Formalización de cáculos lógicos en Isabelle/Hol

Abstract

Natural deduction is a sound and complete proof procedure for propositional logic, that is, it only proves valid formulas and it proves every valid formula. In this work we establish the theory of propositional logic, and we prove the soundness and completeness theorems for natural deduction in propositional logic, following the Melving Fitting’s book First-Order Logic and Automated Theorem Proving. We also present a formalization of this theory in Isabelle/HOL. The formalization covers the sintax and semantic of propositional logic, the model existence theorem, and a natural deduction proof calculus together with a proof of soundness and completeness. For this purpose, we introduce Isabelle/HOL system in this work and the main concepts that we use in the above formalization.