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2002 Shortest Axiomatizations of Implicational S4 and S5
Zachary Ernst, Branden Fitelson, Kenneth Harris, Larry Wos
Notre Dame J. Formal Logic 43(3): 169-179 (2002). DOI: 10.1305/ndjfl/1074290715


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.


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Zachary Ernst. Branden Fitelson. Kenneth Harris. Larry Wos. "Shortest Axiomatizations of Implicational S4 and S5." Notre Dame J. Formal Logic 43 (3) 169 - 179, 2002.


Published: 2002
First available in Project Euclid: 16 January 2004

zbMATH: 1045.03021
MathSciNet: MR2034744
Digital Object Identifier: 10.1305/ndjfl/1074290715

Primary: 03B45
Secondary: 68T15

Keywords: automated reasoning , axiomatization , implication , modal logic , single axiom

Rights: Copyright © 2002 University of Notre Dame

Vol.43 • No. 3 • 2002
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