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Completeness theorems for reactive modal logics

Completeness theorems for reactive modal logics Ann Math Artif Intell (2012) 66:81–129 DOI 10.1007/s10472-012-9315-9 Dov Gabbay Published online: 28 September 2012 © Springer Science+Business Media B.V. 2012 Keywords Modal logic · Temporal logic Mathematics Subject Classifications (2010) 03B44 · 03B45 1 Overview This paper gives completeness theorems for some basic reactive Kripke models and semantics. This section will 1. Introduce reactivity 2. Discuss and compare the kind of Kripke semantics we get with reactivity 3. Explain the challenges in obtaining completeness theorems 1.1 Fibring and reactivity Our starting point is an ordinary Kripke model for modal logic. This has the form m = (S, R, a) where S is a nonempty set of worlds, a ∈ S is the initial (actual) world and R ⊆ S × S is the accessibility relation. The model also has an assignment h, giving for each atomic q a subset h(q) ⊆ S. We shall focus on R. D. Gabbay Bar-Ilan University, Ramat-Gan, Israel D. Gabbay ( ) Department of Computer Science, King’s College London, London, UK e-mail: dov.gabbay@kcl.ac.uk D. Gabbay University of Luxembourg, Luxembourg City, Luxembourg 82 D. Gabbay Let us look at how the modality ♦ is evaluated at a point t ∈ S. This is done http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

Completeness theorems for reactive modal logics

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References (7)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer Science+Business Media B.V.
Subject
Computer Science; Artificial Intelligence (incl. Robotics); Mathematics, general; Computer Science, general; Statistical Physics, Dynamical Systems and Complexity
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/s10472-012-9315-9
Publisher site
See Article on Publisher Site

Abstract

Ann Math Artif Intell (2012) 66:81–129 DOI 10.1007/s10472-012-9315-9 Dov Gabbay Published online: 28 September 2012 © Springer Science+Business Media B.V. 2012 Keywords Modal logic · Temporal logic Mathematics Subject Classifications (2010) 03B44 · 03B45 1 Overview This paper gives completeness theorems for some basic reactive Kripke models and semantics. This section will 1. Introduce reactivity 2. Discuss and compare the kind of Kripke semantics we get with reactivity 3. Explain the challenges in obtaining completeness theorems 1.1 Fibring and reactivity Our starting point is an ordinary Kripke model for modal logic. This has the form m = (S, R, a) where S is a nonempty set of worlds, a ∈ S is the initial (actual) world and R ⊆ S × S is the accessibility relation. The model also has an assignment h, giving for each atomic q a subset h(q) ⊆ S. We shall focus on R. D. Gabbay Bar-Ilan University, Ramat-Gan, Israel D. Gabbay ( ) Department of Computer Science, King’s College London, London, UK e-mail: dov.gabbay@kcl.ac.uk D. Gabbay University of Luxembourg, Luxembourg City, Luxembourg 82 D. Gabbay Let us look at how the modality ♦ is evaluated at a point t ∈ S. This is done

Journal

Annals of Mathematics and Artificial Intelligence – Springer Journals

Published: Sep 28, 2012

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