Symmetries in Modal Logics: A Coinductive Approach

Areces, C., Hoffmann, G., and Orbe, E.. 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, September 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: (download)

@INPROCEEDINGS{arec:symm12,
  author = {Areces, C. and Hoffmann, G. and Orbe, E.},
  title = {Symmetries in Modal Logics: A Coinductive Approach},
  booktitle = {Proceedings of the 7th Workshop on Logical and Semantic Frameworks,
	with Applications (LSFA 2012)},
  year = {2012},
  address = {Rio de Janeiro},
  month = {September},
  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}
}

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