Combining coalgebraic reasoning, stochastic systems and logic, this volume presents the principles of coalgebraic logic from a categorical perspective. Modal logics are also discussed, including probabilistic interpretations and an analysis of Kripke models.

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a comprehensive discussion of the Giry monad as the underlying categorical construction, presenting many new, hitherto unpublished results.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

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 Includes supplementary material: sn.pub/extras

Autorentext

Ernst-Erich Doberkat studierte Mathematik und Philosophie in Bochum, promovierte in Mathematik und habilitierte in Informatik. Er war Professor in den USA, lehrte dreißig Jahre als Ordinarius für Praktische Informatik an deutschen Universitäten, und unterrichtete in Italien und China. Seine Hauptarbeitsgebiete sind modale Logiken und koalgebraische Methoden für probabilistische Transitionssysteme.

Inhalt
Borel Sets, Measures and All That.- Modal Logics.- The Giry Monad: Randomized Morphisms.- Coalgebraic Logic.