Results 1  10
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14
Ultrafilter extensions for coalgebras
 In Algebra and Coalgebra in Computer Science, volume 3629 of LNCS
, 2005
"... Abstract. This paper studies finitary modal logics as specification languages for Setcoalgebras (coalgebras on the category of sets) using Stone duality. It is wellknown that Setcoalgebras are not semantically adequate for finitary modal logics in the sense that bisimilarity does not in general co ..."
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Cited by 13 (5 self)
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Abstract. This paper studies finitary modal logics as specification languages for Setcoalgebras (coalgebras on the category of sets) using Stone duality. It is wellknown that Setcoalgebras are not semantically adequate for finitary modal logics in the sense that bisimilarity does not in general coincide with logical equivalence.
Sahlqvist Formulas Unleashed in Polyadic Modal Languages
 Advances in Modal Logic
, 2000
"... We propose a generalization of Sahlqvist formulae to polyadic modal languages by representing modal polyadic languages in a combinatorial style and thus, in particular, developing what we believe to be the right approach to Sahlqvist formulae at all. The class of polyadic Sahlqvist formulae PSF defi ..."
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Cited by 8 (3 self)
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We propose a generalization of Sahlqvist formulae to polyadic modal languages by representing modal polyadic languages in a combinatorial style and thus, in particular, developing what we believe to be the right approach to Sahlqvist formulae at all. The class of polyadic Sahlqvist formulae PSF defined here expands essentially the so far known one. We prove firstorder definability and canonicity for the class PSF.
HigherOrder Categorical Grammars
 Proceedings of Categorial Grammars 04
"... into two principal paradigms: modeltheoretic syntax (MTS), which ..."
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Cited by 4 (1 self)
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into two principal paradigms: modeltheoretic syntax (MTS), which
Hyperintensional questions
 In: Proceedings of the 15th Workshop on Logic, Language, Information, and Computation (WoLLIC ’08). No. 5110 in Springer Lecture Notes in Artificial Intelligence (2008
"... It has been known for decades that Montague’s (1974 [1970]) possibleworlds semantics, which follows Kripke 1963 in treating worlds as unanalyzed primitives and propositions as sets of worlds, does not provide enough meaning distinctions to make correct predictions about a wide range of naturallang ..."
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Cited by 3 (2 self)
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It has been known for decades that Montague’s (1974 [1970]) possibleworlds semantics, which follows Kripke 1963 in treating worlds as unanalyzed primitives and propositions as sets of worlds, does not provide enough meaning distinctions to make correct predictions about a wide range of naturallanguage entailment
Duality for Lattices with Operators: a modal logic approach.
, 2000
"... This thesis discusses a proposal for a duality theory for bounded lattices with operators, amalgamating work on distributive lattices and on lattices with operators. Introduction 1. This work belongs to the eld of algebraic logic. Algebraic logic has its roots in the 19th century, starting with th ..."
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Cited by 2 (0 self)
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This thesis discusses a proposal for a duality theory for bounded lattices with operators, amalgamating work on distributive lattices and on lattices with operators. Introduction 1. This work belongs to the eld of algebraic logic. Algebraic logic has its roots in the 19th century, starting with the work of Boole. Its main aim is to study logic from an algebraic perspective in order to translate problems in logic to (universal) algebraic questions. At the beginning of the twentieth century, Tarski introduced the connection between boolean algebras and classical propositional calculus. Duality theory serves as a tool for translating questions from one perspective (logic) to another one (universal algebra): the existence of a duality between two categories means that the two categories are essentially the same; this makes it possible to use one category in order to understand the other one. Duality theory between logic and universal algebra has its basis in Stone's duality for boolea...
Weakly Associative Relation Algebras with Polyadic Composition Operations
"... We consider nary relative products j n on subsets of a reflexive and symmetric binary relation and define a variety of weakly associative relation algebras with polyadic composition operations (WA 1 ). A theorem that any A2 WA 1 is representable over a reflexive and symmetric relation is prov ..."
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We consider nary relative products j n on subsets of a reflexive and symmetric binary relation and define a variety of weakly associative relation algebras with polyadic composition operations (WA 1 ). A theorem that any A2 WA 1 is representable over a reflexive and symmetric relation is proved. We also show that the equational theory of WA 1 is decidable.
ReInterpreting the Modal µCalculus
 MODAL LOGIC AND PROCESS ALGEBRA
, 1995
"... We reexamine the modal µcalculus in the light of some classical theory of Boolean algebras and recent results on duality theory for a modal logic with fixed points. We propose interpreting formulas into a field of subsets of states instead of the full power set lattice used by Kozen. Under this in ..."
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We reexamine the modal µcalculus in the light of some classical theory of Boolean algebras and recent results on duality theory for a modal logic with fixed points. We propose interpreting formulas into a field of subsets of states instead of the full power set lattice used by Kozen. Under this interpretation we relate image compact modal frames with Scott continuity of the box modality, msaturated transition systems and descriptive modal frames. Also, it is shown that the class of image compact modal frames satisfies the HennessyMilner property. We conclude by showing that for descriptive modal µframes the standard interpretation coincides with the one we proposed.
Coalgebras, Stone Duality, Modal Logic
, 2006
"... A brief outline of the topics of the course could be as follows. Coalgebras generalise transition systems. Modal logics are the natural logics for coalgebras. Stone duality provides the relationship between coalgebras and modal logic. Furthermore, some basic category theory is needed to understand c ..."
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A brief outline of the topics of the course could be as follows. Coalgebras generalise transition systems. Modal logics are the natural logics for coalgebras. Stone duality provides the relationship between coalgebras and modal logic. Furthermore, some basic category theory is needed to understand coalgebras as well as Stone duality. So we