Uncertain Logic Processing: logic-based inference and reasoning using Dempster–Shafer models

Abstract First order logic lies at the core of many methods in mathematics, philosophy, linguistics, and computer science. Although important efforts have been made to extend first order logic to the task of handling uncertainty, existing solutions are sometimes limited by the way they model uncertainty, or simply by the complexity of the problem formulation. These approaches could be strengthened by adding more flexibility in assigning probabilities (e.g., through intervals) and a more rigorous method of assigning probability/uncertainty measures. In this paper we present the basic theory of Uncertain Logic Processing (ULP), a robust framework for modeling and inference when information is available in the form of first order logic formulas subject to uncertainty. Dempster–Shafer (DS) theory provides the substrate for uncertainty modeling in the proposed ULP formulation. ULP can be tuned to preserve consistency with classical logic, allowing it to incorporate typical inference rules and properties, while preserving the strength of DS theory for representing and manipulating uncertainty.