Goldblatt-Thomason-style Theorems for Graded Modal Language
نویسندگان
چکیده
We prove two main Goldblatt-Thomason-style Theorems for graded modal language in Kripke semantics: full Goldblatt-Thomason Theorem for elementary classes and relative Goldblatt-Thomason Theorem within the class of finite transitive frames. Two different semantic views on GML allow us to prove these results: neighborhood semantics and graph semantics. By neighborhood semantic view, we can define a natural generalization of Jankov-Fine formula for GML and establish relative Goldblatt-Thomason Theorem. By extracting graph semantics from Fine’s completeness proof of GML (1972), we introduce a new notion of graded ultrafilter images and establish full Goldblatt-Thomason Theorem. Therefore we revive Fine’s old idea in the new context of Goldblatt-Thomason-style characterization.
منابع مشابه
Goldblatt-Thomason Theorem for Coalgebraic Graded Modal Logic
Graded modal logic (GML) was originally presented by Kit Fine (1972) to make the modal analogue to counting quantifiers explicit. A graded modal formula ♦k is true at a state w in a Kripke model if there are at least k successor states of w where φ is true. One open problem in GML is to show a Goldblatt-Thomason theorem for it. See M. De Rijke’s notes (2000). Recently, Katsuhiko Sano and Minghu...
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