On the Logical Content of Logic Programs

2025-03-07

AI Summary

This paper addresses the insufficient logical interpretation of knowledge content in logic programming (LP). To this end, it introduces a novel “support relation” grounded in proof-theoretic semantics, formally defined within a base extension semantics framework. This framework uniformly models classical logic, intuitionistic logic, and various intermediate logics, thereby uncovering intrinsic connections between LP semantics and diverse logical systems. By integrating model-theoretic, operational, and parametric logical analyses, the paper rigorously characterizes the expressive power of LP across these logics. The primary contribution is the establishment of the first knowledge semantics for logic programs centered on the support relation—providing a theoretically rigorous and logically broad semantic foundation for knowledge representation, automated reasoning, and formal verification.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Machine Learning: Statistical Relational/Logic Learning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

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
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

Logic programming (LP) is typically understood through operational semantics (e.g., SLD-resolution) or model-theoretic interpretations (e.g., the least Herbrand model). This paper introduces a novel perspective on LP by defining a ``support'' relation that explicates what a program ``knows''. This interpretation is shown to express classical and intuitionistic logic, as well as an intermediate logic, depending on certain choices regarding LP and the meanings of disjunction and negation. These results are formalized using the idea of base-extension semantics within proof-theoretic semantics. Our approach offers new insights into the logical foundations of LP and has potential applications in knowledge representation, automated reasoning, and formal verification.

Problem

• Defines a support relation for logic programs
• Expresses classical, intuitionistic, and intermediate logics
• Applies base-extension semantics in proof-theoretic contexts

Innovation

• Introduces support relation for logic programs
• Uses base-extension semantics for formalization
• Applies to knowledge representation and verification