Shortest Axiomatizations of Implicational S4 and S

Notre Dame Journal of Formal Logic 43 (3):169-179 (2002)
Shortest possible axiomatizations for the implicational fragments of the modal logics S4 and S5 are reported. Among these axiomatizations is included a shortest single axiom for implicational S4—which to our knowledge is the first reported single axiom for that system—and several new shortest single axioms for implicational S5. A variety of automated reasoning strategies were essential to our discoveries
Keywords axiomatization   single axiom   automated reasoning   implication   modal logic
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