Investigating a Generalization of Probabilistic Material Implication and Bayesian Conditionals

Michael Jahn, Matthias Scheutz
Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:932-940, 2023.

Abstract

Probabilistic "if A then B" rules are typically formalized as Bayesian conditionals P(B|A), as many (e.g., Pearl) have argued that Bayesian conditionals are the correct way to think about such rules. However, there are challenges with standard inferences such as modus ponens and modus tollens that might make probabilistic material implication a better candidate at times for rule-based systems employing forward-chaining; and arguably material implication is still suitable when information about prior or conditional probabilities is not available at all. We investigate a generalization of probabilistic material implication and Bayesian conditionals that combines the advantages of both formalisms in a systematic way and prove basic properties of the generalized rule, in particular, for inference chains in graphs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v216-jahn23a, title = {Investigating a Generalization of Probabilistic Material Implication and {B}ayesian Conditionals}, author = {Jahn, Michael and Scheutz, Matthias}, booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence}, pages = {932--940}, year = {2023}, editor = {Evans, Robin J. and Shpitser, Ilya}, volume = {216}, series = {Proceedings of Machine Learning Research}, month = {31 Jul--04 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v216/jahn23a/jahn23a.pdf}, url = {https://proceedings.mlr.press/v216/jahn23a.html}, abstract = {Probabilistic "if A then B" rules are typically formalized as Bayesian conditionals P(B|A), as many (e.g., Pearl) have argued that Bayesian conditionals are the correct way to think about such rules. However, there are challenges with standard inferences such as modus ponens and modus tollens that might make probabilistic material implication a better candidate at times for rule-based systems employing forward-chaining; and arguably material implication is still suitable when information about prior or conditional probabilities is not available at all. We investigate a generalization of probabilistic material implication and Bayesian conditionals that combines the advantages of both formalisms in a systematic way and prove basic properties of the generalized rule, in particular, for inference chains in graphs.} }
Endnote
%0 Conference Paper %T Investigating a Generalization of Probabilistic Material Implication and Bayesian Conditionals %A Michael Jahn %A Matthias Scheutz %B Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2023 %E Robin J. Evans %E Ilya Shpitser %F pmlr-v216-jahn23a %I PMLR %P 932--940 %U https://proceedings.mlr.press/v216/jahn23a.html %V 216 %X Probabilistic "if A then B" rules are typically formalized as Bayesian conditionals P(B|A), as many (e.g., Pearl) have argued that Bayesian conditionals are the correct way to think about such rules. However, there are challenges with standard inferences such as modus ponens and modus tollens that might make probabilistic material implication a better candidate at times for rule-based systems employing forward-chaining; and arguably material implication is still suitable when information about prior or conditional probabilities is not available at all. We investigate a generalization of probabilistic material implication and Bayesian conditionals that combines the advantages of both formalisms in a systematic way and prove basic properties of the generalized rule, in particular, for inference chains in graphs.
APA
Jahn, M. & Scheutz, M.. (2023). Investigating a Generalization of Probabilistic Material Implication and Bayesian Conditionals. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 216:932-940 Available from https://proceedings.mlr.press/v216/jahn23a.html.

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