Shortest Axiomatizations of Implicational S4 and S5
Zachary J. Ernst, Branden Fitelson, Kenneth D. Harris, Larry Wos · Notre Dame Journal of Formal Logic · 2002
Shortest possible axiomatizations for the strict 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.