A Type Theory for Probabilistic and Bayesian Reasoning
Paper in 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

University of Bergen

Bart Jacobs

Radboud University

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,

Subject Categories

Algebra and Logic

Probability Theory and Statistics

Computer Science

Areas of Advance

Information and Communication Technology


Basic sciences



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6/9/2022 1