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We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the existence of a distributive law of T over the powerset monad on categories, one is the preservation by T of exactness of certain squares. Both characterisations are generalisations of the classical results known for set functors: the first characterisation generalises the existence of a distributive law over the genuine powerset monad, the second generalises preservation of weak pullbacks. The results presented in this paper enable us to compute predicate liftings of endofunctors of, for example, generalised (ultra)metric spaces. We illustrate this by studying the coalgebraic cover modality in this setting.
We revisit two well-established verification techniques, $k$-induction and bounded model checking (BMC), in the more general setting of fixed point theory over complete lattices. Our main theoretical contribution is latticed $k$-induction, which (i)
Knowledge-based programs provide an abstract level of description of protocols in which agent actions are related to their states of knowledge. The paper describes how epistemic model checking technology may be applied to discover and verify concrete
This paper shows how to transform explosive many-valued systems into paraconsistent logics. We investigate especially the case of three-valued systems showing how paraconsistent three-valued logics can be obtained from them.
We develop a categorical compositional distributional semantics for Lambek Calculus with a Relevant Modality, which has a limited version of the contraction and permutation rules. The categorical part of the semantics is a monoidal biclosed category
The logics RL, RP, and RG have been obtained by expanding Lukasiewicz logic L, product logic P, and Godel--Dummett logic G with rational constants. We study the lattices of extensions and structural completeness of these three expansions, obtaining r