Correspondence, Canonicity, and Model Theory for Monotonic Modal Logics

DOI10.1007/S11225-020-09911-4arXiv1904.12997MaRDI QIDQ6317971

Publication date: 29 April 2019

Abstract: We investigate the role of coalgebraic predicate logic, a logic for neighborhood frames first proposed by Chang, in the study of monotonic modal logics. We prove analogues of the Goldblatt-Thomason Theorem and Fine's Canonicity Theorem for classes of monotonic neighborhood frames closed under elementary equivalence in coalgebraic predicate logic. The elementary equivalence here can be relativized to the classes of monotonic, quasi-filter, augmented quasi-filter, filter, or augmented filter neighborhood frames, respectively. The original, Kripke-semantic versions of the theorems follow as a special case concerning the classes of augmented filter neighborhood frames.

Mathematics Subject Classification ID

Modal logic (including the logic of norms) (03B45)

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