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.
KeywordsMathematical Logic Study Condition Relation Semantic Computational Linguistic Classical Logic
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