On the ‘classical’ operations in three-valued logics


L. Yu. Devyatkin


The general aim of the present paper is to provide the analysis of the connection between proof-theoretical and functional properties of certain logical matrices. To be more precise, we consider the class of three-valued matrices that induce the classical consequence relation and show that their operations always constitute a subset of one of the maximal classes of functions, which preserve non-trivial equivalence relations. We use a matrix with the single designated value as a sample for in-depth analysis, and generalize the results to suit other cases. Furthermore, on the basis of obtained results we conclude the paper with methodological considerations concerning the nature and interpretation of the truth-values in logical matrices.






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