Refutational theorem proving using term-rewriting systems
Artificial Intelligence
Rewrite method for theorem proving in first order theory with equality
Journal of Symbolic Computation
A computational logic handbook
A computational logic handbook
Multi-valued logic and Gröner bases with applications to modal logic
Journal of Symbolic Computation
Synthesis of ML programs in the system Coq
Journal of Symbolic Computation - Special issue on automatic programming
An Industrial Strength Theorem Prover for a Logic Based on Common Lisp
IEEE Transactions on Software Engineering
Computer-Aided Reasoning: An Approach
Computer-Aided Reasoning: An Approach
Metalogical Frameworks II: Developing a Reflected Decision Procedure
Journal of Automated Reasoning
A Machine-Checked Implementation of Buchberger's Algorithm
Journal of Automated Reasoning
Stålmarck's Algorithm as a HOL Derived Rule
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
Classical Propositional Decidability via Nuprl Proof Extraction
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
An equational approach to theorem proving in first-order predicate calculus
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 2
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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.