Thorsten Wißmann

COOL-A generic reasoner for coalgebraic hybrid logics (System description)

We describe the Coalgebraic Ontology Logic solver Cool, a generic reasoner that decides the satisfiability of modal (and, more generally, hybrid) formulas with respect to a set of global assumptions – in Description Logic parlance, we support a general TBox and internalize a Boolean ABox. The level of generality is that of coalgebraic logic, a logical framework covering a wide range of modal logics, beyond relational semantics. The core of Cool is an efficient unlabelled tableaux search procedure using global caching. Concrete logics are added by implemening the corresponding (one-step) tableaux rules. The logics covered at the moment include standard relational examples as well as graded modal logic and Pauly’s Coalition Logic (the next-step fragment of Alternating-time Temporal Logic), plus every logic that arises as a fusion of the above. We compare the performance of Cool with state-of-the-art reasoners.

A New Foundation for Finitary Corecursion

This paper contributes to a theory of the behaviour of “finite-state” systems that is generic in the system type. We propose that such systems are modeled as coalgebras with a finitely generated carrier for an endofunctor on a locally finitely presentable category. Their behaviour gives rise to a new fixpoint of the coalgebraic type functor called locally finite fixpoint (LFF). We prove that if the given endofunctor preserves monomorphisms then the LFF always exists and is a subcoalgebra of the final coalgebra (unlike the rational fixpoint previously studied by Adamek, Milius and Velebil). Moreover, we show that the LFF is characterized by two universal properties: 1. as the final locally finitely generated coalgebra, and 2. as the initial fg-iterative algebra. As instances of the LFF we first obtain the known instances of the rational fixpoint, e.g. regular languages, rational streams and formal power-series, regular trees etc. And we obtain a number of new examples, e.g. (realtime deterministic resp. non-deterministic) context-free languages, constructively S-algebraic formal power-series (and any other instance of the generalized powerset construction by Silva, Bonchi, Bonsangue, and Rutten) and the monad of Courcelle’s algebraic trees.

Finitary Corecursion for the Infinitary Lambda Calculus

Kurz et al. have recently shown that infinite

Regular Behaviours with Names

\lambda

Predicate Liftings and Functor Presentations in Coalgebraic Expression Languages

-trees with finitely many free variables modulo

A New Foundation for Finitary Corecursion and Iterative Algebras.

\alpha

Efficient and Modular Coalgebraic Partition Refinement.

-equivalence form a final coalgebra for a functor on the category of nominal sets. Here we investigate the rational fixpoint of that functor. We prove that it is formed by all rational

Efficient Coalgebraic Partition Refinement.

\lambda

A Coalgebraic Paige-Tarjan Algorithm.

-trees, i.e. those

Regular Expressions with Dynamic Name Binding

\lambda