Incompatibility, Modal Semantics, and Intrinsic Logic
This chapter uses a normative pragmatic metavocabulary to introduce a notion of the incompatibility of claims, which then serves as a semantic primitive that is shown to suffice to introduce classical logical connectives, including S5 modal operators. A meaning-use analysis of this construction is offered. The semantics is recursive, but not compositional, showing that compositionality is not the only way to secure learnability and projectibility. The notion of the logic that is intrinsic to a consequence relation (whether material or logical) is introduced and applied.
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