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Proving formulas through reduction to decidable classes

Identifieur interne : 001A66 ( Istex/Corpus ); précédent : 001A65; suivant : 001A67

Proving formulas through reduction to decidable classes

Auteurs : Mauro Di Manzo ; Enrico Giunchiglia ; Alessandro Armando ; Paolo Pecchiari

Source :

RBID : ISTEX:581F1F9EB2479D034B487DC561FC0308505190FC

Abstract

Abstract: As it is well known, it is important to enrich the basic deductive machinery of an interactive theorem prover with complex decision procedures. In the GETFOL system we have implemented a hierarchical and modular structure of procedures which can be either invoked individually or jointly with the others. At the top of the hierarchy there is a decision procedure for a set of formulas which can be reduced to the class of prenex universal-existential formulas via finitely many application of rewriting rules. In this paper we give a formal account of such a reduction process, arguing that (i) it greatly enlarges the set of formulas which can proven through a decision process and (ii) in some cases makes the resulting formula easier to prove. We also provide an extensional characterization of a class of formulas which can be reduced and thus decided. The implementation of such reducing procedure in GETFOL is also sketched.

Url:
DOI: 10.1007/3-540-57292-9_36

Links to Exploration step

ISTEX:581F1F9EB2479D034B487DC561FC0308505190FC

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<GivenName>Paolo</GivenName>
<FamilyName>Pecchiari</FamilyName>
</AuthorName>
<Contact>
<Email>peck@dist.unige.it</Email>
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<Affiliation ID="Aff1">
<OrgDivision>Mechanized Reasoning Group</OrgDivision>
<OrgName>DIST - University of Genoa</OrgName>
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<Street>Via Opera Pia 11A</Street>
<Postcode>16145</Postcode>
<City>Genoa</City>
<Country>Italy</Country>
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<Abstract ID="Abs1" Language="En">
<Heading>Abstract</Heading>
<Para>As it is well known, it is important to enrich the basic deductive machinery of an interactive theorem prover with complex decision procedures. In the GETFOL system we have implemented a hierarchical and modular structure of procedures which can be either invoked individually or jointly with the others. At the top of the hierarchy there is a decision procedure for a set of formulas which can be
<Emphasis Type="Italic">reduced</Emphasis>
to the class of prenex universal-existential formulas via finitely many application of rewriting rules. In this paper we give a formal account of such a reduction process, arguing that (
<Emphasis Type="Italic">i</Emphasis>
) it greatly enlarges the set of formulas which can proven through a decision process and (
<Emphasis Type="Italic">ii</Emphasis>
) in some cases makes the resulting formula easier to prove. We also provide an extensional characterization of a class of formulas which can be reduced and thus decided. The implementation of such reducing procedure in GETFOL is also sketched.</Para>
</Abstract>
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<Heading>Keywords</Heading>
<Keyword>interactive theorem proving</Keyword>
<Keyword>decision procedures</Keyword>
</KeywordGroup>
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<title>Proving formulas through reduction to decidable classes</title>
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<title>Proving formulas through reduction to decidable classes</title>
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<name type="personal">
<namePart type="given">Mauro</namePart>
<namePart type="family">Di Manzo</namePart>
<affiliation>Mechanized Reasoning Group, DIST - University of Genoa, Via Opera Pia 11A, 16145, Genoa, Italy</affiliation>
<affiliation>E-mail: mauropeck@dist.unige.it</affiliation>
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<name type="personal">
<namePart type="given">Enrico</namePart>
<namePart type="family">Giunchiglia</namePart>
<affiliation>Mechanized Reasoning Group, DIST - University of Genoa, Via Opera Pia 11A, 16145, Genoa, Italy</affiliation>
<affiliation>E-mail: enrico@dist.unige.it</affiliation>
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</role>
</name>
<name type="personal">
<namePart type="given">Alessandro</namePart>
<namePart type="family">Armando</namePart>
<affiliation>Mechanized Reasoning Group, DIST - University of Genoa, Via Opera Pia 11A, 16145, Genoa, Italy</affiliation>
<affiliation>E-mail: armando@dist.unige.it</affiliation>
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<name type="personal">
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<affiliation>Mechanized Reasoning Group, DIST - University of Genoa, Via Opera Pia 11A, 16145, Genoa, Italy</affiliation>
<affiliation>E-mail: peck@dist.unige.it</affiliation>
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<abstract lang="en">Abstract: As it is well known, it is important to enrich the basic deductive machinery of an interactive theorem prover with complex decision procedures. In the GETFOL system we have implemented a hierarchical and modular structure of procedures which can be either invoked individually or jointly with the others. At the top of the hierarchy there is a decision procedure for a set of formulas which can be reduced to the class of prenex universal-existential formulas via finitely many application of rewriting rules. In this paper we give a formal account of such a reduction process, arguing that (i) it greatly enlarges the set of formulas which can proven through a decision process and (ii) in some cases makes the resulting formula easier to prove. We also provide an extensional characterization of a class of formulas which can be reduced and thus decided. The implementation of such reducing procedure in GETFOL is also sketched.</abstract>
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<title>Advances in Artificial Intelligence</title>
<subTitle>Third Congress of the Italian Association for Artificial Intelligence, AI*IA '93 Torino, Italy, October 26–28, 1993 Proceedings</subTitle>
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<namePart type="given">Pietro</namePart>
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