# Towards a Categorical Account of Conditional Probability

@article{Furber2013TowardsAC, title={Towards a Categorical Account of Conditional Probability}, author={Robert Furber and Bart Jacobs}, journal={ArXiv}, year={2013}, volume={abs/1306.0831} }

QPL 2015 : 12th International Workshop on Quantum Physics and Logic, 13-17 July 2015, Oxford, United Kingdom

## 11 Citations

### Effectuses in Categorical Quantum Foundations

- PhilosophyArXiv
- 2019

This thesis develops the theory of effectuses as a categorical axiomatic approach to quantum theory. It provides a comprehensive introduction to effectus theory and reveals its connections with…

### Extensions and composites in topos quantum theory

- Mathematics
- 2016

Topos quantum theory provides representations of quantum states as direct generalizations of the probability distribution, namely probability valuation. In this article, we consider extensions of a…

### Semantics for a Quantum Programming Language by Operator Algebras

- MathematicsNew Generation Computing
- 2016

It is shown that the opposite of the category of W*-algebras and normal completely positive subunital maps is an elementary quantum flow chart category in the sense of Selinger, which gives a denotational semantics for Selinger’s first-order functional quantum programming language.

### New Directions in Categorical Logic, for Classical, Probabilistic and Quantum Logic

- Computer ScienceLog. Methods Comput. Sci.
- 2015

It is shown that in the special case of C ∗ -algebras, side-effects appear exclusively in the non- commutative (properly quantum) case, and four successive assumptions are described, towards a categorical axiomatisation of quantitative logic for probabilistic and quantum systems, in which the above mentioned elements occur.

### From probability monads to commutative effectuses

- MathematicsJ. Log. Algebraic Methods Program.
- 2018

### Affine Monads and Side-Effect-Freeness

- MathematicsCMCS
- 2016

A new property of a monad (‘strongly affine’) is introduced and it is shown that for such strongly affine monads predicates are in bijective correspondence with side-effect-free instruments.

### Aﬃne Monads and Side-Eﬀect-Freeness (cid:63)

- Mathematics
- 2016

. The notions of side-eﬀect-freeness and commutativity are typical for probabilistic models, as subclass of quantum models. This paper connects these notions to properties in the theory of monads. A…

### A Categorical Basis for Conditional Probability

- Mathematics
- 2016

This paper identifies several key properties of a monad that allow us to formulate the basics of conditional probability theory, using states for distributions/measures and predicates for…

### Bayesian Networks as Coalgebras

- Computer Science, Mathematics
- 2014

A coalgebraic description of (discrete) Bayesian networks is presented and some new structure of the distribution monad is identified and isolate it in what it is called a ‘relatively monoidal’.

### Hyper Normalisation and Conditioning for Discrete Probability Distributions

- Computer ScienceLog. Methods Comput. Sci.
- 2017

A novel description of normalisation is given as a mathematically well-behaved total function, which is put to use in a similarly new description of conditioning, producing a distribution of conditional distributions.

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- Computer ScienceLog. Methods Comput. Sci.
- 2015

It is shown that in the special case of C ∗ -algebras, side-effects appear exclusively in the non- commutative (properly quantum) case, and four successive assumptions are described, towards a categorical axiomatisation of quantitative logic for probabilistic and quantum systems, in which the above mentioned elements occur.

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