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Cut Free Labelled Sequent Calculus for Dynamic Logic of Relation Changers

  • Ryo HatanoEmail author
  • Katsuhiko Sano
  • Satoshi Tojo
Conference paper
Part of the Logic in Asia: Studia Logica Library book series (LIAA)

Abstract

Dynamic epistemic logic (\(\mathbf {DEL}\)) is known as a large family of logics that extend standard epistemic logic with dynamic operators. Such dynamic operators can be regarded as epistemic actions over Kripke semantics (or its variant). Therefore, \(\mathbf {DEL}\) is often used to model changes of agents’ knowledge, belief or preference over Kripke semantics in terms of dynamic operators in many literatures. As a variant of \(\mathbf {DEL}\), (van Benthem and Liu, J Appl Non-Classical Logics 17(2):157–18 2007; Liu, Reasoning about preference dynamics, Springer Science & Business Media, Berlin 2011) proposed dynamic logic of relation changers (\(\mathbf {DLRC}\)). They provided a general framework to capture many dynamic operators in terms of relation changing operation written in programs of propositional dynamic logic, and they also provided a sound and complete Hilbert-style axiomatization for \(\mathbf {DLRC}\). While \(\mathbf {DLRC}\) can cover many dynamic operators in a uniform manner, proof theory for \(\mathbf {DLRC}\) is not well-studied except the Hilbert-style axiomatization. Therefore, we propose a cut-free labelled sequent calculus for \(\mathbf {DLRC}\). We show that our sequent calculus is equipollent with the Hilbert-style axiomatization.

Keywords

Labelled Sequent Calculus Propositional Dynamic Logic Complete Hilbert-style Axiomatization Kripke Semantics Relation Changing Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We would like to thank an anonymous reviewer for his/her helpful comments to revise our manuscript. We would be grateful to the audiences and organizing committee of the joint conference of the 3rd Asian workshop on philosophical logic and the 3rd Taiwan philosophical logic colloquium (AWPL-TPLC 2016). During the conference, the first author was supported by travel grants from the organizing committee of AWPL-TPLC 2016. The work of the second author was partially supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant-in-Aid for Young Scientists (B) Grant Number 15K21025. The work of the second and the third authors were also supported by JSPS Core-to-Core Program (A. Advanced Research Networks).

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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Faculty of Science and TechnologyTokyo University of ScienceNodaJapan
  2. 2.Graduate School of LettersHokkaido UniversityHokkaidoJapan
  3. 3.School of Information ScienceJapan Advanced Institute of Science and TechnologyNomiJapan

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