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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…
There is a wide range of modal logics whose semantics goes beyond relational structures, and instead involves, e.g., probabilities, multi-player games, weights, or neighbourhood structures. Coalgebraic logic serves as a unifying semantic…
We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in reactive verification; coalgebraic generality implies in particular that we cover not only classical…
Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with…
Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier…
Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted…
Hybrid logic extends modal logic with support for reasoning about individual states, designated by so-called nominals. We study hybrid logic in the broad context of coalgebraic semantics, where Kripke frames are replaced with coalgebras for…
Denotational semantics can be based on algebras with additional structure (order, metric, etc.) which makes it possible to interpret recursive specifications. It was the idea of Elgot to base denotational semantics on iterative theories…
Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually…
Predictive processing and active inference posit that the brain is a system performing Bayesian inference on the environment. By virtue of this, a prominent interpretation of predictive processing states that the generative model (a POMDP)…
Coalgebra is a currently quite active field, which aims to look at generic state-based systems (most prominently automata) from a very abstract point of view, mainly using tools from category theory. One of its achievements is to give a…
We investigate the duality between algebraic and coalgebraic recognition of languages to derive a generalization of the local version of Eilenberg's theorem. This theorem states that the lattice of all boolean algebras of regular languages…
The analysis of concurrent and reactive systems is based to a large degree on various notions of process equivalence, ranging, on the so-called linear-time/branching-time spectrum, from fine-grained equivalences such as strong bisimilarity…
Regular expressions are commonly understood in terms of their denotational semantics, that is, through formal languages -- the regular languages. This view is inductive in nature: two primitives are equivalent if they are constructed in the…
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…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
In the first part of the paper we recall the coalgebraic approach to handling the so-called invisible transitions that appear in different state-based systems semantics. We claim that these transitions are always part of the unit of a…
Originally inspired by categorical quantum mechanics (Abramsky and Coecke, LiCS'04), the categorical compositional distributional model of natural language meaning of Coecke, Sadrzadeh and Clark provides a conceptually motivated procedure…
The syntactic behaviour of texts can highly vary depending on their contexts (e.g. author, genre, etc.). From the standpoint of stylometry, it can be helpful to objectively measure this behaviour. In this paper, we discuss how coalgebras…
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…