Probabilistic Abduction in a Fuzzy Logic Framework

2026-04-23

AI Summary

This study addresses the problem of inferring probability distributions or statements consistent with frequency-based observations—such as “it rains 20% of the time”—within the framework of Fuzzy Probability logic (FP). It presents the first systematic formalization of probabilistic abduction in FP, rigorously defining solutions and fully characterizing their computational complexity. The work establishes precise complexity classifications for the abductive reasoning problem both in the full FP language and in its disjunctive clause fragment. Furthermore, it provides an effective reduction from classical probabilistic abduction to FP, thereby offering a novel formal foundation and algorithmic perspective for reasoning under uncertainty.

Technology Category

Reasoning under Uncertainty: Probabilistic ProgrammingKnowledge Representation and Reasoning: Diagnosis and Abductive ReasoningCognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsWeb Mining and Content Analysis: Robustness and generalizability of Web mining methodsUser Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We study the problem of explaining observations about the probabilities of events, such as "it rains $20\%$ of the time", "rain and snow are equally likely", etc. We explain these statements with a probability distribution or a statement about probabilities of (other) events that are consistent with our knowledge and entail the observation. We formalise this problem in a fuzzy probabilistic logic $\mathsf{FP}$. We define and motivate the notions of abduction problems and their solutions. Our main technical contribution is a comprehensive study of the complexity of solution recognition and existence for a given abduction problem in $\mathsf{FP}$ for the case of full language and its disjunctive-clause fragments. We also obtain a translation of classical probabilistic abduction (finding the most likely explanation of a given event) to $\mathsf{FP}$.

Problem

• probabilistic abduction
• fuzzy logic
• probability explanation
• abduction problem
• probabilistic reasoning

Innovation

• probabilistic abduction
• fuzzy logic
• computational complexity
• probability logic
• abduction problem