Stochastic Coalgebraic Logic [Paperback]

Coalgebraic logic is an important research topic in the areas of concurrency theory, semantics, transition systems and modal logics. It provides a general approach to modeling systems, allowing us to apply important results from coalgebras, universal algebra and category theory in novel ways. Stochastic systems provide important tools for systems modeling, and recent work shows that categorical reasoning may lead to new insights, previously not available in a purely probabilistic setting.

This book combines coalgebraic reasoning, stochastic systems and logics. It provides an insight into the principles of coalgebraic logic from a categorical point of view, and applies these systems to interpretations of stochastic coalgebraic logics, which include well-known modal logics and continuous time branching logics. The author introduces stochastic systems together with their probabilistic and categorical foundations and gives a comprehensive discussion of the Giry monad as the underlying categorical construction, presenting many new, hitherto unpublished results. He discusses modal logics, introduces their probabilistic interpretations, and then proceeds to an analysis of Kripke models for coalgebraic logics.

The book will be of interest to researchers in theoretical computer science, logic and category theory.

From the reviews:

Stochastic coalgebraic logic is a detailed study devoted to the modal logic of general probability spaces. & the reader is not only exposed to formal logic but also to an extensive amount of measure theory that is summarised in the first chapter. & the book is a self-contained and readable discussion of the subject, and even the versed reader will find new results. (Dirk A. Pattinson, Mathematical Reviews, March, 2013)

The book begins with anl7