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.

Capturing Graded Knowledge and Uncertainty in a Modalized Fragment of OWL

Abstract: Natural language statements uttered in diagnosis (e.g., in medicine), but more general in daily life are usually graded, i.e., are associated with a degree of uncertainty about the validity of an assessment and is often expressed through specific verbs, adverbs, or adjectives in natural language. In this paper, we look into a representation of such graded statements by presenting a simple non-standard modal logic which comes with a set of modal operators, directly associated with the words indicating the uncertainty and interpreted through confidence intervals in the model theory. We complement the model theory by a set of RDFS-/OWL 2 RL-like entailment (if-then) rules, acting on the syntactic representation of modalized statements. Our interest in such a formalization is related to the use of OWL as the de facto language in today’s ontologies and its weakness to represent and reason about assertional knowledge that is uncertain or that changes over time.

S4LP and local realizability

Abstract: The logic S4LP combines the modal logic S4 with the justification logic LP, both axiomatically and semantically. We introduce a simple restriction on the behavior of constants in S4LP, having no effect on the LP sublogic. Under this restriction some powerful derived rules are established. Then these are used to show completeness relative to a semantics having what we call the local realizability property: at each world and for each formula true at that world there is a realization also true at that world, where a realization is the result of replacing all modal operators with explicit justification terms. This is a part of a project to understand the deeper aspects of Artemov's Realization Theorem.

Modal semantics, modal dynamics and the problem of state preparation

Abstract: It has been suggested that the Modal Interpretation of Quantum Mechanics (QM) is "incomplete" if it lacks a dynamics for possessed values. I argue that this is only one of two possible attitudes one might adopt toward a Modal Interpretation without dynamics. According to the other attitude, such an interpretation is a complete interpretation of QM as standardly formulated, an interpretation whose innovation is to attempt to make sense of the quantum realm without the expedient of novel physics. Then I explain why this attitude, though available, is unattractive. Without dynamics, the Modal Interpretation vanquishes the measurement problem only, it seems, to succumb to the problem of state preparation. On this view, the Modal Interpretation needs dynamics not to be an interpretation at all, but to be an adequate one. I review reasons to suspect that the dynamics which would best suit the Modal Interpretation--a dynamics equivalent to a set of two time transition probabilities of the sort used to solve the ...

The Reduction Method

Abstract: We obtain decidability results for propositional calculi using the reduction method. We treat languages containing one or two modal operators of the form □A, where □ could be necessity L or tense operators G, H. Let ◊ be ∼□∼. Before we begin with the body of this chapter, let us discuss other available methods for obtaining decidability, mainly through the finite model property. (For the convenience of the reader we shall also recall briefly some of the material of Chapters 8 and 9).

Description of fuzzy first-order modal logic based on constant domain semantics

Abstract: As an extension of the traditional modal logic, the fuzzy first-order modal logic is discussed in this paper. A description of fuzzy first-order modal logic based on constant domain semantics is given, and a formal system of fuzzy reasoning based on the semantic information of models of first-order modal logic is established. It is also introduced in this paper the notion of the satisfiability of the reasoning system and some properties associated with the satisfiability are proved.