A Bunched Logic for Conditional Independence

Independence and conditional independence are fundamental concepts for reasoning about groups of random variables in probabilistic programs. Verification methods for independence are still nascent, and existing methods cannot handle conditional independence. We extend the logic of bunched implicatio...

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Bibliographic Details
Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 14
Main Authors: Bao, Jialu, Docherty, Simon, Hsu, Justin, Silva, Alexandra
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
Cognition
Computational modeling
Computer science
Markov processes
Probabilistic logic
Random variables
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Summary:Independence and conditional independence are fundamental concepts for reasoning about groups of random variables in probabilistic programs. Verification methods for independence are still nascent, and existing methods cannot handle conditional independence. We extend the logic of bunched implications (BI) with a non-commutative conjunction and provide a model based on Markov kernels; conditional independence can be directly captured as a logical formula in this model. Noting that Markov kernels are Kleisli arrows for the distribution monad, we then introduce a second model based on the powerset monad and show how it can capture join dependency, a non-probabilistic analogue of conditional independence from database theory. Finally, we develop a program logic for verifying conditional independence in probabilistic programs.
DOI:10.1109/LICS52264.2021.9470712