Introduction to higher order categorical logic
Introduction to higher order categorical logic
A probabilistic powerdomain of evaluations
Proceedings of the Fourth Annual Symposium on Logic in computer science
Probabilistic non-determinism
The Powerdomain of Indexed Valuations
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
A Powerdomain for Countable Non-Determinism (Extended Abstract)
Proceedings of the 9th Colloquium on Automata, Languages and Programming
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Distributing probability over non-determinism
Mathematical Structures in Computer Science
Combining effects: sum and tensor
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
RETRACTED: Semantic Domains for Combining Probability and Non-Determinism
Electronic Notes in Theoretical Computer Science (ENTCS)
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
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This work continues ongoing research in combining theories of nondeterminism and probabilistic choice. First, we adapt the above choice theories to allow for uncountably indexed nondeterministic operators, and countably indexed probabilistic operators. Classically, models for mixed choice were obtained by enhancing arbitrary models for probabilistic choice with appropriately distributive nondeterministic operations. In this paper, we focus on the dual approach: constructing mixed choice models by completing nondeterministic models with suitably behaved probabilistic operations. We introduce a functorial construction, called convex completion, which freely computes set-theoretical and posetal mixed choice models from the appropriate semilattices. The completion construction relies upon a new closure operation on convex sets, dependant on the given semilattice. Finally, we show that building a free mixed choice model is equivalent to applying the convex completion functor to its corresponding free nondeterministic model.