Coalgebraic speciications are used to formally describe the behaviour of classes in object-oriented languages. In this paper, a general notion of reenement between two such coalgebraic speciications is deened, capturing the idea that one \concrete" class speciication realises the behaviour of the other, \abstract" class spec-iication. Two (complete) proof-techniques are given to establish such ...

The Sig programming language is a total functional, clocked synchronous data-flow language. Its core has been designed to admit concise coalgebraic semantics. Universal coalgebra is an expressive theoretical framework for behavioral semantics, but traditionally phrased in abstract categorical language, and generally considered inaccessible. In the present paper, we rephrase the coalgebraic conc...

We investigate logics for coalgebraic simulation from a compositional perspective. Specifically, we show that the expressiveness of an inductively-defined language for coalgebras w.r.t. a given notion of simulation comes as a consequence of an expressivity condition between the language constructor used to define the language for coalgebras, and the relator used to define the notion of simulati...

This paper generalizes existing connections between automata and logic to a coalgebraic abstraction level. Let F : Set→ Set be a standard functor that preserves weak pullbacks. We introduce various notions of F-automata, devices that operate on pointed F-coalgebras. The criterion under which such an automaton accepts or rejects a pointed coalgebra is formulated in terms of an infinite two-playe...

The coalgebraic approach to modal logic provides a uniform framework that captures the semantics of a large class of structurally different modal logics, including e.g. graded and probabilistic modal logics and coalition logic. In this paper, we introduce the coalgebraic μ-calculus, an extension of the general (coalgebraic) framework with fixpoint operators. Our main results are completeness of...