# Conditioning in Probabilistic Programming

arXiv: https://arxiv.org/abs/1504.00198 · HTML: https://mlsanity.com/paper/1504.00198/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2015.

## Built on by (most cited first, 3 of 3)

- [Control-Data Separation and Logical Condition Propagation for Efficient Inference on Probabilistic Programs](https://mlsanity.com/paper/2101.01502/) (2021)
- [Mixed Nondeterministic-Probabilistic Automata: Blending graphical probabilistic models with nondeterminism](https://mlsanity.com/paper/2201.07474/) (2022)
- [Probabilistic unifying relations for modelling epistemic and aleatoric uncertainty: semantics and automated reasoning with theorem proving](https://mlsanity.com/paper/2303.09692/) (2023)

## Abstract (arXiv)

We investigate the semantic intricacies of conditioning, a main feature in probabilistic programming. We provide a weakest (liberal) pre-condition (w(l)p) semantics for the elementary probabilistic programming language pGCL extended with conditioning. We prove that quantitative weakest (liberal) pre-conditions coincide with conditional (liberal) expected rewards in Markov chains and show that semantically conditioning is a truly conservative extension. We present two program transformations which entirely eliminate conditioning from any program and prove their correctness using the w(l)p-semantics. Finally, we show how the w(l)p-semantics can be used to determine conditional probabilities in a parametric anonymity protocol and show that an inductive w(l)p-semantics for conditioning in non-deterministic probabilistic programs cannot exist.