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.