Theories in propositional logiс and the converse of substitution

I. A. Gorbunov

Tver State University, 33 Zhelyabova str., Tver, 170100 Russia

Abstract: The paper considers the question of the existence and number of substitutional logics. It is proved that every tabular logic with a functionally complete system of connectives is substitutional. For these logics, the existence of an algorithm is proved, which, for a recursive consistent axiomatic of the theory, constructs an exact unifying substitution for it. A countable set of substitutional tabular logics is constructed. Some substitutional tabular logics with meaningful interpretation are presented. In addition, it is proved that every substitutional logic has a characteristic matrix. It is proved that there are continuum of nonsubstitutional logics.

Keywords: substitutional tabular logic, superintuitionistic logic, Lukasiewicz's logic.

UDC: 510.644

Received: 24.07.2021
Revised: 14.03.2022
Accepted: 08.04.2022

DOI: 10.26907/0021-3446-2022-5-33-41

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2022, 66:5, 26–32