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International Workshop on Logic, Rationality and Interaction

LORI 2015: Logic, Rationality, and Interaction pp 255–267Cite as

Algebraic Semantics for Dynamic Dynamic Logic

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9394))

Abstract

Dynamic dynamic logic (DDL) is a generalisation of propositional dynamic logic PDL and dynamic epistemic logic. In this paper, we develop algebraic semantics for DDL without the constant program. We introduce inductive and continuous modal Kleene algebras for PDL and show the validity of reduction axioms in algebraic models and hence the algebraic completeness of DDL.

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Author information

Authors and Affiliations

  1. Institute for Logic and Intelligence, Southwest University, Chongqing, China

    Minghui Ma & Jeremy Seligman

  2. Department of Philosophy, University of Auckland, Aukland, New Zealand

    Jeremy Seligman

Authors
  1. Minghui Ma
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  2. Jeremy Seligman
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Corresponding author

Correspondence to Minghui Ma .

Editor information

Editors and Affiliations

  1. Dept of Comp Sci, Univ of Liverpool, Liverpool, United Kingdom

    Wiebe van der Hoek

  2. Department of Philosophy, Group in Logic & the Methodology of Sci. University of California, Berkeley, California, USA

    Wesley H. Holliday

  3. Institute of Philosophy of Mind and Cognition, National Yang-Ming University, Taipei, Taiwan

    Wen-fang Wang

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Ma, M., Seligman, J. (2015). Algebraic Semantics for Dynamic Dynamic Logic. In: van der Hoek, W., Holliday, W., Wang, Wf. (eds) Logic, Rationality, and Interaction. LORI 2015. Lecture Notes in Computer Science(), vol 9394. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48561-3_21

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  • DOI: https://doi.org/10.1007/978-3-662-48561-3_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48560-6

  • Online ISBN: 978-3-662-48561-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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