Shortest Axiomatizations of Implicational S4 and S5

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.

• Type: Journal
• Year: 2002
• Where: NDJFL
• Authors: Zachary Ernst, Branden Fitelson, Kenneth Harris, Larry Wos
• Keywords: Modal Logics, NDJFL 2002, Shortest Possible Axiomatizations, Shortest Single Axioms