Structured proof procedures

  • Enrico Giunchiglia
  • Alessandro Armando
  • Paolo Pecchiari
Article
  • 46 Downloads

Abstract

In this paper, we address the problem of enriching an interactive theorem prover with complex proof procedures. We show that the approach of building complex proof procedures out of deciders for (decidable) quantifier-free theories has many advantages: (i) deciders for quantifier-free theories provide powerful, high level functionalities which greatly simplify the activity of designing and implementing complex and higher level proof procedures; (ii) this approach is of wide applicability since most of the proof procedures are composed by steps of propositional reasoning intermixed with steps carrying out higher level strategical functionalities; (iii) decidability and efficiency are retained on important (decidable) subclasses, while they are often sacrificed by uniform proof strategies for the sake of generality; and finally (iv), from a software engineering perspective, the modularity of the procedures guarantees that any modification in the implementation can be accomplished locally. As a case study, we present and discuss a proof procedure for the existential fragment of first-order logic (prenex existential formulas without function symbols) built on top of a propositional decider.

Keywords

Neural Network Artificial Intelligence Complex System Nonlinear Dynamics Theorem Prover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© J.C. Baltzer AG, Science Publishers 1995

Authors and Affiliations

  • Enrico Giunchiglia
    • 1
  • Alessandro Armando
    • 1
  • Paolo Pecchiari
    • 1
  1. 1.Mechanized Reasoning Group, Dipartimento di Informatica, Sistemistica e TelematicaUniversità di GenovaGenovaItaly

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