Proving formulas through reduction to decidable classes
Identifieur interne : 001A66 ( Istex/Curation ); précédent : 001A65; suivant : 001A67Proving formulas through reduction to decidable classes
Auteurs : Mauro Di Manzo [Italie] ; Enrico Giunchiglia [Italie] ; Alessandro Armando [Italie] ; Paolo Pecchiari [Italie]Source :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 1993.
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
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University of Genoa, Via Opera Pia 11A, 16145, Genoa, Italy</mods:affiliation><country xml:lang="fr">Italie</country><wicri:regionArea>Mechanized Reasoning Group, DIST - University of Genoa, Via Opera Pia 11A, 16145, Genoa</wicri:regionArea></affiliation><affiliation wicri:level="1"><mods:affiliation>E-mail: armando@dist.unige.it</mods:affiliation><country wicri:rule="url">Italie</country></affiliation></author><author><name sortKey="Pecchiari, Paolo" sort="Pecchiari, Paolo" uniqKey="Pecchiari P" first="Paolo" last="Pecchiari">Paolo Pecchiari</name><affiliation wicri:level="1"><mods:affiliation>Mechanized Reasoning Group, DIST - University of Genoa, Via Opera Pia 11A, 16145, Genoa, Italy</mods:affiliation><country xml:lang="fr">Italie</country><wicri:regionArea>Mechanized Reasoning Group, DIST - University of Genoa, Via Opera Pia 11A, 16145, Genoa</wicri:regionArea></affiliation><affiliation wicri:level="1"><mods:affiliation>E-mail: peck@dist.unige.it</mods:affiliation><country wicri:rule="url">Italie</country></affiliation></author></analytic><monogr></monogr><series><title level="s">Lecture Notes in Computer Science</title><title level="s" type="sub">Lecture Notes in Artificial Intelligence</title><imprint><date>1993</date></imprint><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series><idno type="istex">581F1F9EB2479D034B487DC561FC0308505190FC</idno><idno type="DOI">10.1007/3-540-57292-9_36</idno><idno type="ChapterID">Chap1</idno><idno type="ChapterID">1</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml: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.</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
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