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Next: Programme and Methodology
Up: Background
Previous: Open Problem: Error Quantification
To define a semantics for probabilistic programs requires the
consideration of mathematical notions such as measure space,
measurable functions, etc., to capture the quantitative aspects
of the computation. The probabilistic semantics that results
can then be used also for conventional (non-probabilistic) programs
by considering the latter as a special case of probabilistic
programs.
In our work we developed a denotational semantics for
a probabilistic version of Concurrent Constraint Programming.
This approach is based on linear spaces and operator algebras,
which themselves stem from measure theoretic structures
(e.g. Banach or Hilbert spaces of measurable functions).
The starting point in the area of probabilistic semantics are the
fundamental papers of Saheb-Djahromi [60], who first
introduced measure-theoretic ideas in the subject of denotational
semantics, and Kozen [43], whose main contribution
is the usage of Banach space structures for this purpose.
Some other approaches towards the semantics of probabilistic
programming languages are [38] -- which generalises
Saheb-Djahromi's work in a categorical setting -- probabilistic
predicate transformers [51], probabilistic
process algebras [9, 10],
and Markov processes [11, 20].
Next: Programme and Methodology
Up: Background
Previous: Open Problem: Error Quantification
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