## Notre Dame Journal of Formal Logic

### Shortest Axiomatizations of Implicational S4 and S5

#### 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

#### 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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