# Paraconsistency

 Title: Paraconsistency Authors: Anders Schlichtkrull and Jørgen Villadsen Submission date: 2016-12-07 Abstract: Paraconsistency is about handling inconsistency in a coherent way. In classical and intuitionistic logic everything follows from an inconsistent theory. A paraconsistent logic avoids the explosion. Quite a few applications in computer science and engineering are discussed in the Intelligent Systems Reference Library Volume 110: Towards Paraconsistent Engineering (Springer 2016). We formalize a paraconsistent many-valued logic that we motivated and described in a special issue on logical approaches to paraconsistency (Journal of Applied Non-Classical Logics 2005). We limit ourselves to the propositional fragment of the higher-order logic. The logic is based on so-called key equalities and has a countably infinite number of truth values. We prove theorems in the logic using the definition of validity. We verify truth tables and also counterexamples for non-theorems. We prove meta-theorems about the logic and finally we investigate a case study. BibTeX: ```@article{Paraconsistency-AFP, author = {Anders Schlichtkrull and Jørgen Villadsen}, title = {Paraconsistency}, journal = {Archive of Formal Proofs}, month = dec, year = 2016, note = {\url{http://isa-afp.org/entries/Paraconsistency.shtml}, Formal proof development}, ISSN = {2150-914x}, }``` License: BSD License