A Note on Calculi for Non-deterministic Many-valued Logics

Issue title: Special Issue of Invited Papers in Honor of the Boris Trakhtenbrot Centenary

Guest editors: Arnon Avron, Nachum Dershowitz and Alexander Rabinovich

Article type: Research Article

Authors: Kaminski, Michael^{; *}

Affiliations: Department of Computer Science, Technion – Israel Institute of Technology, Haifa 3200003, Israel. kaminski@as.technion.ac.il

Correspondence: [*] Address of correspondence: Department of Computer Science, Technion – Israel Institute of Technology, Haifa 3200003, Israel

Abstract: We present two deductively equivalent calculi for non-deterministic many-valued logics. One is defined by axioms and the other – by rules of inference. The two calculi are obtained from the truth tables of the logic under consideration in a straightforward manner. We prove soundness and strong completeness theorems for both calculi and also prove the cut elimination theorem for the calculi defined by rules of inference.

DOI: 10.3233/FI-222123

Journal: Fundamenta Informaticae, vol. 186, no. 1-4, pp. 143-153, 2022