Abstract
The 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.
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Bílková, M., Dostál, M. (2013). Many-Valued Relation Lifting and Moss’ Coalgebraic Logic. In: Heckel, R., Milius, S. (eds) Algebra and Coalgebra in Computer Science. CALCO 2013. Lecture Notes in Computer Science, vol 8089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40206-7_7
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