Elementary Canonical Formulae: A Survey on Syntactic, Algorithmic, and Modeltheoretic Aspects

In Renate Schmidt, Ian Pratt-Hartmann, Mark Reynolds & Heinrich Wansing (eds.), Advances in Modal Logic, Volume 5. Kings College London Publ.. pp. 17-51 (2005)
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Abstract
In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called canonical. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main ideas and results, and outline further research perspectives.
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