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New Formalized Results on the Meta-Theory of a Paraconsistent Logic

Author Anders Schlichtkrull

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Anders Schlichtkrull
  • DTU Compute - Department of Applied Mathematics and Computer Science, Technical University of Denmark, Richard Petersens Plads, Building 324, DK-2800 Kongens Lyngby, Denmark

Acknowledgements

Jørgen Villadsen, Jasmin Christian Blanchette and John Bruntse Larsen provided valuable feedback on the paper and the formalization. Thanks to Freek Wiedijk for discussions. Thanks to the anonymous reviewers for many constructive comments.

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Anders Schlichtkrull. New Formalized Results on the Meta-Theory of a Paraconsistent Logic. In 24th International Conference on Types for Proofs and Programs (TYPES 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 130, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.TYPES.2018.5

Abstract

Classical logics are explosive, meaning that everything follows from a contradiction. Paraconsistent logics are logics that are not explosive. This paper presents the meta-theory of a paraconsistent infinite-valued logic, in particular new results showing that while the question of validity for a given formula can be reduced to a consideration of only finitely many truth values, this does not mean that the logic collapses to a finite-valued logic. All definitions and theorems are formalized in the Isabelle/HOL proof assistant.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
  • Theory of computation → Logic and verification
  • Theory of computation → Higher order logic
  • Theory of computation → Logic and databases
Keywords
  • Paraconsistent logic
  • Many-valued logic
  • Formalization
  • Isabelle proof assistant
  • Paraconsistency

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