Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Modal Logic of Transition Systems in the Topos of Trees

Colin Riba 1, 2 Guilhem Jaber 1, 2
2 PLUME - Preuves et Langages
LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : 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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [34 references]  Display  Hide  Download
Contributor : Colin Riba <>
Submitted on : Sunday, October 22, 2017 - 6:00:03 PM
Last modification on : Wednesday, November 20, 2019 - 3:11:04 AM
Long-term archiving on: : Tuesday, January 23, 2018 - 12:26:58 PM


Files produced by the author(s)


  • HAL Id : hal-01620992, version 1



Colin Riba, Guilhem Jaber. Modal Logic of Transition Systems in the Topos of Trees. 2017. ⟨hal-01620992⟩



Record views


Files downloads