Sahlqvist preservation for topological fixed-point logic

Sahlqvist theorem for modal fixed point logic

We define Sahlqvist fixed point formulas. By extending the technique of Sambin and Vaccaro we show that (1) for each Sahlqvist fixed point formula φ there exists an LFPformula χ(φ), with no free first-order variable or predicate symbol, such that a descriptive μ-frame (an order-topological structure that admits topological interpretations of least fixed point operators as intersections of clope...

Preservation of Sahlqvist fixed point equations in completions of relativized fixed point Boolean algebras with operators

We define Sahlqvist fixed point equations and relativized fixed point Boolean algebras with operators (relativized fixed point BAOs). We show that every Sahlqvist fixed point equation is preserved under completions of conjugated relativized fixed point BAOs. This extends the result of Givant and Venema [8] to the setting of relativized fixed point BAOs.

ALBA-style Sahlqvist preservation for modal compact Hausdorff spaces

Algorithmic correspondence for intuitionistic modal mu-calculus, Part 2

Sahlqvist-style correspondence results remain a perennial theme and an active topic of research within modal logic. Recently, there has been interest in extending the classical results in this area to the modal mu-calculus [7]. For instance, in [8] van Benthem, Bezhanishvili and Hodkinson define a class of Sahlqvist formulas for the modal mu-calculus, all of which have frame correspondents in f...

Constructive Canonicity for Lattice-Based Fixed Point Logics

The present contribution lies at the crossroads of at least three active lines of research in nonclassical logics: the one investigating the semantic and proof-theoretic environment of fixed point expansions of logics algebraically captured by varieties of (distributive) lattice expansions [1, 19, 24, 2, 16]; the one investigating constructive canonicity for intuitionistic and substructural log...