133 research outputs found
A Note on the Coalgebraic Interpretation of Game Logic
We propose a coalgebraic interpretation of game logic, making the results of coalgebraic logic available for this context. We study some properties of a coalgebraic interpretation, showing among others that Aczel's Theorem on the characterization of bisimilar models through spans of morphisms is valid here. We investigate also congruences as those equivalences on the state space which preserve the structure of the model
Measures and all that --- A Tutorial
This tutorial gives an overview of some of the basic techniques of measure
theory. It includes a study of Borel sets and their generators for Polish and
for analytic spaces, the weak topology on the space of all finite positive
measures including its metrics, as well as measurable selections. Integration
is covered, and product measures are introduced, both for finite and for
arbitrary factors, with an application to projective systems. Finally, the
duals of the Lp-spaces are discussed, together with the Radon-Nikodym Theorem
and the Riesz Representation Theorem. Case studies include applications to
stochastic Kripke models, to bisimulations, and to quotients for transition
kernels
Kleisli morphisms and randomized congruences for the Giry monad
AbstractStochastic relations are the Kleisli morphisms for the Giry monad. This paper proposes the study of the associated morphisms and congruences. The relationship between kernels of these morphisms and congruences is studied, and a unique factorization of a morphism through this kernel is shown to exist. This study is based on an investigation into countably generated equivalence relations on the space of all subprobabilities. Operations on these relations are investigated quite closely. This utilizes positive convex structures and indicates cross-connections to Eilenberg–Moore algebras for the Giry monad. Hennessy–Milner logic serves as an illustration for randomized morphisms and congruences
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