Stochastic Coalgebraic Logic

  • Ernst-Erich Doberkat

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a comprehensive discussion of the Giry monad as the underlying categorical construction, presenting many new, hitherto unpublished results.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

  • Ernst-Erich Doberkat
    • 1
  1. 1.FB Informatik Universität DortmundDortmundGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-02995-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science
  • Print ISBN 978-3-642-02994-3
  • Online ISBN 978-3-642-02995-0
  • Series Print ISSN 1431-2654
  • About this book