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A theorem-proving language for experimentation
Communications of the ACM, 1974Because of the large number of strategies and inference rules presently under consideration in automated theorem proving, there is a need for developing a language especially oriented toward automated theorem proving. This paper discusses some of the features and instructions of this language.
L Henschen, L Wöß
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Journal of Automated Reasoning, 2003
The authors argue that theorem proving can be divided into a computation part and a deduction part. Deduction modulo is a method to remove the computational arguments from proofs. A proof search method is presented based on extended narrowing and resolution which is sound and complete with respect to the sequent calculus modulo, for a large class of ...
Dowek, Gilles +2 more
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The authors argue that theorem proving can be divided into a computation part and a deduction part. Deduction modulo is a method to remove the computational arguments from proofs. A proof search method is presented based on extended narrowing and resolution which is sound and complete with respect to the sequent calculus modulo, for a large class of ...
Dowek, Gilles +2 more
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Proving Theorems by Program Transformation [PDF]
Fundamenta Informaticae, 2013 In this paper we present an overview of the unfold/fold proof method, a method for proving theorems about programs, based on program transformation. As a metalanguage for specifying programs and program properties we adopt constraint logic programming (CLP), and we present a set of transformation rules (including the familiar unfolding and folding ...
Fabio Fioravanti +3 more
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Journal of the ACM, 1976
The concern here is with proof procedures which are generalizations of input or unit deduction. The author's generalizations of input deduction involve lemmas, whereas those of unit deduction involve longer clauses and are akin to Robinson's P1 deduction.
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The concern here is with proof procedures which are generalizations of input or unit deduction. The author's generalizations of input deduction involve lemmas, whereas those of unit deduction involve longer clauses and are akin to Robinson's P1 deduction.
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1986
We describe resolution proof systems for several modal logics. First we present the propositional versions of the systems and prove their completeness. The first-order resolution rule for classical logic is then modified to handle quantifiers directly.
Martín Abadi, Zohar Manna
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We describe resolution proof systems for several modal logics. First we present the propositional versions of the systems and prove their completeness. The first-order resolution rule for classical logic is then modified to handle quantifiers directly.
Martín Abadi, Zohar Manna
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The Specialization of Programs by Theorem Proving
SIAM Journal on Computing, 1973Suppose a program P is written to accept a set of inputs I. If we are only interested in a nonempty subset $I^ * $ of I, we usually can simplify P to another program $P^ * $ such that $P^ * $ runs faster on $I^ * $ than P does. The problem of specialization is to find such $P^ * $. In this paper, the program P and the input $I^ * $ will be specified by
Chin-Liang Chang +2 more
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1998
In this section, we give an outline of the proof of the PCP-Theorem, which states that NP=PCP(logn,1). The key idea for reducing the number of random bits, which also implies a reduction of the length of the proof, is a more concise encoding of an assignment. Instead of linear functions we use multivariate polynomials of low degree as an encoding.
Volker Heun +2 more
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In this section, we give an outline of the proof of the PCP-Theorem, which states that NP=PCP(logn,1). The key idea for reducing the number of random bits, which also implies a reduction of the length of the proof, is a more concise encoding of an assignment. Instead of linear functions we use multivariate polynomials of low degree as an encoding.
Volker Heun +2 more
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WIREs Cognitive Science, 2014
Automated theorem proving is the use of computers to prove or disprove mathematical or logical statements. Such statements can express properties of hardware or software systems, or facts about the world that are relevant for applications such as natural language processing and planning.
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Automated theorem proving is the use of computers to prove or disprove mathematical or logical statements. Such statements can express properties of hardware or software systems, or facts about the world that are relevant for applications such as natural language processing and planning.
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Analogy in Inductive Theorem Proving
Journal of Automated Reasoning, 1999In this paper the authors describe analogy-driven proof plan construction in inductive theorem proving. The analogies investigated are external analogies. An analogy procedure is obtained that is incorporated into the generic proof planner CLAM. Several examples to illustrate this procedure are presented.
Erica Melis, Jon Whittle 0001
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Proceedings of the annual conference on - ACM'73, 1973
The results of Notice 72-H2 of the NAMS of June 1972, issue 138, were proven using the Theorem Proving Program of Allen & Luckham1. Proofs of the results stated by Cowen, Frisz & Grenadir in their notice Some New Axiomatizations in Group Theory, a Preliminary Report and an extension of their results, namely, a new single axiom characterizing abelian ...
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The results of Notice 72-H2 of the NAMS of June 1972, issue 138, were proven using the Theorem Proving Program of Allen & Luckham1. Proofs of the results stated by Cowen, Frisz & Grenadir in their notice Some New Axiomatizations in Group Theory, a Preliminary Report and an extension of their results, namely, a new single axiom characterizing abelian ...
openaire +1 more source