Formalizing a Paraconsistent Logic in the Isabelle Proof Assistant

  • Jørgen VilladsenEmail author
  • Anders Schlichtkrull
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10620)


We present a formalization of a so-called paraconsistent logic that avoids the catastrophic explosiveness of inconsistency in classical logic. The paraconsistent logic has a countably infinite number of non-classical truth values. We show how to use the proof assistant Isabelle to formally prove theorems in the logic as well as meta-theorems about the logic. In particular, we formalize a meta-theorem that allows us to reduce the infinite number of truth values to a finite number of truth values, for a given formula, and we use this result in a formalization of a small case study.


Paraconsistent logic Many-valued logic Formalization Isabelle proof assistant Inconsistency Paraconsistency 



Thanks to Andreas Halkjær From, Alexander Birch Jensen and John Bruntse Larsen for comments on drafts of the paper. Also thanks to Hendrik Decker and the anonymous reviewers for many constructive comments.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.DTU Compute, Technical University of DenmarkKongens LyngbyDenmark

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