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Predicate Liftings and Functor Presentations in Coalgebraic Expression Languages

Abstract : We introduce a generic expression language describing behaviours of finite coalgebras over sets; besides relational systems, this covers, e.g., weighted, probabilistic, and neighbourhood-based system types. We prove a generic Kleene-type theorem establishing a correspondence between our expressions and finite systems. Our expression language is similar to one introduced in previous work by Myers but has a semantics defined in terms of a particular form of predicate liftings as used in coalgebraic modal logic; in fact, our expressions can be regarded as a particular type of modal fixed point formulas. The predicate liftings in question are required to satisfy a natural preservation property; we show that this property holds in particular for the Moss liftings introduced by Marti and Venema in work on lax extensions.
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Ulrich Dorsch, Stefan Milius, Lutz Schröder, Thorsten Wißmann. Predicate Liftings and Functor Presentations in Coalgebraic Expression Languages. 14th International Workshop on Coalgebraic Methods in Computer Science (CMCS), Apr 2018, Thessaloniki, Greece. pp.56-77, ⟨10.1007/978-3-030-00389-0_5⟩. ⟨hal-02044640⟩

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