RETRACTED: Semantic Domains for Combining Probability and Non-Determinism

Semantic Domains for Combining Probability and Non-Determinism

We present domain-theoretic models that support both probabilistic and nondeterministic choice. In [36], Morgan and McIver developed an ad hoc semantics for a simple imperative language with both probabilistic and nondeterministic choice operators over a discrete state space, using domaintheoretic tools. We present a model also using domain theory in the sense of D.S. Scott (see e.g. [15]), but...

Semanti Domains for Combining Probability and Non-Determinism

Distributing probability over non-determinism

We study the combination of probability and nondeterminism from a categorical point of view. In category theory, nondeterminism and probability are represented by suitable monads. Those two monads do not combine well, as they are. To overcome this problem we introduce the notion of indexed valuations. This notion is used to define a new monad that can be combined with the usual nondeterministic...

Predicate transformers for extended probability and non-determinism

We investigate laws for predicate transformers for the combination of nondeterministic choice and (extended) probabilistic choice, where predicates are taken to be functions to the extended nonnegative reals, or to closed intervals of such reals. These predicate transformers correspond to state transformers, which are functions to conical powerdomains, the appropriate powerdomains for the combi...

Probability Out Of Determinism

This paper offers a metaphysics of physical probability in (or if you prefer, truth conditions for probabilistic claims about) deterministic systems based on an approach to the explanation of probabilistic patterns in deterministic systems called the method of arbitrary functions. Much of the appeal of the method is its promise to provide an account of physical probability on which probability ...