Partial Rewriting and Value Interpretation of Logically Constrained Terms (Full Version)

2026-01-29

AI Summary

This study investigates the semantic relationship and distinctions between partial rewriting and universally (most general) constrained rewriting in logic-constrained term rewriting systems. To this end, the work proposes a novel partial constrained rewriting approach, introducing the concept of “value interpretation” and integrating instantiated interpretations, existentially quantified constrained terms, subsumption relations, and equivalence analysis to rigorously characterize the semantic behaviors of both rewriting paradigms. The paper establishes a precise correspondence between partial and most general rewriting under subsumption and equivalence, while also uncovering subtle semantic differences between them. These results provide a refined formal foundation for both theoretical analysis and practical applications of constrained rewriting systems.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Logic Programming
• Machine Learning: Statistical Relational/Logic Learning

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: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

Logically constrained term rewrite systems (LCTRSs) are a rewriting formalism that naturally supports built-in data structures, including integers and bit-vectors. The recent framework of existentially constrained terms and most general constrained rewriting on them (Takahata et al., 2025) has many advantages over the original approach of rewriting constrained terms. In this paper, we introduce partial constrained rewriting, a variant of rewriting existentially constrained terms whose underlying idea has already appeared implicitly in previous analyses and applications of LCTRSs. We examine the differences between these two notions of constrained rewriting. First, we establish a direct correspondence between them, leveraging subsumption and equivalence of constrained terms where appropriate. Then we give characterizations of each of them, using the interpretation of existentially constrained terms by instantiation. We further introduce the novel notion of value interpretation, that highlights subtle differences between partial and most general rewriting.

Problem

• logically constrained term rewriting
• partial rewriting
• existentially constrained terms
• most general constrained rewriting
• value interpretation

Innovation

• partial constrained rewriting
• existentially constrained terms
• value interpretation
• most general constrained rewriting
• logically constrained term rewrite systems