Notre Dame Journal of Formal Logic

Shortest Axiomatizations of Implicational S4 and S5

Zachary Ernst, Branden Fitelson, Kenneth Harris, and Larry Wos

Abstract

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.

Article information

Source
Notre Dame J. Formal Logic Volume 43, Number 3 (2002), 169-179.

Dates
First available in Project Euclid: 16 January 2004

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1074290715

Digital Object Identifier
doi:10.1305/ndjfl/1074290715

Mathematical Reviews number (MathSciNet)
MR2034744

Zentralblatt MATH identifier
1045.03021

Subjects
Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}
Secondary: 68T15: Theorem proving (deduction, resolution, etc.) [See also 03B35]

Keywords
axiomatization single axiom automated reasoning implication modal logic

Citation

Ernst, Zachary; Fitelson, Branden; Harris, Kenneth; Wos, Larry. Shortest Axiomatizations of Implicational S4 and S5 . Notre Dame J. Formal Logic 43 (2002), no. 3, 169--179. doi:10.1305/ndjfl/1074290715. http://projecteuclid.org/euclid.ndjfl/1074290715.


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