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© 2009

Stochastic Coalgebraic Logic

Benefits

  • 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

Book

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Ernst-Erich Doberkat
    Pages 1-68
  3. Ernst-Erich Doberkat
    Pages 69-111
  4. Ernst-Erich Doberkat
    Pages 113-155
  5. Ernst-Erich Doberkat
    Pages 157-214
  6. Back Matter
    Pages 1-14

About this book

Introduction

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a comprehensive discussion of the Giry monad as the underlying categorical construction, presenting many new, hitherto unpublished results.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.

Keywords

Categories, category theory Coalgebraic logics Giry Monad Markov transition systems Modal logic Morphisms Probability theory Stochastic logic Stochastic systems concurrency grammar grammars logic modeling semantics

Authors and affiliations

  1. 1.FB Informatik Universität DortmundDortmundGermany

Bibliographic information

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Reviews

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 an extensive and useful introduction to basic concepts from the theory of measurable and analytic spaces required for the further technical development. … the book provides an overview of a large amount of technically challenging material; it is suitable reading, e.g., for graduate students in the field of stochastic logics.” (Lutz Schröder, Zentralblatt MATH, Vol. 1207, 2011)

“Stochastic coalgebraic logic generically allows such formulations to be defined by a coalgebra. This compact, four-chapter monograph packs in many mathematical details about such logics. … The treatment is mathematical throughout, with the author pointing out the key concepts used in proofs. … a good reference for theoretical researchers interested in the mathematical underpinnings of this area.” (K. Lodaya, ACM Computing Reviews, December, 2010)