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: The expressive capabilities of multi-modal logics of minimal knowledge are illustrated to provide a formal semantics to peer-to-peer data integration systems, which constitute one of the most recent and complex architectures for distributed information systems.
Abstract: In this paper we introduce multi-modal logics of minimal knowledge. Such a family of logics constitutes the first proposal in the field of epistemic nonmonotonic logic in which the three following aspects are simultaneously addressed: (1) the possibility of formalizing multiple agents through multiple modal operators; (2) the possibility of using first-order quantification in the modal language; (3) the possibility of formalizing nonmonotonic reasoning abilities for the agents modeled, based on the principle of minimal knowledge. We illustrate the expressive capabilities of multi-modal logics of minimal knowledge to provide a formal semantics to peer-to-peer data integration systems, which constitute one of the most recent and complex architectures for distributed information systems.
2 citations
Proceedings Article•
01 Jan 2004
TL;DR: Applying the extended modal logic operators Dα over IFSs, a new class of two–valued inclusion indicators is constructed, parallelling and clarifying earlier work on (direct) generalizations of fuzzy inclusion measures.
Abstract: In this paper, we revisit the notion of inclusion for intuitionistic fuzzy sets (IFSs). Applying the extended modal logic operators Dα over IFSs, we construct a new class of two–valued inclusion indicators; we compare it to the original proposal from [1]; and finally we exploit it to define an intuitively meaningful notion of graded inclusion indicators over IFSs, parallelling and clarifying earlier work on (direct) generalizations of fuzzy inclusion measures.
2 citations
TL;DR: In this article, it was shown that the category of multi-relational Kripke frames for monomodal logics is dually equivalent to that of neighborhood frames.
Abstract: In this paper, we show that the category of $$\kappa $$
-additive complete atomic modal algebras is dually equivalent to the category of $$\kappa $$
-downward directed multi-relational Kripke frames, for any cardinal number $$\kappa $$
. Multi-relational Kripke frames are not Kripke frames for multi-modal logics, but frames for monomodal logics in which the modal operator $$\Diamond $$
does not distribute over (possibly infinite) disjunction, in general. We first define homomorphisms of multi-relational Kripke frames, and discuss the relationship between the category of multi-relational Kripke frames and the category of neighborhood frames. Then we give two kinds of proofs for the duality theorem between the category of $$\kappa $$
-additive complete atomic modal algebras and the category of $$\kappa $$
-downward directed multi-relational Kripke frames. The first proof is given by making use of Dosen duality theorem between the category of modal algebras and the category of neighborhood frames, and the second one is based on the idea given by Minari.
2 citations
TL;DR: This work defines the method for logics arising from the combination of linear tense operators with an “orthogonal” S5-like modality, and shows that the existence of a model for a given set of formulas is equivalent to a suitable set of partial models, called mosaics.
Abstract: We present an extension of the mosaic method aimed at capturing many-dimensional modal logics. As a proof-of-concept, we define the method for logics arising from the combination of linear tense operators with an “orthogonal” S5-like modality. We show that the existence of a model for a given set of formulas is equivalent to the existence of a suitable set of partial models, called mosaics, and apply the technique not only in obtaining a proof of decidability and a proof of completeness for the corresponding Hilbert-style axiomatization, but also in the development of a mosaic-based tableau system. We further consider extensions for dealing with the case when interactions between the two dimensions exist, thus covering a wide class of bundled Ockhamist branching-time logics, and present for them some partial results, such as a non-analytic version of the tableau system.
2 citations
29 Oct 2018
TL;DR: In this article, a logic that combines propositional logic, relevance logic, and modal logic to reason about Boolean contact algebras is presented, and a natural deduction system for this logic is presented.
Abstract: Boolean contact algebras constitute a suitable algebraic theory for qualitative spatial reasoning. They are Boolean algebras with an additional contact relation grasping the topological aspect of spatial entities. In this paper we present a logic that combines propositional logic, relevance logic, and modal logic to reason about Boolean contact algebras. This is done in two steps. First, we use the relevance logic operators to obtain a logic suitable for Boolean algebras. Then we add modal operators that are based on the contact relation. In both cases we present axioms that are equivalent to requirement that every frame for the logic is indeed a Boolean algebra resp. Boolean contact algebra. We also provide a natural deduction system for this logic by defining introduction and eliminations rules for each logical operator. The system is shown to be sound. Furthermore, we sketch an implementation of the natural deduction system in the functional programming language and interactive theorem prover Coq.
2 citations