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A Gödel-Artemov-Style Analysis of Constructible Falsity

  • Thomas Macaulay FergusonEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10703)

Abstract

David Nelson’s logic of constructible falsity \(\mathsf {N}\) is a well-known conservative extension to intuitionistic logic \(\mathsf {Int}\). Heinrich Wansing has suggested that extending the provability interpretation of \(\mathsf {Int}\) to such extensions requires that one enriches the single category of formal proofs assumed intuitionistically with further categories representing formal refutations. This paper adapts the framework of Sergei Artemov’s justification logic—which has provided incredible insight into \(\mathsf {Int}\)—to capture a proof/refutation interpretation of \(\mathsf {N}\). To represent distinct types of justification, we identify the distinct agents of Tatiana Yavorskaya-Sidon’s two-agent logic of proofs \(\mathsf {LP}^{2}_{\uparrow {\uparrow }}\) with categories of proof and refutation, permitting an embedding of \(\mathsf {N}\) into \(\mathsf {LP}^{2}_{\uparrow {\uparrow }}\). In conclusion, we describe how a Gödel-Artemov-style analysis can be given for Cecylia Rauszer’s Heyting-Brouwer logic and show that Melvin Fitting’s semantic realization proof can be extended to normal multimodal logics in general.

Keywords

Justification logic Constructible falsity Refutation Intuitionistic logic Logic of proofs 

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.CycorpAustinUSA
  2. 2.Saul Kripke CenterCUNY Graduate CenterNew YorkUSA

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