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23
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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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.
Strongly complete logics for coalgebras
, 2006
"... Coalgebras for a functor T on a category X model many different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary strongly complete specification languages for Setbased coalgebras. We show how to associate a finitary logic to any finitesets preservin ..."
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Cited by 12 (4 self)
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Coalgebras for a functor T on a category X model many different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary strongly complete specification languages for Setbased coalgebras. We show how to associate a finitary logic to any finitesets preserving functor T and prove the logic to be strongly complete under a mild condition on T. The proof is based on the following result. An endofunctor on a variety has a presentation by operations and equations iff it preserves sifted colimits. 1
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 11 (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.
Elementary canonical formulae: a survey on syntactic, algorithmic, and modeltheoretic aspects
 Advances in Modal Logic, volume 5, Kings College Publ
, 2005
"... abstract. In terms of validity in Kripke frames, a modal formula expresses a universal monadic secondorder condition. Those modal formulae which are equivalent to firstorder conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in ..."
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Cited by 11 (3 self)
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abstract. In terms of validity in Kripke frames, a modal formula expresses a universal monadic secondorder condition. Those modal formulae which are equivalent to firstorder conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called canonical. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main ideas and results, and outline further research perspectives. 1
Dimensions of content
 In
, 1994
"... NOTICE: Mhen goverment or other drawings, specifications or other data are used for any purpose other than in connection with a definitely related government procurement operation, the U. S. Government thereby incurs no responsibility, nor any obligation whatsoever; and the fact that the Governmen ..."
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Cited by 7 (0 self)
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NOTICE: Mhen goverment or other drawings, specifications or other data are used for any purpose other than in connection with a definitely related government procurement operation, the U. S. Government thereby incurs no responsibility, nor any obligation whatsoever; and the fact that the Government may have formu ated, furnished, or in any way supplied the said drawings, specifications, or other data is not to be regarded by implication or otherwise as in any manner licensing the holder or any other person or corporation, or conveying any rights or permission to manufacture, use or sell any patented invention that may in any way be related thereto. rA Iec pj YSFQ R~DG ELTtM ETIC Q NX IN 3c5 ps'REGION'
Agnostic possible worlds semantics
 In Logical Aspects of Computational Linguistics, number 7351 in Lecture Notes in Computer Science
, 2012
"... Abstract. Working within standard classical higherorder logic, we propose a possible worlds semantics (PWS) which combines the simplicity of the familiar Montague semantics (MS), in which propositions are sets of worlds, with the finegrainedness of the older but less wellknown tractarian semantic ..."
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Abstract. Working within standard classical higherorder logic, we propose a possible worlds semantics (PWS) which combines the simplicity of the familiar Montague semantics (MS), in which propositions are sets of worlds, with the finegrainedness of the older but less wellknown tractarian semantics (TS) of Wittgenstein and C.I. Lewis, wherein worlds are maximal consistent sets of propositions. The proposed agnostic PWS makes neither montagovian nor tractarian ontological commitments, but is consistent with (and easily extensible to) either alternative (among many others). It is technically straightforward and, we believe, capable of everything linguists need PWS to do, such as interfacing with a logical grammar and serving as a basis for dynamic semantics.
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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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...
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 5 (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
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
Some Sahlqvist completeness results for Coalgebraic Logics
"... Abstract. This paper presents a first step towards completenessviacanonicity results for coalgebraic modal logics. Specifically, we consider the relationship between classes of coalgebras for ωaccessible endofunctors and logics defined by Sahlqvistlike frame conditions. Our strategy is based on ..."
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Abstract. This paper presents a first step towards completenessviacanonicity results for coalgebraic modal logics. Specifically, we consider the relationship between classes of coalgebras for ωaccessible endofunctors and logics defined by Sahlqvistlike frame conditions. Our strategy is based on conjoining two wellknown approaches: we represent accessible functors as (equational) quotients of polynomial functors and then use canonicity results for boolean algebras with operators to transport completeness to the coalgebraic setting. 1