Shortest Axiomatizations of Implicational S4 and S
Notre Dame Journal of Formal Logic 43 (3):169-179 (2002)
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 discoveriesAuthor's Profile
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10.1305/ndjfl/1074290715
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Citations of this work
Unification with parameters in the implication fragment of classical propositional logic.Philippe Balbiani & Mojtaba Mojtahedi - 2022 - Logic Journal of the IGPL 30 (3):454-464.
References found in this work
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.
