Generalized Jeffrey Conditionalization
A Frequentist Semantics of Partial Conditionalization
Dirk Draheim
Springer, 2017
Foreword by Bruno Buchberger: [PDF]
Full text: [PDF]
The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-69868-7
About this book: This book provides a frequentist semantics for conditionalization on partially known events, which is given as a straightforward generalization of classical conditional probability via so-called probability testbeds. It analyzes the resulting partial conditionalization, called frequentist partial (F.P.) conditionalization, from different angles, i.e., with respect to partitions, segmentation, independence, and chaining. It turns out that F.P. conditionalization meets and generalizes Jeffrey conditionalization, i.e., from partitions to arbitrary collections of events, opening it for reassessment and a range of potential applications. A counterpart of Jeffrey’s rule for the case of independence holds in our frequentist semantics. This result is compared to Jeffrey’s commutative chaining of independent updates. The postulate of Jeffrey's probability kinematics, which is rooted in the subjectivism of Frank P. Ramsey, is found to be a consequence in our frequentist semantics. This way the book creates a link between the Kolmogorov system of probability and one of the important Bayesian frameworks. Furthermore, it shows a preservation result for conditional probabilities under the full update range and compares F.P. semantics with an operational semantics of classical conditional probability in terms of so-called conditional events. Lastly, it looks at the subjectivist notion of desirabilities and proposes a more fine-grained analysis of desirabilities a posteriori.
Semantics of the Probabilistic Typed Lambda Calculus
Markov Chain Semantics, Termination Behavior, and Denotational Semantics
Dirk Draheim
Springer, 2017
ISBN: 978-3-642-55197-0
About this book: This book takes a foundational approach to the semantics of probabilistic programming. It elaborates a rigorous Markov chain semantics for the probabilistic typed lambda calculus, which is the typed lambda calculus with recursion plus probabilistic choice. The book establishes a Markov chain semantics and, furthermore, both a graph and a tree semantics. Based on that, it investigates the termination behavior of probabilistic programs. It introduces the notions of termination degree, bounded termination and path stoppability and investigates their mutual relationships. Path stoppability characterizes a broadened class of termination and allows for the computation of program runs that are otherwise considered as non-terminating. Lastly, the book defines a denotational semantics of the probabilistic lambda calculus, based on continuous functions over probability distributions as domains.
Business Process Technology
A Unified View on Business Processes, Workflows and Enterprise Applications
Dirk Draheim
Springer, September 2010
ISBN: 978-3-642-01587-8
About this book: Businesses consist of processes and strive for excellence in business processes. There are different communities addressing business processes, each with different objectives, tools and terminology - business process reengineering, business process modeling, business process management, workflow execution, and even current strands of service-oriented architecture. In concrete business process projects, we are still faced again and again with similar questions: Which decomposition mechanism to use? Which is the correct granularity for business process activities? Which implementing technology is optimal in a given situation? This book offers an approach to the systematization of the field. It provides a landscape of rationales and concepts for business process tools and technologies. The message of the book is that currently emerging integrated business process platforms are the enabling technology of the future, which will allow us to use the huge potential for automation in today's enterprise.
Form-Oriented Analysis
A New Methodology to Model Form-Based Applications
Dirk Draheim, Gerald Weber
Springer, 2005
ISBN: 978-3-540-20593-7
About this book: Form-based applications range from simple Web shops to complex enterprise resource planning systems. Draheim and Weber adapt well-established basic modeling techniques in a novel way to achieve a modeling framework optimized for this broad application domain. They introduce new modeling artifacts, such as page diagrams and form storyboards, and separate dialogue patterns to allow for reuse. In their implementation they have developed new constructs such as typed server pages, and tools for forward and reverse engineering of presentation layers. The methodology is explained using an online bookshop as a running example, in which the user can experience the modeling concepts in action. The combination of theoretical achievements and hands-on practical advice and tools makes this book a reference work for both researchers in the areas of software architectures and submit-response style user interfaces, and professionals designing and developing such applications. More information and additional material is available online.