Similarity-Based Constraint Solving Modulo Commutativity: A Unified Framework

This paper introduces a similarity-based constraint-solving algorithm modulo commutativity, extending classical methods to accommodate fuzzy relations and approximate reasoning. We present a framework capable of solving equations even with function symbol mismatches. We prove the soundness, completeness, and termination of the proposed algorithm. The algorithm is implemented via a web-based interface, improving accessibility and usability.