abstract: Retaining all the key features of the previous editions, Introduction to Mathematical Logic, Fifth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gdel, Church, Kleene, Rosser, and Turing.New to the Fifth Edition A new section covering basic ideas and results about nonstandard models of number theoryA second appendix that introduces modal propositional logicAn expanded bibliography Additional exercises and selected answers This long-established text continues to expose students to natural proofs and set-theoretic methods. Only requiring some experience in abstract mathematical thinking, it offers enough material for either a one- or two-semester course on mathematical logic.

1,973 citations