Shortest Axiomatizations of Implicational S4 and S

Notre Dame Journal of Formal Logic 43 (3):169-179 (2002)
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Abstract

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

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Branden Fitelson
Northeastern University

Citations of this work

Axioms in Mathematical Practice.Dirk Schlimm - 2013 - Philosophia Mathematica 21 (1):37-92.

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References found in this work

A completeness theorem in modal logic.Saul Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
What is strict implication?Ian Hacking - 1963 - Journal of Symbolic Logic 28 (1):51-71.
The pure calculus of entailment.Alan Ross Anderson & Nuel D. Belnap - 1962 - Journal of Symbolic Logic 27 (1):19-52.
Investigations into implicational s5.C. A. Meredith & A. N. Prior - 1964 - Mathematical Logic Quarterly 10 (13‐17):203-220.
A note on ${\bf R}$-Mingle and Sobociński's three-valued logic.R. Zane Parks - 1972 - Notre Dame Journal of Formal Logic 13 (2):227-228.

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