Normal Form for Deductions in Predicate Calculus with Equality and Functional Symbols

Lifshits, V. A.

doi:10.1007/978-1-4684-8968-2_5

Cited by 8 publications

(21 citation statements)

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“…applications in which the depth of t is not greater than the depth of s. Second, he restricted himself to regular derivations only. Lifschitz 96,97] and Orevkov 125] considered some extravagant ways of orientation of equations. For example, Orevkov 125] oriented equations using any asymmetric binary relation R. The replacement of s by t using s t has only been allowed when it is not true that sRt.…”

Section: The Inverse Methodsmentioning

confidence: 99%

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Equality Reasoning in Sequent-Based Calculi

Degtyarev¹,

Воронков²

2001

Handbook of Automated Reasoning

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Section: The Inverse Methodsmentioning

confidence: 99%

“…The rst extensive analysis of sequent calculi for equational logic have been made inKanger 91] and in the papers of the Leningrad group of mathematical logic (Rogava 137],Lifschitz 96,97],Orevkov 125] and Pliu skeviciene 131]). The main rule for handling equality used by Kanger is based on the simultaneous replacement of all occurrences of the same subterm:…”

mentioning

confidence: 99%

Equality Reasoning in Sequent-Based Calculi

Degtyarev¹,

Воронков²

2001

Handbook of Automated Reasoning

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“…Now the only remaining family of well-known deductive inference systems is that of sequent (cf. Gentzen (1935), Lifschitz (1971)), tableau (cf. Smullyan (1968), Fitting (1996), and matrix calculi (cf.…”

Section: Sequent and Tableau Calculimentioning

confidence: 99%

Descente Infinie + Deduction

Wirth¹

2004

Logic Journal of IGPL

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Although induction is omnipresent, inductive theorem proving in the form of descente infinie has not yet been integrated into full first-order deductive calculi. We present such an integration for (possibly even higher-order) classical logic. This integration is based on lemma and induction hypothesis application for free variable sequent and tableau calculi. We discuss the appropriateness of these types of calculi for this integration. The deductive part of this integration requires the first combination of raising, explicit variable dependency representation, the liberalized -rule, and preservation of solutions.

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“…Later, the derivations of this form have been named regular e.g. Lifschitz 1967], and used in the generalization of the inverse method to predicate calculus with equality in Maslov 1971].…”

Section: Logic With Equality and Variable Instantiation In -Rulesmentioning

confidence: 99%