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.
Papers published on a yearly basis
Papers
More filters
Posted Content•
TL;DR: In this article, the authors consider modal propositional logic and look for the constraints that are imposed to the propositions of the special type $\Box a$ by the structure of the relevant finite Kripke frame.
Abstract: In the present paper we consider modal propositional logic and look for the constraints that are imposed to the propositions of the special type $\Box a$ by the structure of the relevant finite Kripke frame. We translate the usual language of modal propositional logic in terms of notions of commutative algebra, namely polynomial rings, ideals, and bases of ideals. We use extensively the perspective obtained in previous works in Algebraic Statistics. We prove that the constraints on $\Box a$ can be derived through a binomial ideal containing a toric ideal and we give sufficient conditions under which the toric ideal fully describes the constraints.
TL;DR: In this article, the authors give a representation of physical properties in terms of modal operators on Heyting algebras, and introduce a classical type study of the mentioned properties.
Abstract: In the framework of the topos approach to quantum mechanics we give a representation of physical properties in terms of modal operators on Heyting algebras. It allows us to introduce a classical type study of the mentioned properties.
18 May 2023
TL;DR: The COOL 2 reasoner as discussed by the authors provides uniform reasoning algorithms that are easily instantiated to particular, concretely given modal fixpoint logics, e.g., probabilities, multi-player games, weights, or neighbourhood structures.
Abstract: There is a wide range of modal logics whose semantics goes beyond relational structures, and instead involves, e.g., probabilities, multi-player games, weights, or neighbourhood structures. Coalgebraic logic serves as a unifying semantic and algorithmic framework for such logics. It provides uniform reasoning algorithms that are easily instantiated to particular, concretely given logics. The COOL 2 reasoner provides an implementation of such generic algorithms for coalgebraic modal fixpoint logics. As concrete instances, we obtain in particular reasoners for the aconjunctive and alternation-free fragments of the graded $\mu$-calculus and the alternating-time $\mu$-calculus. We evaluate the tool on standard benchmark sets for fixpoint-free graded modal logic and alternating-time temporal logic (ATL), as well as on a dedicated set of benchmarks for the graded $\mu$-calculus.
14 May 2012
TL;DR: Some fundamental properties of monotone modal operators on (non-commutative) residuated lattices (RL) are proved and a simple characterization of pseudo MV-algebras in terms of residency lattices is given.
Abstract: We prove some fundamental properties of monotone modal operators on (non-commutative) residuated lattices (RL). Moreover we give a simple characterization of pseudo MV-algebras in terms of residuated lattices.
09 Oct 2006
TL;DR: In this work an original method for coping with agents' incomplete knowledge is introduced and how neural network approach might be used in order to determined some tendencies to occurrence specific states of objects.
Abstract: In this work an original method for coping with agents' incomplete knowledge is introduced. This method called the algorithm for the messages generation is applied by the cognitive agents when the states of external objects can not be directly perceived. To approximate the current states of objects all agent's experience as temporal data base is taken into account. As a result of the algorithm the logic formulas with modal operators are generated. One of the steps of proposed algorithm is the classification of the observations. It is shown how neural network approach might be used in order to determined some tendencies to occurrence specific states of objects.