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Semantics of the Probabilistic Typed Lambda Calculus
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Statistics is the language of science; however, the semantics of probabilistic computation and probabilistic reasoning is still matter of discourse. 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.
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