CATEGORICAL LOGIC

A Type Theory for Probabilistic and Bayesian Reasoning

Resource type
Authors/contributors
Title
A Type Theory for Probabilistic and Bayesian Reasoning
Abstract
This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes our probabilistic type theory from quantum type theory, namely the bijective correspondence between predicates and side-effect free actions (called instrument, or assert, maps). The paper shows how suitable computation rules can be derived from this predicate-action correspondence, and uses these rules for calculating conditional probabilities in two well-known examples of Bayesian reasoning in (graphical) models. Our type theory may thus form the basis for a mechanisation of Bayesian inference.
Publication
arXiv:1511.09230 [cs, math]
Date
2015-11-30
Accessed
2019-11-21T20:40:43Z
Library Catalog
Extra
ZSCC: 0000013 arXiv: 1511.09230
Notes

Comment: 38 pages

Citation
Jacobs, B., & Adams, R. (2015). A Type Theory for Probabilistic and Bayesian Reasoning. ArXiv:1511.09230 [Cs, Math]. Retrieved from http://arxiv.org/abs/1511.09230
CATEGORICAL LOGIC
PROBABILITY & STATISTICS
PROGRAMMING LANGUAGES
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