[isabelle] new AFP entry: Paraconsistency

by Anders Schlichtkrull and JÃrgen Villadsen

  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.



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