Semiring Programming: A Declarative Framework for Generalized Sum Product Problems

TL;DR

This paper introduces Semiring Programming, a declarative framework that unifies various AI problem-solving paradigms like SAT, Bayesian inference, and optimization through semiring-based semantics, enabling integrated reasoning across disciplines.

Contribution

It presents a novel declarative programming framework that supports the integration of diverse AI problems using semiring semantics, facilitating cross-disciplinary problem solving.

Findings

Unified framework for diverse AI problems

Semiring semantics enable flexible problem composition

Supports integration of logic, probabilistic, and optimization problems

Abstract

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 introduce a new declarative programming framework that provides abstractions of well-known problems such as SAT, Bayesian inference, generative models, and convex optimization. The semantics of programs is defined in terms of first-order structures with semiring labels, which allows us to freely combine and integrate problems from different AI disciplines.