Abstract
AbstractIn this paper, we introduce the notions of connexive and bi-intuitionistic multilattices and develop on their base the algebraic semantics for Kamide, Shramko, and Wansing’s connexive and bi-intuitionistic multilattice logics which were previously known in the form of sequent calculi and Kripke semantics. We prove that these logics are sound and complete with respect to the presented algebraic structures.
Publisher
Springer Science and Business Media LLC
Reference22 articles.
1. Arieli, O., & Avron, A. (1996). Reasoning with logical bilattices. Journal of Logic, Language and Information, 5, 25–63.
2. Belnap, N. D. (1977). A useful four-valued logic. In: Dunn, J. M., Epstein, G. (Eds.), Modern uses of multiple-valued logic (pp. 7–37). Reidel Publishing Company.
3. Belnap, N. D. (1977). How a computer should think. In: Rule, G. (Ed.), Contemporary aspects of philosophy (pp. 30–56). Oriel Press.
4. Dunn, J. M. (1976). Intuitive semantics for first-degree entailment and coupled trees. Philosophical Studies, 29, 149–168.
5. Dunn, J. M., & Restall, G. (2002). Relevance logic. Handbook of philosophical logic. New York: Springer.