# Probabilistic Observations and Valuations (Extended Abstract)

Matthias Schröder, Alexander Simpson

Research output: Contribution to journalArticle

## Abstract

We give a universal property for an "abstract probabilistic powerdomain" based on an analysis of observable properties of probabilistic computation. The universal property determines an abstract notion of integration satisfying the usual equational laws. In the category of topological spaces, the abstract probabilsitic powerdomain is given explicitly by the space of continuous probability valuations with weak topology. Thus our abstract notion of integration coincides with the usual integration for probability valuations. We end by discussing how our approach might adapt to provide "abstract effect spaces" for other computational effects.
Original language English 605-615 11 Electronic Notes in Theoretical Computer Science 155 https://doi.org/10.1016/j.entcs.2005.11.075 Published - 2006

## Keywords

• Domain theory
• probabilistic powerdomain
• probability measures
• integration
• computational effects

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• ### Topological Models for Computational Metalanguages

Simpson, A.

EPSRC

1/10/0330/09/06

Project: Research

• ### Models and Axioms for the Semantics of Computation

Simpson, A.

EPSRC

1/10/0130/09/06

Project: Research