Related papers: On coalgebras with internal moves
Hybrid computation combines discrete and continuous dynamics in the form of an entangled mixture inherently present both in various natural phenomena, and in applications ranging from control theory to microbiology. The emergent behaviours…
This article proposes a formal rapprochement between cognitive load theory and embodied cognition by reconceptualizing psychological representations as dynamic multiscale attractors within a temporal-hierarchical prediction architecture.…
We introduce continuation semantics for both fixpoint modal logic (FML) and Computation Tree Logic* (CTL*), parameterised by a choice of branching type and quantitative predicate lifting. Our main contribution is proving that they are…
Automata learning is a popular technique for inferring minimal automata through membership and equivalence queries. In this paper, we generalise learning to the theory of coalgebras. The approach relies on the use of logical formulas as…
We study a composition operation on monads, equivalently presented as large equational theories. Specifically, we discuss the existence of tensors, which are combinations of theories that impose mutual commutation of the operations from the…
We use the connection between automata and logic to prove that a wide class of coalgebraic fixpoint logics enjoys uniform interpolation. To this aim, first we generalize one of the central results in coalgebraic automata theory, namely…
In this article we describe properties of the 2-functor from the 2-category of comonads to the 2-category of functors that sends a comonad to its forgetful functor. This allows us to describe contexts where algebras over a monad are…
We use modal logic as a framework for coalgebraic trace semantics, and show the flexibility of the approach with concrete examples such as the language semantics of weighted, alternating and tree automata, and the trace semantics of…
FuTS, state-to-function transition systems are generalizations of labeled transition systems and of familiar notions of quantitative semantical models as continuous-time Markov chains, interactive Markov chains, and Markov automata. A…
This short note contains random thoughts about a factorization theorem for closure/interior operators on a powerset which is reminiscent to the notion of resolution for a monad/comonad. The question originated from formal topology but is…
We introduce an interleaving operational semantics for describing the client-observable behaviour of atomic transactions on distributed key-value stores. Our semantics builds on abstract states comprising centralised, global key-value…
A class of models is presented, in the form of continuation monads polymorphic for first-order individuals, that is sound and complete for minimal intuitionistic predicate logic. The proofs of soundness and completeness are constructive and…
Notions of computation can be modelled by monads. Algebraic effects offer a characterization of monads in terms of algebraic operations and equational axioms, where operations are basic programming features, such as reading or updating the…
Formalising the pi-calculus is an illuminating test of the expressiveness of logical frameworks and mechanised metatheory systems, because of the presence of name binding, labelled transitions with name extrusion, bisimulation, and…
This paper proposes a bisimulation theory based on multiparty session types where a choreography specification governs the behaviour of session typed processes and their observer. The bisimulation is defined with the observer cooperating…
State monads in cartesian closed categories are those defined by the familiar adjunction between product and exponential. We investigate the structure of their algebras, and show that the exponential functor is monadic provided the base…
It came to the attention of myself and the coauthors of (S., Rozowski, Silva, Rot, 2022) that a number of process calculi can be obtained by algebraically presenting the branching structure of the transition systems they specify. Labelled…
This paper studies the relationships between three notions of behavioural preorder that have been proposed in the literature: refinement over modal transition systems, and the covariant-contravariant simulation and the partial bisimulation…
We provide a compositional coalgebraic semantics for strategic games. In our framework, like in the semantics of functional programming languages, coalgebras represent the observable behaviour of systems derived from the behaviour of the…
We consider the structures given by repeatedly generalising the definition of finite state automata by symmetry considerations, and constructing analogues of transition monoids at each step. This approach first gives us non-deterministic…