A Type Theory for Probabilistic and Bayesian Reasoning
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2015
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| _version_ | 1866908292874240000 |
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| author | Adams, Robin Jacobs, Bart |
| author_facet | Adams, Robin Jacobs, Bart |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1511_09230 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | A Type Theory for Probabilistic and Bayesian Reasoning Adams, Robin Jacobs, Bart Logic in Computer Science Logic Probability F.4.1; G.3; F.3.1 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. |
| title | A Type Theory for Probabilistic and Bayesian Reasoning |
| topic | Logic in Computer Science Logic Probability F.4.1; G.3; F.3.1 |
| url | https://arxiv.org/abs/1511.09230 |