A Certified Polynomial-Based Decision Procedure for Propositional Logic

  • Inmaculada Medina-Bulo
  • 1Francisco Palomo-Lozano
  • José A. Alonso-Jiménez
Conference paper

DOI: 10.1007/3-540-44755-5_21

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2152)
Cite this paper as:
Medina-Bulo I., Palomo-Lozano ., Alonso-Jiménez J.A. (2001) A Certified Polynomial-Based Decision Procedure for Propositional Logic. In: Boulton R.J., Jackson P.B. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2001. Lecture Notes in Computer Science, vol 2152. Springer, Berlin, Heidelberg

Abstract

In this paper we present the formalization of a decision procedure for Propositional Logic based on polynomial normalization. This formalization is suitable for its automatic verification in an applicative logic like Acl2. This application of polynomials has been developed by reusing a previous work on polynomial rings [19], showing that a proper formalization leads to a high level of reusability. Two checkers are defined: the first for contradiction formulas and the second for tautology formulas. The main theorems state that both checkers are sound and complete. Moreover, functions for generating models and counterexamples of formulas are provided. This facility plays also an important role in the main proofs. Finally, it is shown that this allows for a highly automated proof development.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Inmaculada Medina-Bulo
    • 1
  • 1Francisco Palomo-Lozano
  • José A. Alonso-Jiménez
    • 2
  1. 1.Department of Computer Languages and SystemsUniversity of CádizCádizSpain
  2. 2.Department of Sciences and Artificial IntelligenceUniversity of Sevilla Fac. de Informática y EstadísticaSevillaSpain

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