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Modal Logics of Reactive Frames

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Abstract

A reactive graph generalizes the concept of a graph by making it dynamic, in the sense that the arrows coming out from a point depend on how we got there.

This idea was first applied to Kripke semantics of modal logic in [2]. In this paper we strengthen that unimodal language by adding a second operator. One operator corresponds to the dynamics relation and the other one relates paths with the same endpoint. We explore the expressivity of this interpretation by axiomatizing some natural subclasses of reactive frames.

The main objective of this paper is to present a methodology to study reactive logics using the existent classic techniques.

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Authors and Affiliations

  1. King’s College, London, UK

    Dov M. Gabbay & Sérgio Marcelino

  2. Bar-Alan University, Ramat Gan, Israel

    Dov M. Gabbay

  3. University of Luxembourg, Luxembourg, Belgium

    Dov M. Gabbay

  4. Instituto de Telecomunicações, Lisboa, Portugal

    Sérgio Marcelino

Authors
  1. Dov M. Gabbay
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  2. Sérgio Marcelino
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Correspondence to Dov M. Gabbay.

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Gabbay, D.M., Marcelino, S. Modal Logics of Reactive Frames. Stud Logica 93, 405 (2009). https://doi.org/10.1007/s11225-009-9214-1

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  • DOI: https://doi.org/10.1007/s11225-009-9214-1

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