Theorem Proving in Higher Order Logics

Volume 2152 of the series Lecture Notes in Computer Science pp 297-312


A Certified Polynomial-Based Decision Procedure for Propositional Logic

  • Inmaculada Medina-BuloAffiliated withDepartment of Computer Languages and Systems, University of Cádiz
  • , 1Francisco Palomo-Lozano
  • , José A. Alonso-JiménezAffiliated withDepartment of Sciences and Artificial Intelligence, University of Sevilla Fac. de Informática y Estadística

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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.