Symmetries in Modal Logics

C. Areces, G. Hoffmann, and E. Orbe. Symmetries in Modal Logics. Electronic Proceedings in Theoretical Computer Science, 113:27–44, Open Publishing Association, 2013. Proceedings of the 7th Workshop on Logical and Semantic Frameworks, with Applications

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Abstract

We generalize the notion of symmetries of propositional formulas in conjunctive normal form to modal formulas. Our framework uses the coinductive models introduced in [4] and, hence, the results apply to a wide class of modal logics including, for example, hybrid logics. Our main result shows that the symmetries of a modal formula preserve entailment: if $\sigma$ is a symmetry of $\varphi$ then $\varphi \models \psi$ if and only if $\varphi \models \sigma(\psi)$.

BibTeX

@Article{Areces2013b,
  author =       "C. Areces and G. Hoffmann and E. Orbe",
  note =         "Proceedings of the 7th Workshop on Logical and
                 Semantic Frameworks, with Applications",
  title =        "Symmetries in Modal Logics",
  year =         "2013",
  editor =       "D. Kesner and P. Viana",
  pages =        "27--44",
  publisher =    "Open Publishing Association",
  volume =       "113",
  abstract =     "We generalize the notion of symmetries of
                 propositional formulas in conjunctive normal form to
                 modal formulas. Our framework uses the coinductive
                 models introduced in [4] and, hence, the results apply
                 to a wide class of modal logics including, for example,
                 hybrid logics. Our main result shows that the
                 symmetries of a modal formula preserve entailment: if
                 $\sigma$ is a symmetry of $\varphi$ then $\varphi
                 \models \psi$ if and only if $\varphi \models
                 \sigma(\psi)$.",
  journal =      "Electronic Proceedings in Theoretical Computer
                 Science",
  owner =        "areces",
  ISSN =         "2075-2180",
  timestamp =    "2013.06.24",
}