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.

Logics of Contingency

Abstract: We introduce the logic of positive and negative contingency. Together with modal operators of necessity and impossibility they allow to dispense of negation. We study classes of Kripke models where the number of points is restricted, and show that the modalities reduce in the corresponding logics.

Temporalization of Modal Logic

Abstract: A temporalization of a modal logic is a temporal logic containing the modal logic and the temporalization problem is the problem of construction and classification of temporalization for a given modal logic. A temporal logic carries two dual pairs of modal operators and . By taking each pair of them, one obtains a normal modal logic. In this situation, we refer to the temporal logic as a strict temporalization of the normal modal logic. Under mathematical morphological investigation over non-classical logics, the author showed that an adjoint pair of modal operators gives rise to a temporal logic ([1]). This result can be used to show the existence of a temporalization for a normal modal logic. By combining with canonical models, mathematical morphology illustrates the relationship between a modal logic and its temporalization. In this article, we will show how morphological analysis is applied to the temporalization problem.

Reasoning about Context Information in Cloud Computing Environments

Abstract: The notion of context provides flexibility and adaptation to cloud computing services. Location, time identity and activity of users are examples of primary context types. The motivation of this paper is to formalize reasoning about context information in cloud computing environments. To formalize such context-aware reasoning, the logic LCM of context-mixture is introduced based on a Gentzen-type sequent calculus for an extended resource-sensitive logic. LCM has a specific inference rule called the context-mixture rule, which can naturally represent a mechanism for merging formulas with context information. Moreover, LCM has a specific modal operator called the sequence modal operator, which can suitably represent context information. The cut-elimination and embedding theorems for LCM are proved, and a fragment of LCM is shown to be decidable. These theoretical results are intended to provide a logical justification of context-aware cloud computing service models such as a flowable service model.

Reply to Baldwin on De Re Modalities

Abstract: However, Baldwin claims that (io) will not do as an analysis of the proposition in question, and consequently that my approach to de re modalities is 'incompatible with the intended understanding of essentialist claims' (p. 255), and he suggests that the mistake lies in my trying to use a sentential modal operator where only a predicate modal operator can do the job properly. Here I shall try to show that, while (io) may not be the most perspicuous way of analysing Baldwin's essentialist proposition, I was not mistaken in using a sentential modal operator in dealing with de re modalities. Baldwin's argument turns on the issue of how we are to interpret a sentence of the form '(Ax)(OFx)[a]' (the first conjunct of (io) and the negation of its second being sentences of this form). He considers first the proposal (based on a theory of Stalnaker and Thomason) that '(Ax)(oFx)[a]' is true iff the thing which is actually a is F in all possible worlds. But Baldwin points out that this proposal inevitably makes (io)'s first conjunct false, thus failing to do justice to the essentialist claim, since by this account that conjunct 'is true iff the person who is actually Elizabeth II was begotten by George VI in all possible worlds', yet 'neither George VI nor Elizabeth II exist in all possible worlds' (p. 255). He therefore suggests that we consider instead the strategy of 'taking the modal sentence operator in (io) to express "weak necessity". . . i.e. truth only in all those possible worlds in which the things denoted by the terms within the scope of the modal operator exist' (ibid.). But then it seems we fall foul of (i o)'s second conjunct, since 'we want it not to be essential of George VI that he begat Elizabeth II even though in all possible worlds in which she . . exist[s], George VI did beget Elizabeth II' (ibid.). Baldwin goes on to remark: