Overview
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a comprehensive discussion of the Giry monad as the underlying categorical construction, presenting many new, hitherto unpublished results.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.
Full Product Details
Author: Ernst-Erich Doberkat
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: 2009 ed.
Dimensions:
Width: 15.50cm
, Height: 1.50cm
, Length: 23.50cm
Weight: 0.541kg
ISBN: 9783642029943
ISBN 10: 3642029949
Pages: 231
Publication Date: 19 November 2009
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: In Print
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.
Reviews
From the reviews: 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)
From the reviews: ""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)
From the reviews: 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)
