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.

Modal Logics and mu-Calculi: An Introduction

Abstract: We briefly survey the background and history of modal and temporal logics. We then concentrate on the modal mu-calculus, a modal logic which subsumes most other commonly used logics. We provide an informal introduction, followed by a summary of the main theoretical issues. We then look at model-checking, and finally at the relationship of modal logics to other formalisms.

Algebraic Semantics for Modal Logics I

Abstract: This paper is a sequel to [7], and the terminology of [7] is largely presupposed here. In [7], the algebraic methods of McKinsey-Tarski were employed and extended to yield semantic results of a Kripke kind for a class of relatively weak modal logics, the strongest of which was the Feysvon Wright system T. Deontic versions of both T and E2, called T(D) and D2, and even weaker systems, were handled. The main aim of the present paper is to extend these results to stronger systems of modal logic. Thus the Lewis systems S2–S5, the Brouwersche system B of Kripke [4], the systems E3–E5 of [5], and Łukasiewicz's modal logic, as well as certain new systems, are considered.Certain modifications of the method of [7] have proved convenient. Thus in Section I, some further results concerning model structures are proved in order that the relationship between S2 and E2, S3 and E3, can be properly stated; in particular, the notions of a refined and connected model structure play a pervasive role throughout.

The Present Perfect as an Epistemic Modal

Abstract: In a number of languages from various language families, the morphology of the present perfect or a form historically derived from the present perfect, expresses a particular evidential category, one that indicates the availability of indirect evidence for the truth of a proposition (the exact interpretation i s discussed in more detai l in the next two sections) . l The phenomenon, to which I give the name PERFECT OF EVIDENTIALITY (PE), i s i l lustrated in ( I ) :

Properties of independently axiomatizable bimodal logics

Abstract: In mono-modal logic there is a fair number of high-powered results on completeness covering large classes of modal systems, witness for example Fine [74,85] and Sahlqvist [75]. Mono-modal logic is therefore a well-understood subject in contrast to poly-modal logic where even the most elementary questions concerning completeness, decidability etc. have been left unanswered. Given that so many applications of modal logic one modality is not sufficient, the lack of general results is acutely felt by the “users” of modal logics, contrary to logicians who might entertain the view that a deep understanding of modality alone provides enough insight to be able to generalize the results to logics with several modalities. Although this view has its justification, the main results we are going to prove are certainly not of this type, for they require a fundamentally new technique. The results obtained are called transfer theorems in Fine and Schurz [91] and are of the following type. Let L 63 ⊥ be an independently axiomatizable bimodal logic and L2 as well as L its mono-modal fragments. Then L has a property P iff L2 and L have P . Properties which will be discussed are completeness, finite model property, compactness, persistence, interpolation and Hallden-completeness. In our discussion we will show transfer theorems for the most simple case when there are just two modal operators but it will be clear that the proof works in the general case as well.