Higher-Order Pattern Unification Modulo Similarity Relations

• URL: http://arxiv.org/abs/2507.13208v1
• Date: Thu, 17 Jul 2025 15:18:22 GMT
• Title: Higher-Order Pattern Unification Modulo Similarity Relations
• Authors: Besik Dundua, Temur Kutsia,
• Abstract summary: Combination of higher-order theories and fuzzy logic can be useful in decision-making tasks.<n>We adopt a more straightforward approach aiming at integrating two well-established and computationally well-behaved components.<n>We propose a unification algorithm for higher-order patterns modulo these similarity relations and prove its termination, soundness, and completeness.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The combination of higher-order theories and fuzzy logic can be useful in decision-making tasks that involve reasoning across abstract functions and predicates, where exact matches are often rare or unnecessary. Developing efficient reasoning and computational techniques for such a combined formalism presents a significant challenge. In this paper, we adopt a more straightforward approach aiming at integrating two well-established and computationally well-behaved components: higher-order patterns on one side and fuzzy equivalences expressed through similarity relations based on minimum T-norm on the other. We propose a unification algorithm for higher-order patterns modulo these similarity relations and prove its termination, soundness, and completeness. This unification problem, like its crisp counterpart, is unitary. The algorithm computes a most general unifier with the highest degree of approximation when the given terms are unifiable.

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