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.

On Brouwer’s Intuitionism and Intuitionistic Fuzziness

Abstract: Aristotle made the first steps to the establishment of the mathematical logic by giving ideas for the concepts “sentence” and “predicate”; the fundamental logical functions as conjunction, disjunction and negation, the logical quantifiers, modal operators, and many others. He was the first who justified the need for axioms and presented the first examples of such. For 23 centuries one of his proposed axioms—the Law of Excluded Middle (LEM)—has been among the main tools for proving mathematical assertions.

Logic and Modal Intuitions

Abstract: Claims concerning what is or is not possible abound in contemporary phi losophy. The epistemology of such claims, however, remains largely unex plored. Anything imaginable is possible, we are told, with the proviso that imag ination be governed by logic. Many who defend this methodology argue that logic frees us from recourse to some mysterious a priori faculty of intuition. Anything is possible so long as it does not contain a contradiction?and we don't need intuition to tell us what is contradictory, just logic. Logic is thus supposed to provide us with a non-mysterious, intuition-free, modal epistemology. The purpose of this paper is to argue that logic does not deliver on this promise. The argument proceeds along two fronts. First, I argue that logic is not sufficient for the task. Not only are there consistent but impossible propositions, there are even inconsistent propositions that are possible. Second, and more fundamen tally, I question the epistemic independence of appeals to logical consistency. I will argue that in judging a proposition to be consistent we rely upon our intu itions concerning what is possible. In other words, our modal beliefs undergird our judgments about consistency and not vice-versa.

A Uniform Approach to Three-Valued Semantics for μ-Calculus on Abstractions of Hybrid Automata

Abstract: ion/refinement methods play a central role in the analysis of hybrid automata, that are rarely decidable. Soundness (of evaluated properties) is a major challenge for these methods, since abstractions can introduce unrealistic behaviors. In this paper, we consider the definition of a three-valued semantics for μ -calculus on abstractions of hybrid automata. Our approach relies on two steps: First, we develop a framework that is general in the sense that it provides a preservation result that holds for several possible semantics of the modal operators. In a second step, we instantiate our framework to two particular abstractions. To this end, a key issue is the consideration of both over- and under-approximated reachability analysis, while classic simulation-based abstractions rely only on overapproximations, and limit the preservation to the universal (μ -calculus') fragment. To specialize our general result, we consider (1) so-called discrete bounded bisimulation abstractions, and (2) modal abstractions based on may/must transitions.

A BDMI-VSK-T logic-based formal model in war simulation

Abstract: With the cross-disciplinary development of agent technology and war simulation technology, there are many problems when classical BDI logic is used in war simulation. Aiming at the characteristic of agent in war simulation, the BDMIVSK- T model frame is built, which combines with classic BDI-VSK-T model and imports a non-normal modal operator mission. Basic axioms and interaction axioms in BDMI-VSK-T logic are discussed and its soundness and completeness are proved. It is also proved that operator mission avoid the side-effect and the logical omniscience problem.