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Sahlqvist preservation for topological fixed-point logic. (English) Zbl 1444.03044

Summary: We introduce a new order-topological semantics for the positive modal mu-calculus over modal compact Hausdorff spaces, which are generalizations of descriptive frames. We define Sahlqvist sequents in this language, prove Esakia’s lemma and Sahlqvist preservation theorem for this semantics. We show that every Sahlqvist sequent has a frame correspondent in first-order logic with fixed-point operators.

MSC:

03B45 Modal logic (including the logic of norms)
03B70 Logic in computer science
06D22 Frames, locales
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