Communication Dans Un Congrès Année : 2025

Combining Generalization Algorithms in Regular Collapse-Free Theories

Résumé

We look at the generalization problem modulo some equational theories. This problem is dual to the unification problem: given two input terms, we want to find a common term whose respective two instances are equivalent to the original terms modulo the theory. There exist algorithms for finding generalizations over various equational theories. We focus on modular construction of equational generalization algorithms for the union of signature-disjoint theories. Specifically, we consider the class of regular and collapse-free theories, showing how to combine existing generalization algorithms to produce specific solutions in these cases. Additionally, we identify a class of theories that admit a generalization algorithm based on the application of axioms to resolve the problem. To define this class, we rely on the notion of syntactic theories, a concept originally introduced to develop unification procedures similar to the one known for syntactic unification. We demonstrate that syntactic theories are also helpful in developing generalization procedures similar to those used for syntactic generalization.

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hal-05318420 , version 1 (16-10-2025)

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Mauricio Ayala-Rincón, David M Cerna, Temur Kutsia, Christophe Ringeissen. Combining Generalization Algorithms in Regular Collapse-Free Theories. FSCD 2025 - 10th International Conference on Formal Structures for Computation and Deduction, Jul 2025, Birmingham, United Kingdom. pp.7:1-7:18, ⟨10.4230/LIPIcs.FSCD.2025.7⟩. ⟨hal-05318420⟩
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