Modal Logic of Transition Systems in the Topos of Trees
Résumé
We investigate the adjunction between the category of transition systems (with not nec. bounded morphisms) and the topos of trees S from the perspective of the basic modal logic K on transition systems. More specifically, we show how the modal logic K over an object of S seen as a transition system can be lifted back as a subobject of S. This relies on the usual mutually transpose formulations of modal satisfaction as either a map of transition system or as a map of Boolean algebras with operators. Moreover, thanks to the usual geometric morphism from the Boolean topos Psh(|N * |) of presheaves over the discrete category of natural numbers to S , we can give a characterization of modal satisfaction within S as a map from formulae to total subobjects of S whose image in the Boolean topos Psh(|N * |) is an internal map of Boolean algebras.
Domaines
Logique en informatique [cs.LO]Origine | Fichiers produits par l'(les) auteur(s) |
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