THE LOGIC K OF STRICT IMPLICATION AND ITS RELATIVES
Magdalena Fabisiak · 2004
The logics of strict implication (cf. [2]) are usually deflned on the standard propositional language L = (L;^;_;!;:) in which the sign \! is interpreted as a connective of strict implication. At times, in order to formulate only essential properties of pure strict implication and to avoid some possible in∞uence or even distortion from the other connectives, a purely implicational language L = (L;!) seems to be more appropriate. In this paper I am going to consider three logics of strict implication deflned on such a language. The main aim of the paper is to provide a set of axioms adequate for the logic of strict implication corresponding to modal logic K. Moreover, the paper contains some new sets of axioms for the logics T and S4 of strict implication, obtained rather non-standard method { without application of Lindenbaum lemma.