PROBABILITY & STATISTICS

From probability monads to commutative effectuses

Resource type
Author/contributor
Title
From probability monads to commutative effectuses
Abstract
Effectuses have recently been introduced as categorical models for quantum computation, with probabilistic and Boolean (classical) computation as special cases. These ‘probabilistic’ models are called commutative effectuses, and are the focus of attention here. The paper describes the main known ‘probability’ monads: the monad of discrete probability measures, the Giry monad, the expectation monad, the probabilistic power domain monad, the Radon monad, and the Kantorovich monad. It also introduces successive properties that a monad should satisfy so that its Kleisli category is a commutative effectus. The main properties are: partial additivity, strong affineness, and commutativity. It is shown that the resulting commutative effectus provides a categorical model of probability theory, including a logic using effect modules with parallel and sequential conjunction, predicate- and state-transformers, normalisation and conditioning of states.
Publication
Journal of Logical and Algebraic Methods in Programming
Volume
94
Pages
200-237
Date
01/2018
Language
en
DOI
10/gct2wr
ISSN
23522208
Accessed
2019-11-28T14:39:17Z
Library Catalog
Crossref
Extra
ZSCC: 0000028
Citation
Jacobs, B. (2018). From probability monads to commutative effectuses. Journal of Logical and Algebraic Methods in Programming, 94, 200–237. https://doi.org/10/gct2wr
CATEGORICAL LOGIC
PROBABILITY & STATISTICS
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