## 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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