Towards a Categorical Account of Conditional Probability

Towards a Categorical Account of Conditional Probability

This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain “triangle-fill-in” condition, connecting marginal and joint probabilities, in the Kleisli category of the distribution monad. The conditional probabilities are induced by a map together with a predicate (the condit...

A Categorical Basis for Conditional Probability

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 events/probability density functions (pdf’s). The distribution monad for discrete probability and the Giry monad for continuous probability are leading examples. Our categorical description handles discrete an...

Further Investingation in Conditional Probability

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A categorical account of two-level languages

Towards an algebraic framework for many-valued conditional probability

We investigate probability functions defined over many valued conditional events. During the last decade or so considerable research effort has been directed towards the understanding of what (subjective) conditional probability might look like in the context of many-valued logics. Given its centrality in the area, a particularly well-studied case is that of Lukasiewicz’s infinite-valued logic ...