Bpf Bart Jacobs

Exemplaric Expressivity of Modal Logics

This article investigates expressivity of modal logics for transition systems, multitransition systems, Markov chains and Markov processes, as coalgebras of the powerset, finitely supported multiset, finitely supported distribution and measure functor, respectively. Expressivity means that logically indistinguishable states, satisfying the same formulas, are behaviourally indistinguishable. The investigation is based on the framework of dual adjunctions between spaces and logics and focuses on a crucial injectivity property. The approach is generic both in the choice of systems and modalities, and in the choice of a ‘base logic’. Most of these expressivity results are already known, but the applicability of the uniform setting of dual adjunctions to these particular examples is what constitutes the contribution of the article.

Distributive laws for the coinductive solution of recursive equations

This paper illustrates the relevance of distributive laws for the solution of recursive equations, and shows that one approach for obtaining coinductive solutions of equations via infinite terms is in fact a special case of a more general approach using an extended form of coinduction via distributive laws.

Probabilities, Distribution Monads, and Convex Categories

Probabilities are understood abstractly as forming a monoid in the category of eect algebras. They can be added, via a partial operation, and multiplied. This generalises key properties of the unit interval [0; 1]. Such eect

Filter models with polymorphic types

Abstract Using ideas and results from Barendrecht (1983) and Coppo (1984) on intersection types, a comparable theory is developed for (second order) polymorphic types. The set of filters constructed with polymorphic type forms, with inclusion, a continuous lattice which yields a model of what we call βη-expansion (i.e. the value of a term increases under βη-reduction), but not of β-conversion. Combining intersection with polymorphic types does give filter λ-models, but the two standard ways of interpreting λ-terms do not coincide.