Partial and paraconsistent three-valued logics
DOI:
https://doi.org/10.12775/LLP.2016.003Keywords
four-valued logic, three-valued logic, partial logic, paraconsistent logic, sequent calculus, functional completeness, cut redundancy, proof-search procedureAbstract
On the sidelines of classical logic, many partial and paraconsistent three-valued logics have been developed. Most of them differ in the notion of logical consequence or in the definition of logical connectives. This article aims, firstly, to provide both a model-theoretic and a proof-theoretic unified framework for these logics and, secondly, to apply these general frameworks to several well-known three-valued logics. The proof-theoretic approach to which we give preference is sequent calculus. In this perspective, several results concerning the properties of functional completeness, cut redundancy, and proof-search procedure are shown. We also provide a general proof for the soundness and the completeness of the three sequent calculi discussed.References
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