Constructive CK for Contexts
Michael Mendler, Valeria de Paiva · 2005
Abstract. This note describes possible world semantics for a constructive modal logic CK. The system CK is weaker than other constructive modal logics K as it does not satisfy distribution of possibility over disjunctions, neither binary (✸(A ∨ B) → ✸A ∨ ✸B) nor nullary (✸ ⊥ → ⊥). We are interested in this version of constructive K for its application to contexts in AI [dP03]. However, our previous work on CK described only a categorical semantics [BdPR01] for the system, while most logicians interested in contexts prefer their semantics possible worlds style. This note fills the gap by providing the possible worlds model theory for the constructive modal system CK, showing soundness and completeness of the proposed semantics, as well as the finite model property and (hence) decidability of the system. Wijesekera [Wij90] investigated possible worlds semantics of a system similar to CK, without the binary distribution, but satisfying the nullary one. The semantics presented here for CK is new and considerably simpler than the one of Wijesekera. 1