### 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.

### License

BSD License

### Topics

- Logic/General logic/Paraconsistent logics

### Session Paraconsistency

- Paraconsistency

## Cite

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Paraconsistency-AFP

    @article{Paraconsistency-AFP,
      author  = {Anders Schlichtkrull and Jørgen Villadsen},
      title   = {Paraconsistency},
      journal = {Archive of Formal Proofs},
      month   = {December},
      year    = {2016},
      note    = {\url{https://isa-afp.org/entries/Paraconsistency.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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