## 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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