Conditions for the applicability of classical logic in the framework of languages of nonclassical logics (Q2751825)

The central notion discussed in the paper is: given two propositional logics \(L_1\) and \(L_2\), where the language of \(L_1\) is a sublanguage of the language of \(L_2\), the logic \(L_1\) is applicable to a given formula \(A\) of the logic \(L_2\) if for every theorem \(T\) of \(L_1\), every formula obtained by a uniform substitution of \(A\) for a variable in \(T\) is a theorem of \(L_2\). NEWLINENEWLINENEWLINEThe paper discusses the question under what formal conditions classical propositional logic is applicable to various nonclassical logics, such as intuitionistic logic, Łukasiewicz's logic \({\L}_3\), Kleene's logic, and the logic FL4 with operators for truth and falsity, introduced by the author, as well as the applicability of the former logics to FL4. Some results are stated with no proofs.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00036].