The PRIZ system and propositional calculus

Volozh, B. B.; Matskin, Mihhail; Mint︠s︡, Grigori; Tyugu, Enn

doi:10.1007/bf01069164

Cited by 3 publications

(8 citation statements)

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“…Despite the fact that several intuitionistic theorem provers have been implemented (see [3], [13], [1]), only very few published papers describe the actual implementation of an automated theorem prover and bring the results of running the prover on some benchmarks: [17] and [12] are known to us. The prover described in [17] is limited to propositional calculus.…”

Section: Introductionmentioning

confidence: 99%

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A resolution theorem prover for intuitionistic logic

Tammet

1996

Automated Deduction — Cade-13

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Abstract. We use the general scheme of building resolution calculi (also called the inverse method) originating from S.Maslov and G.Mints to design and implement a resolution theorem prover for intuitionistic logic. A number of search strategies are introduced and proved complete. The resolution method is shown to be a decision procedure for a new syntactically described decidable class of intuitionistic logic. The performance of our prover is compared with the performance of a tableau prover for intuitionistic logic presented in [12], using both the benchmarks from the latter and the theorems from J. yon Plato-s constructive geometry [9].

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Section: Introductionmentioning

confidence: 99%

“…Relatively few papers are devoted on proof search in intuitionistic logic. The following is an incomplete list of such papers: [17], [5], [1], [7], [18], [10], [16], [12], [13], [3], [8].…”

Section: Introductionmentioning

confidence: 99%

A resolution theorem prover for intuitionistic logic

Tammet

1996

Automated Deduction — Cade-13

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“…The idea of the main construction, however, originates from G.E.Mints. For ordinary intuitionistic propositional calculus, similar construction was described in detail in a 1983 article (Volozh, Matskin, Mints and Tyugu 1983). Its essence is to \project" second-order equivalences: F , 8P:P and a _ b , 8P:((a ) P)&(b ) P) ) P)…”

Section: Introductionmentioning

confidence: 99%

“…Using this, one can eliminate some connectives and constants (ordinary intuitionistic disjunction and \false" in (Volozh, Matskin, Mints and Tyugu 1983)) and preserve derivability.…”

Section: Introductionmentioning

confidence: 99%

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Reductions in Intuitionistic Linear Logic

Soloviev

1995

Math. Struct. Comp. Sci.

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In this work we show how some useful reductions known from ordinary intuitionistic propositional calculus can be modified for Intuitionistic Linear Logic (without modalities). The main reductions we consider are: (1) the reduction of the depth of formulas in the sequents by addition of new variables, and (2) the elimination of linear disjunction, tensor and constant F. Both transformations preserve deducibility, that is, a transformed sequent is deducible if and only if the initial one was deducible. The size of the sequent grows linearly in case (1) and ≤ On8 in case (2).

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Gentzen-type systems and resolution rules part I propositional logic

Mint︠s︡

1990

Colog-88

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The PRIZ system and propositional calculus

Cited by 3 publications

References 1 publication

A resolution theorem prover for intuitionistic logic

A resolution theorem prover for intuitionistic logic

Reductions in Intuitionistic Linear Logic

Gentzen-type systems and resolution rules part I propositional logic

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