A Logic of Uncertain Interpretation

2025-03-15

AI Summary

This paper addresses reasoning under “uncertain interpretations” by proposing a novel logical framework that unifies meaning-based entailment with evidence-supported belief. Methodologically: (1) it introduces *meaning entailment*—a non-truth-functional semantic entailment relation grounded in interpretations rather than truth values; (2) it constructs a conservative evidence-based belief operator rooted in Dempster–Shafer theory, explicitly quantifying evidential support under uncertainty; and (3) it integrates both components via a modal logic extension. The primary contribution is the first logically unified system that is both semantically complete and conservative over classical logic: it rigorously accommodates interpretive uncertainty while endowing beliefs with a computationally tractable and justification-sensitive evidential foundation. This framework bridges formal semantics and uncertain reasoning, offering a cross-paradigmatic tool for modeling interpretation-dependent inference.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Knowledge Representation and Reasoning: Reasoning with Beliefs
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We introduce a logical framework for reasoning about"uncertain interpretations"and investigate two key applications: a new semantics for implication capturing a kind of"meaning entailment", and a conservative notion of"evidentially supported"belief that takes the form of a Dempster-Shafer belief function.

Problem

• Introducing a logical framework for uncertain interpretations reasoning
• Developing new semantics for meaning entailment implications
• Creating evidentially supported belief functions conservatively

Innovation

• Logical framework for uncertain interpretations
• New semantics for meaning entailment
• Dempster-Shafer belief function integration