Modal Logic of Multivalued Frames over Inversely Well-Ordered Sets

Studies in Logic, Vol. 15, No. 3 (2022): 52–72   PII: 1674-3202(2022)-03-0052-21

Fan He

Abstract.

Multivalued frames generalize Kripke frames via introducing a set of values for pairs of states. A set of values Q is supposed to be an inversely well-ordered set. The intended multimodal language is interpreted in models based on multivalued frames over Q. Goldblatt-Thomason theorems for certain classes of Q-frames are established. Normal Q-modal logics are introduced, and some completeness results are naturally given by adjusting the canonical model method. Makinson’s classification theorem as well as some logical properties are established for normal Q-modal logics.