Journal ArticleDOI
Sahlqvist Formulas in Hybrid Polyadic Modal Logics
TLDR
Sahlqvist formulas in hybrid polyadic modal languages containing nominals and universal modality or satisfaction operators are defined to ensure first-order definability and canonicity of these formulas immediately transfers to arbitrary polyadic languages.Abstract:
Building on a new approach to polyadic modal languages and Sahlqvist formulas introduced in [10] we define Sahlqvist formulas in hybrid polyadic modal languages containing nominals and universal modality or satisfaction operators. Particularly interesting is the case of reversive polyadic languages, closed under all ‘inverses’ of polyadic modalities because the minimal valuations arising in the computation of the first-order equivalents of polyadic Sahlqvist formulae are definable in such languages and that makes the proof of first-order definability and canonicity of these formulas a simple syntactic exercise. Furthermore, the first-order definability of Sahlqvist formulas immediately transfers to arbitrary polyadic languages, while the direct transfer of canonicity requires a more involved proof-theoretic analysis.read more
Citations
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Journal ArticleDOI
Representation, reasoning, and relational structures: a hybrid logic manifesto
TL;DR: This paper is about the good side of modal logic, the bad side of modem logic, and how hybrid logic takes the good and fixes the bad, and why hybrid logic is a rather unusual modal upgrade.
Book ChapterDOI
14 Hybrid logics
Carlos Areces,Balder ten Cate +1 more
TL;DR: This chapter discusses the proof theory, expressivity, and complexity of a number of the well-known hybrid logics and provides a snapshot of the logical territory lying between the basic modal languages and their classical companions.
Book
Model theory for extended modal languages
TL;DR: In this article, the authors propose a method to solve the problem of "uniformity" in the following: 1.207.5.0.1.0, 1.
Journal ArticleDOI
Algorithmic correspondence and canonicity for distributive modal logic
TL;DR: Evidence is given to the effect that inductive inequalities are the distributive counterparts of the inductive formulas of Goranko and Vakarelov in the classical setting.
References
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Journal ArticleDOI
Using the Universal Modality: Gains and Questions·
Valentin Goranko,Solomon Passy +1 more
TL;DR: The universal modality is advertised as a natural and helpful tool, providing a better medium for the mission of modality; and second, to illustrate the typical problems arising when enricha ments of modal languages are investigated.
Proceedings Article
What Are Hybrid Languages
Patrick Blackburn,Jerry Seligman +1 more
TL;DR: It is shown that all three binders give rise to languages strictly weaker than the corresponding first-order language, that full first- order expressivity can be gained by adding the universal modality, and that allThree binders can force the existence of infinite models and have undecidable satisfiability problems.
Journal ArticleDOI
Modal logic with names
George Gargov,Valentin Goranko +1 more
TL;DR: Every ℒc-logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete and strong completeness of the normal ℓc- logics is proved with respect to models in which all worlds are named.