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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<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>
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