Many-Valued Relation Lifting and Moss’ Coalgebraic Logic

Abstract

AbstractThe notion of relation lifting can be generalised to work with many-valued relations while retaining many vital properties of the “classical” relation lifting. We show that polynomial endofunctors of the category of sets and mappings admit \(\mathcal{V}\)-relation lifting for relations taking values from a commutative quantale \(\mathcal{V}\). Using the technique of functor presentations, we then show that every finitary weak pullback preserving functor admits a \(\mathcal{V}\)-relation lifting for \(\mathcal{V}\) being a complete Heyting algebra. As an application of the many-valued lifting we inspect the notion of many-valued bisimulation and we introduce an expressive many-valued variant of Moss’ logic for T-coalgebras, parametric in the functor T.Keywordscoalgebracoalgebraic logicrelation liftingmany-valued logic