Cut-free sequent calculi for C-systems with generalized finite-valued semantics
In the paper Cut-free ordinary sequent calculi for logics having generalized finite-valued semantics by A. Avron, J. Ben-Naim, and B. Konikowska. (Logica Universalis, 1:41-69, 2006), a general method was developed for generating cut-free ordinary sequent calculi for logics that can be characterized by finite-valued semantics based on non-deterministic matrices (Nmatrices). In this paper, a substantial step towards automation of paraconsistent reasoning is made by applying that method to a certain crucial family of thousands of paraconsistent logics, all belonging to the class of C-systems. For that family, the method produces in a modular way uniform Gentzen-type rules corresponding to a variety of axioms considered in the literature.
sequent calculi paraconsistent logic proof systems many-valued logic automated deduction non-deterministic semantics