Abstract
The sentential logic S extends classical logic by an implication-like connective. The logic was first presented by Chellas as the smallest system modelled by contraining the Stalnaker-Lewis semantics for counterfactual conditionals such that the conditional is effectively evaluated as in the ternary relations semantics for relevant logics. The resulting logic occupies a key position among modal and substructural logics. We prove completeness results and study conditions for proceeding from one family of logics to another.
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References
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We are grateful to Peter Apostoli, Kosta Došen, and anonymous referees for their comments on an earlier version of this paper. A.F.'s work has been supported by a grant from the Volkswagen-Stiftung.
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Fuhrmann, A., Mares, E.D. On S. Stud Logica 53, 75–91 (1994). https://doi.org/10.1007/BF01053023
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DOI: https://doi.org/10.1007/BF01053023