Symmetries in Modal Logics

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

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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: (download)

@INPROCEEDINGS{arec:symm13,
  author = {Areces, C. and Hoffmann, G. and Orbe, E.},
  title = {Symmetries in Modal Logics},
  booktitle = {Proceedings of the 7th Workshop on Logical and Semantic Frameworks,
	with Applications},
  year = {2013},
  editor = {Kesner, D. and Viana, P.},
  volume = {113},
  pages = {27-44},
  publisher = {Open Publishing Association},
  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},
  timestamp = {2013.06.24}
}

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