Some paraconsistent sentential calculi (Q1068811)

Let \(X\) be a normal modal propositional logic. Let \(M\) be a modality, i.e., string of modal operators and negation signs. Let \(M(X)=\{A\mid A\) is a formula and \(MA\in X\}\). This paper investigates sets of formulas of the form \(M(X)\). In particular, results about their axiomatizability are proved. A partial answer to a problem of \textit{N. C. A. da Costa} and \textit{J. Kotas} [Stud. Logic Found. Math. 89, 57--73 (1977; Zbl 0359.02011)], concerning axiomatizable \(X\), is produced.