The operational semantics of interactive systems is usually described by labeled transition systems. Abstract semantics (that is defined in terms of bisimilarity) is characterized by the final morphism in some category of coalgebras. Since the behaviour of interactive systems is for many reasons infinite, symbolic semantics were introduced as a mean to define smaller, possibly finite, transitio...

This paper introduces an endofunctor VT on the category of frames, parametrized by an endofunctor T on the category Set that satisfies certain constraints. This generalizes Johnstone’s construction of the Vietoris powerlocale, in the sense that his construction is obtained by taking for T the finite covariant power set functor. Our construction of the T -powerlocale VTL out of a frame L is base...

Abstract In the theory of coalgebras, trace semantics can be defined in various distinct ways, including through algebraic logics, Kleisli category a monad or its Eilenberg–Moore category. This paper elaborates two new unifying ideas: (i) coalgebraic,draftrules is naturally presented terms corecursive algebras, and (ii) all three approaches arise as instances same abstract setting. Our perspect...

The aim of this paper is an integration of graph grammars with diierent kinds of behavioural constraints, in particular with temporal logic constraints. Since the usual algebraic semantics of graph transformation systems is not able to express constrained behaviour we introduce-in analogy to other approaches-a coalgebraic semantics which associates with each system a category of models (determi...

We introduce a notion of bisimulation on labelled Markov Processes over generic measurable spaces in terms of arbitrary binary relations. Our notion of bisimulation is proven to coincide with the coalgebraic definition of Aczel and Mendler in terms of the Giry functor, which associates with a measurable space its collection of (sub)probability measures. This coalgebraic formulation allows one t...

This paper presents a modular framework for the specification of certain inductivelydefined coalgebraic types. Modal logics for coalgebras of polynomial endofunctors on the category of sets have been studied in [16,8]. These logics are here generalised to endofunctors on categories of sorted sets, in order to allow collections of interrelated types to be specified simultaneously. The inductive ...

We study the finitary version of the coalgebraic logic introduced by L. Moss. The syntax of this logic, which is introduced uniformly with respect to a coalgebraic type functor, required to preserve weak pullbacks, extends that of classical propositional logic with a so-called coalgebraic cover modality depending on the type functor. Its semantics is defined in terms of a categorically defined ...

In this chapter I discuss the deep mutations occurring today in our society and in our culture, the natural and mathematical sciences included, from the standpoint of the “transcendental of language”, and of the primacy of language over knowledge. That is, from the standpoint of the “completion of the linguistic turn” in the foundations of logic and mathematics using Peirce’s algebra of relatio...

In this paper we describe the coalgebraic models for state-based software components and componentbased systems. The behaviour patterns of components are specified by strong monads. A family of operators for combining components based on the category of coalgebras are defined and a set of algebraic laws are also presented to specify the properties being satisfied by these operators.

We present a coalgebraic approach to trace equivalence semantics based on lifting behaviour endofunctors for deterministic action to Kleisli categories of monads for non-deterministic choice. In Set , this gives a category with ordinary transition systems as objects and with morphisms characterised in terms of a linear notion of bisimulation. The final object in this category is the canonical a...