License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2023.8
URN: urn:nbn:de:0030-drops-179926
URL: https://drops.dagstuhl.de/opus/volltexte/2023/17992/
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Ehrhard, Thomas ; Faggian, Claudia ; Pagani, Michele

The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic

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LIPIcs-FSCD-2023-8.pdf (1 MB)


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.

BibTeX - Entry

@InProceedings{ehrhard_et_al:LIPIcs.FSCD.2023.8,
  author =	{Ehrhard, Thomas and Faggian, Claudia and Pagani, Michele},
  title =	{{The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17992},
  URN =		{urn:nbn:de:0030-drops-179926},
  doi =		{10.4230/LIPIcs.FSCD.2023.8},
  annote =	{Keywords: Linear Logic, Proof-Nets, Denotational Semantics, Probabilistic Programming}
}

Keywords: Linear Logic, Proof-Nets, Denotational Semantics, Probabilistic Programming
Collection: 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)
Issue Date: 2023
Date of publication: 28.06.2023


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