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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Dissertation•
01 Jan 2001
TL;DR: This work proposed a first-order, many sorted and multimodal logic, including a new action operator that captures the notion of action of an agent in a role, which is used in the formal specification of institutional agents, societies of agents and of normative interactions between agents.
Abstract: The main objective of this work was to contribute to the formal study of concepts and models suited to the normative specification of organized collective entities, that also support a rigorous analysis of them.
Based on the legal concept of artificial person and on the legal relationships of mandate and representation, the concepts of role, action in a role, representation, contract and institutional agent are introduced. Such concepts are the basis for the characterization of a model for organized collective entities. They also allow the characterization of normative relationships that agents in a society may establish between each other. The formal characterization of those concepts in done through the definition of deontic and action modal logics, following the tradition initiated by S. Kanger, I. Porn and L. Lindahl. It is proposed a first-order, many sorted and multimodal logic, including a new action operator that captures the notion of action of an agent in a role. The properties of this logic are analyzed, and the soundness of the given axiomatization (with respect to the semantic defined which is based in the minimal models) is proved. This logic is used in the formal specification of institutional agents, societies of agents and of normative interactions between agents. With this logical model it is possible to analyze in a rigorous way the effects of agents actions in a society. Namely, it is possible to analyze the effects of an action of an agent, when he is acting in a role, in the actions of other agents, in the attribution of new obligations or permissions to the same agent or to other agents, or in the detection of non-ideal behaviour (unfulfillment of obligations).
Finally, some extensions to the proposed logic are discussed. Some new concepts are introduced as well as some modal operators that express them. The extended logic is then explored in the representation of problems related with the recognition of an action in a role and with the detection of frauds that may occur when an agent tries to act in a role.
3 citations
07 Oct 2019
TL;DR: Hybrid logics are an extension of modal logics where it is possible to refer to a specific state, thus allowing the description of what happens at specific states, equalities and transitions between them, making hybrid logics very desirable to work with relational structures.
Abstract: Hybrid logics are an extension of modal logics where it is possible to refer to a specific state, thus allowing the description of what happens at specific states, equalities and transitions between them. This makes hybrid logics very desirable to work with relational structures.
3 citations
TL;DR: The notion of a context in formal concept analysis and that of an approximation space in rough set theory are unified in this article to define a Kripke context, which gives rise to complex algebras based on the collections of protoconcepts and semiconcepts of the underlying context.
Abstract: The notion of a context in formal concept analysis and that of an approximation space in rough set theory are unified in this study to define a Kripke context. For any context (G,M,I), a relation on the set G of objects and a relation on the set M of properties are included, giving a structure of the form ((G,R), (M,S), I). A Kripke context gives rise to complex algebras based on the collections of protoconcepts and semiconcepts of the underlying context. On abstraction, double Boolean algebras (dBas) with operators and topological dBas are defined. Representation results for these algebras are established in terms of the complex algebras of an appropriate Kripke context. As a natural next step, logics corresponding to classes of these algebras are formulated. A sequent calculus is proposed for contextual dBas, modal extensions of which give logics for contextual dBas with operators and topological contextual dBas. The representation theorems for the algebras result in a protoconcept-based semantics for these logics.
3 citations
TL;DR: This special issue discusses temporal logics, a much investigated class of logics that deserves increased widespread recognition and application in engineering, a domain where other kinds of temporal models are by now a fairly standard part of the modelling toolbox.
Abstract: Logic-based models are thriving within artificial intelligence. A great number of new logics have been defined, and their theory investigated. Epistemic logics introduce modal operators for knowledge or belief; deontic logics are about norms, and introduce operators of deontic necessity and possibility (i.e., obligation or prohibition). And then we have a much investigated class—temporal logics—to whose application to engineering this special issue is devoted. This kind of formalism deserves increased widespread recognition and application in engineering, a domain where other kinds of temporal models (e.g., Petri nets) are by now a fairly standard part of the modelling toolbox.
3 citations
01 Jan 2008
TL;DR: The paper puts forth a formal definition of linguistic relevance in terms of logical semantics, and provides an axiomatization of it in modal logic.
Abstract: The paper shows how a specific notion of (ir)relevance can elegantly be captured in modal logic. More concretely, the paper puts forth a formal definition of linguistic relevance in terms of logical semantics, and provides an axiomatization of it in modal logic.
3 citations