On some classes of formulas in S5 which are pre-complete relative to existential expressibility

Abstract

Existential expressibility for all $k$-valued functions was proposed by A.~V. Kuz\-ne\-tsov and later was investigated in more details by S.~S.~Mar\-chen\-kov. In the present paper, we consider existential expressibility in the case of formulas defined by a logical calculus and find out some conditions for a system of formulas to be closed relative to existential expressibility. As a consequence, it has been established some pre-complete as to existential expressibility classes of formulas in some finite extensions of the paraconsistent modal logic $S5$.

Keywords

• paraconsistent logic
• existential expressibility
• logical calculi