Dirk Draheim: Semantics of the Probabilistic Typed Lambda Calculus, Gebunden
Semantics of the Probabilistic Typed Lambda Calculus
Buch
- Markov Chain Semantics, Termination Behavior, and Denotational Semantics
- Verlag:
- Springer Berlin Heidelberg, 03/2017
- Einband:
- Gebunden, HC runder Rücken kaschiert
- Sprache:
- Englisch
- ISBN-13:
- 9783642551970
- Artikelnummer:
- 4943408
- Umfang:
- 228 Seiten
- Sonstiges:
- 5 SW-Abb., 5 Tabellen,
- Nummer der Auflage:
- 17001
- Ausgabe:
- 1st ed. 2017
- Copyright-Jahr:
- 2015
- Gewicht:
- 505 g
- Maße:
- 246 x 159 mm
- Stärke:
- 20 mm
- Erscheinungstermin:
- 10.3.2017
- Hinweis
-
Achtung: Artikel ist nicht in deutscher Sprache!
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Beschreibung
In its first part, the book analyses symbolic computation involving probabilism from scratch. The book establishes rigorous Markov Chain semantics for the typed lambda calculus with recursion and probabilistic choices. It exploits statistical distributions as domains and defines appropriate denotational semantics for the introduced lambda calculus. It proofs important correspondence theorems between the established operational and denotational semantics. In the second part, we review the power of inductive logics as the foundation for expert reasoning systems.Inhaltsangabe
Part I: The Probabilistic Lambda-Calculus and its Semantics.- Introduction.- Syntax and Operational Semantics.- The Working Probabilistic Lambda Calculus.- Properties of the Markov Chain Semantics.- Denotational Semantics.- Semantical Correspondences.- Categorical Treatment.- Probabilism and Non-Determinism.- Part II: Natural Probabilistic Reasoning.- On Natural Two-Tier Semantics for Propositional Logics.- Natural Semantics of Propositions.- Finite Discrete Stochastics Reconsidered.- Lambda-Calculus Definitions.- Markov Chains.- Basic Logic Language and Semantics Definitions.- References.- Index.Klappentext
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 starts with a recapitulation of the basic mathematical tools needed throughout the book, in particular Markov chains, graph theory and domain theory, and also explores the topic of inductive definitions. It then defines the syntax and establishes the Markov chain semantics of the probabilistic lambda calculus 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. Lastly, it defines a denotational semantics of the probabilistic lambda calculus, based on continuous functions over probability distributionsas domains.
The work mostly appeals to researchers in theoretical computer science focusing on probabilistic programming, randomized algorithms, or programming language theory.
