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 some Modal Logical Systems Defined in Connexion with Jaśakowski's Problem

Abstract: Publisher Summary This chapter focuses on some modal logical systems defined in connection with Jaśkowski's problem. Jaśkowski formulated the problem of finding logical systems that could be employed as underlying logics of deductive systems not devoid of inconsistency and presented one solution of the problem at the level of the propositional calculus. A normal modal system is a set of modal propositional formulas closed under substitution, detachement for material implication, and the rule of Godel. The chapter discusses various systems, properties of defined normal modal system, Kripke's system, axiomatics studies, Henkin semantics, semantical characterization, problems of normal modal system and its counterparts, and various theorems.

Lattice-Based Graded Logic: a Multimodal Approach

Abstract: Experts do not always feel very, comfortable when they have to give precise numerical estimations of certainty degrees. In this paper we present a qualitative approach which allows for attaching partially ordered symbolic grades to logical formulas. Uncertain information is expressed by means of parameterized modal operators. We propose a semantics for this multimodal logic and give a sound and complete axiomatization. We study the links with related approaches and suggest how this framework might be used to manage both uncertain and incomplere knowledge.

Expressive Power of Now and Then Operators

Abstract: Natural language provides motivation for studying modal backwards-looking operators such as "now", "then" and "actually" that evaluate their argument formula at some previously considered point instead of the current one. This paper investigates the expressive power over models of both propositional and first-order basic modal language enriched with such operators. Having defined an appropriate notion of bisimulation for first-order modal logic, I show that backwards-looking operators increase its expressive power quite mildly, contrary to beliefs widespread among philosophers of language and formal semanticists. That in turn presents a strong argument for the use of operator-based systems in the semantics of natural language, instead of systems with explicit quantification over worlds and times that have become a de-facto standard for such applications. The popularity of such explicit-quantification systems is shown to be based on the misinterpretation of a claim by Cresswell (Entities and indices, Kluwer, Dordrecht, 1990), which led many philosophers and linguists to assume (wrongly) that introducing "now" and "then" is expressively equivalent to explicitly quantifying over worlds and times.

How meaningful are modal operators

Abstract: (1966) How meaningful are modal operators? Australasian Journal of Philosophy: Vol 44, No 3, pp 331-337

Belief change and dynamic logic.

Abstract: In this paper we compare standard ways to perform belief change with attempts to model such change with dynamic modal operators. We address both belief expansion, belief contraction, belief revision, and update. Public announcement logic is an implementation of a belief expansion operator in a dynamic epistemic setting. The postulates of success and minimal change cannot be satisfied in their original AGM formulation. Dynamic doxastic logic provides various implementations of a belief revision operator in a dynamic epistemic setting. We provide an example of the application of such a dynamic doxastic semantics, which can also be seen as a realization of a proposal by Spohn. The purpose of this paper is to provide an overview of different approaches to dynamic logics for belief change, including some of our own contributions to the area, in a way that is accessible to an interdisciplinary audience. It does not contain new technical results not published elsewhere. However, the comparison of different approaches provides, we hope, new insights not seen before. A final version of this paper may include new technical results.