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Normal modal logic

About: Normal modal logic is a research topic. Over the lifetime, 2649 publications have been published within this topic receiving 75735 citations.


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TL;DR: This work presents a straightforward embedding of modal nonmonotonic logics into default logic and shows how this embedding can be applied to deterministic and non- deterministic systems.
Abstract: We present a straightforward embedding of modal nonmonotonic logics into default logic.
Journal ArticleDOI
TL;DR: In this article, a general criterion for cut elimination in sequent calculi for propositional modal logics was developed, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system.
Abstract: We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies also to a wide variety of logics outside the realm of normal modal logic. We give extensive example instantiations of our framework to various conditional logics. For these, we obtain fully internalised calculi which are substantially simpler than those known in the literature, along with leaner proofs of cut elimination and complexity. In one case, conditional logic with modus ponens and conditional excluded middle, cut elimination and complexity were explicitly stated as open in the literature.
01 Jan 2009
TL;DR: In this article, a framework for generating the models of Epistemic Temporal Logic (ETL) from the model of Dynamic Epistemics (DEL) is presented.
Abstract: van Bentham et al. (Merging frameworks for interaction: DEL and ETL, 2007) provides a framework for generating the models of Epistemic Temporal Logic (ETL: Fagin et al., Reasoning about knowledge, 1 995; Parikh and Ramanujam, Journal of Logic, Language, and Information, 2003) from the models of Dynamic Epistemic
01 Jan 2010
TL;DR: This talk describes several algorithmic approaches to the famous Sahlqvist theorem for first-order definability and completeness in modal logic, which describes by a direct syntactic definition a large effective class of modal formulas which are first- order definable and canonical.
Abstract: One of the nice features of modal languages is that sometimes they can talk about abstract properties of the corresponding semantic structures. For instance the truth of the modal formula p ⇒ p in the Kripke frame (W, R )i s equivalent to the reflexivity of the relation R. Using a terminology from modal logic [13], we say that the condition of reflexivity – (∀x)(xRx), is a first-order equivalent of the modal formula p ⇒ p, or, that the formula p ⇒ p is first-order definable by the condition (∀x)(xRx). More over, adding the formula p ⇒ p to the axioms of the minimal modal logic K we obtain a complete logic with respect to the class of reflexive frames and the completeness proof can be done by the well known in modal logic canonical method (such formulas are called canonical). Let us note that definability and completeness are some of the good features in the applications of modal logic, and hence it is important to have algorithmic methods for establishing such properties. In our talk we will describe several algorithmic approaches to this problem. The first algorithmic result of such a kind is the famous Sahlqvist theorem [9] for first-order definability and completeness in modal logic. It describes by a direct syntactic definition a large effective class of modal formulas (subsequently called Sahlqvist formulas) which are first-order definable and canonical, and more over it presents an algorithm for computing their first-order equivalents. For a long time the class of Sahlqvist formulas was considered as the optimal syntactically defined class with these two properties. Sahlqvist theorem was recently generalized in several ways extending considerably the original Sahlqvist class for the most general modal languages [8,10]. This method will be called syntactical, because it gives explicit syntactical definition of the class of formulas on which definability algorithm works. Extending in such a way the Sahlqvist class has some unpleasant features, the definitions of the extension are quite complicate and the formulas in the extension have numerous syntactic limitations.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202334
202281
20216
20207
201913
201818