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The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic

Authors Thomas Ehrhard , Claudia Faggian, Michele Pagani

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Author Details

Thomas Ehrhard
  • Université de Paris Cité, CNRS, IRIF, F-75013, Paris, France
Claudia Faggian
  • Université de Paris Cité, CNRS, IRIF, F-75013, Paris, France
Michele Pagani
  • Université de Paris Cité, IRIF, F-75013, Paris, France

Funding

This work was partially supported by ANR PRC project PPS ANR-19-CE48-0014.

Cite AsGet BibTex

Thomas Ehrhard, Claudia Faggian, and Michele Pagani. The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.FSCD.2023.8

Abstract

We consider an extension of multiplicative linear logic which encompasses bayesian networks and expresses samples sharing and marginalisation with the polarised rules of contraction and weakening. We introduce the necessary formalism to import exact inference algorithms from bayesian networks, giving the sum-product algorithm as an example of calculating the weighted relational semantics of a multiplicative proof-net improving runtime performance by storing intermediate results.

Subject Classification

ACM Subject Classification
  • Theory of computation → Linear logic
  • Theory of computation → Denotational semantics
  • Mathematics of computing → Variable elimination
Keywords
  • Linear Logic
  • Proof-Nets
  • Denotational Semantics
  • Probabilistic Programming

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