Semiring Programming: A Semantic Framework for Generalized Sum Product Problems

Vaishak Belle, Luc De Raedt

Research output: Contribution to journalArticlepeer-review


To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration amongst these, contemporary representation methodologies offer little support for this.

In an attempt to alleviate this situation, we position and motivate a new declarative programming framework in this paper. We focus on the semantical foundations in service of providing abstractions of well-known problems such as SAT, Bayesian inference, generative models, learning and convex optimization. Programs are understood in terms of first-order logic structures with semiring labels, which allows us to freely combine and integrate problems from different AI disciplines and represent non-standard problems over unbounded domains. Thus, the main thrust of this paper is to view such well-known problems through a unified lens in the hope that appropriate solver strategies (exact, approximate, portfolio or hybrid) may emerge that tackle real-world problems in a principled way.
Original languageEnglish
Pages (from-to)181-201
Number of pages21
JournalInternational Journal of Approximate Reasoning
Early online date26 Aug 2020
Publication statusPublished - 1 Nov 2020


  • Weighted model counting
  • Declarative Languages
  • Semantic abstractions
  • Semiring frameworks


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