Kripke-type semantics for da Costa's paraconsistent logic ${\rm C}_\omega$.
Matthias Baaz · Notre Dame Journal of Formal Logic · 1986
This paper should be considered as an example of the formal derivation of semantics in connection with propositional logics extending positive logic.These constructions can be applied to many similar problems and should be compared to those proposed in Hacking [4]: The Kripke-type structure of the resulting semantics depends on the previous choice of Gentzen-style formulations.The details of the semantics are read off from the adopted introduction and elimination rules.In Arruda [1], p. 27, problem 8, the problem is formulated to adapt world semantics to C ω .The proposed construction of an adequate semantics for C ω is based on Raggio's Gentzen-type formulation CG ω of C* [5], and on the proof-theoretic analysis of intuitionistic logic in Takeuti [6], Section 8.