Topic
Modal operator
About: Modal operator is a research topic. Over the lifetime, 1151 publications have been published within this topic receiving 22865 citations. The topic is also known as: modal connective.
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TL;DR: In this paper, the problem of introducing variables in temporal logic programs under the formalism of Temporal Equilibrium Logic, an extension of Answer Set Programming for dealing with linear-time modal operators, is considered.
Abstract: In this note, we consider the problem of introducing variables in temporal logic programs under the formalism of Temporal Equilibrium Logic, an extension of Answer Set Programming for dealing with linear-time modal operators. To this aim, we provide a definition of a first-order version of Temporal Equilibrium Logic that shares the syntax of first-order Linear-time Temporal Logic but has different semantics, selecting some Linear-time Temporal Logic models we call temporal stable models. Then, we consider a subclass of theories (called splittable temporal logic programs) that are close to usual logic programs but allowing a restricted use of temporal operators. In this setting, we provide a syntactic definition of safe variables that suffices to show the property of domain independence – that is, addition of arbitrary elements in the universe does not vary the set of temporal stable models. Finally, we present a method for computing the derivable facts by constructing a non-temporal logic program with variables that is fed to a standard Answer Set Programming grounder. The information provided by the grounder is then used to generate a subset of ground temporal rules which is equivalent to (and generally smaller than) the full program instantiation.
3 citations
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TL;DR: In this paper, the modal formulae that can be derived in Multiplicative Additive Linear Logic (MALL) and some extensions by using Tarksi's extensional modal operators are examined.
Abstract: We briefly examine the modal formulae that can be derived in Multiplicative Additive Linear Logic (MALL) and some extensions by using Tarksi's extensional modal operators. We also breifly compare this with a substructural form of the modal logic K.
3 citations
22 Jul 2008
TL;DR: Examples proofs are presented for both the negations and the modal operators to show that the results from Intuitionistic Fuzzy Sets carry over to the extended versions incorporating contradictory evidence.
Abstract: Some relations between intuitionistic fuzzy negations and intuitionistic fuzzy modal operations (from standard type) are studied. In particular versions of negation are extended to deal with contradictory evidence. Example proofs are presented for both the negations and the modal operators to show that the results from Intuitionistic Fuzzy Sets carry over to the extended versions incorporating contradictory evidence.
3 citations
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TL;DR: This paper provides an axiom system that captures the authors' desiderata, and shows that it has a semantics that corresponds to it, and provides a complete axiomatization for satisfiability in the logic K45.
Abstract: Levesque introduced a notion of ``only knowing'', with the goal of capturing certain types of nonmonotonic reasoning. Levesque's logic dealt with only the case of a single agent. Recently, both Halpern and Lakemeyer independently attempted to extend Levesque's logic to the multi-agent case. Although there are a number of similarities in their approaches, there are some significant differences. In this paper, we reexamine the notion of only knowing, going back to first principles. In the process, we simplify Levesque's completeness proof, and point out some problems with the earlier definitions. This leads us to reconsider what the properties of only knowing ought to be. We provide an axiom system that captures our desiderata, and show that it has a semantics that corresponds to it. The axiom system has an added feature of interest: it includes a modal operator for satisfiability, and thus provides a complete axiomatization for satisfiability in the logic K45.
3 citations
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TL;DR: This paper provides a direct, choice-free proof of the equivalence of MKRFrm and MDV, and details connections between modal compact regular frames and the Vietoris construction for frames, and how it is linked to modal de Vries algebras.
Abstract: In Bezhanishvili et al. (2012) we introduced the category MKHaus of modal compact Hausdorff spaces, and showed these were concrete realizations of coalgebras for the Vietoris functor on compact Hausdorff spaces, much as modal spaces are coalgebras for the Vietoris functor on Stone spaces. Also in Bezhanishvili et al. (2012) we introduced the categories MKRFrm and MDV of modal compact regular frames, and modal de Vries algebras as algebraic counterparts to modal compact Hausdorff spaces, much as modal algebras are algebraic counterparts to modal spaces. In Bezhanishvili et al. (2012), MKRFrm and MDV were shown to be dually equivalent to MKHaus, hence equivalent to one another. Here we provide a direct, choice-free proof of the equivalence of MKRFrm and MDV. We also detail connections between modal compact regular frames and the Vietoris construction for frames (Johnstone 1982, 1985), discuss a Vietoris construction for de Vries algebras, and how it is linked to modal de Vries algebras. Also described is an alternative approach to the duality of MKRFrm and MKHaus obtained by using modal de Vries algebras as an intermediary.
3 citations