Symmetries in Modal Logics: A Coinductive Approach

C. Areces, G. Hoffmann, and E. Orbe. Symmetries in Modal Logics: A Coinductive Approach. In Proceedings of the 7th Workshop on Logical and Semantic Frameworks, with Applications (LSFA 2012), Rio de Janeiro, 2012.

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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 \phi then \phi |= \psi if and only if \phi |= \sigma(\psi).

BibTeX

@InProceedings{Areces2012b,
  author =       "C. Areces and G. Hoffmann and E. Orbe",
  booktitle =    "Proceedings of the 7th Workshop on Logical and
                 Semantic Frameworks, with Applications (LSFA 2012)",
  title =        "Symmetries in Modal Logics: {A} Coinductive Approach",
  year =         "2012",
  address =      "Rio de Janeiro",
  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 \phi then \phi |= \psi if and
                 only if \phi |= \sigma(\psi).",
  owner =        "areces",
  timestamp =    "2012.08.04",
}