A Type Theory for Probabilistic and Bayesian Reasoning
Paper i proceeding, 2018

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.

type theory

effect module

Bayesian reasoning

Probabilistic programming

probabilistic algorithm


Robin Adams

Universitetet i Bergen

Bart Jacobs

Radboud Universiteit

Leibniz International Proceedings in Informatics (LIPIcs)

1868-8969 (ISSN)

Vol. 69 11-134
978-3-95977-030-9 (ISBN)

21st International Conference on Types for Proofs and Programs, TYPES 2015
Tallinn, Estonia,


Algebra och logik

Sannolikhetsteori och statistik

Datavetenskap (datalogi)


Informations- och kommunikationsteknik


Grundläggande vetenskaper



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