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Reseña: Completeness theorems for first-order logic analysed in constructive type theory

Se ha publicado un artículo de razonamiento formalizado en Coq sobre lógica titulado Completeness theorems for first-order logic analysed in constructive type theory.

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We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic natural deduction and sequent calculi with respect to model-theoretic, algebraic, and game-theoretic semantics. As completeness with respect to the standard model-theoretic semantics à la Tarski and Kripke is not readily constructive, we analyse connections of completeness theorems to Markov’s Principle and Weak König’s Lemma and discuss non-standard semantics admitting assumption-free completeness. We contribute a reusable Coq library for first-order logic containing all results covered in this paper.

El trabajo se ha presentado en el Logical Foundations of Computer Science (LFCS 2020) y publicado en el Journal of Logic and Computation.

El código de las correspondientes teorías se encuentra aquí.

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