In this paper, we model fresh names in the π-calculus using abstractions with respect to a new binding operator θ. Both the theory and the metatheory of the π-calculus benefit from this simple extension. The operational semantics of this new calculus is finitely branching. Bisimulation can be given without mentioning any constraint on names, thus allowing for a straightforward definition of a c...

Categories with algebraic structure—the most prominent example being monoidal categories—satisfy equational axioms only up-to coherent isomorphisms. Therefore they are pseudo algebras. We extend Lawvere’s functorial semantics to such pseudo structure: in contrast to standard strict algebras which are identified with productpreserving functors, pseudo algebras are product-preserving pseudo funct...

This paper studies coalgebras from the perspective of the nitary observations that can be made of their behaviours. Based on the terminal sequence, notions of nitary behaviours and nitary predicates are introduced. A category Behω(T ) of coalgebras with morphisms preserving nitary behaviours is de ned. We then investigate de nability and compactness for nitary coalgebraic modal logic, show that...

We analyze the Brandenburger-Keisler paradox in epistemic game theory, which is a ‘two-person version of Russell’s paradox’. Our aim is to understand how it relates to standard one-person arguments, and why the ‘believes-assumes’ modality used in the argument arises. We recast it as a fixpoint result, which can be carried out in any regular category, and show how it can be reduced to a relation...

This paper contributes a feedback operator, in the form of a monoidal trace, to the theory of coalgebraic, state-based modelling of components. The feedback operator on components is shown to satisfy the trace axioms of Joyal, Street and Verity. We employ McCurdy’s tube diagrams, an extension of standard string diagrams for monoidal categories, for representing and manipulating component diagra...

The paper builds on recent results regarding the expressiveness of modal logics for coalgebras in order to introduce a specification framework for coalgebraic structures which offers support for modular specification. An equational specification framework for algebraic structures is obtained in a similar way. The two frameworks are then integrated in order to account for structures comprising b...

In this paper we regard languages and their acceptors – such as deterministic or weighted automata, transducers, or monoids – as functors from input categories that specify the type of the languages and of the machines to categories that specify the type of outputs. Our results are as follows: a) We provide sufficient conditions on the output category so that minimization of the corresponding a...

We lay the foundations of a first-order correspondence theory for coalgebraic logics that makes the transition structure explicit in the first-order modelling. In particular, we prove a coalgebraic version of the van Benthem/Rosen theorem stating that both over arbitrary structures and over finite structures, coalgebraic modal logic is precisely the bisimulation invariant fragment of first-orde...

Every endofunctor B on the category Set can be lifted to a fibred functor on the category (fibred over Set) of equivalence relations and relation-preserving functions. In this paper, the least (fibre-wise) of such liftings, L(B), is characterized for essentially any B. The lifting has all the useful properties of the relation lifting due to Jacobs, without the usual assumption of weak pullback ...

This paper relates labelled transition systems and coalgebras with the motivation of comparing and combining their complementary contributions to the theory of concurrent systems. The well-known mismatch between these two notions concerning the morphisms is resolved by extending the coalgebraic framework by lax cohomomorphisms. Enriching both labelled transition systems and coalgebras with alge...