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oai:drops-oai.dagstuhl.de:17992 2024-03-12T12:01:20Z ddc:004 open_access

The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic Ehrhard, Thomas Faggian, Claudia Pagani, Michele Linear Logic Proof-Nets Denotational Semantics Probabilistic Programming 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Thomas Ehrhard and Claudia Faggian and Michele Pagani 2023 Is Part Of LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2023.8 urn:nbn:de:0030-drops-179926 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.8 eng https://creativecommons.org/licenses/by/4.0/legalcode