Proving formulas through reduction to decidable classes

  • Mauro Di Manzo
  • Enrico Giunchiglia
  • Alessandro Armando
  • Paolo Pecchiari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 728)


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.


interactive theorem proving decision procedures 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Mauro Di Manzo
    • 1
  • Enrico Giunchiglia
    • 1
  • Alessandro Armando
    • 1
  • Paolo Pecchiari
    • 1
  1. 1.Mechanized Reasoning GroupDIST - University of GenoaGenoaItaly

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