SMTB: Fast Structure-Mapping with Tight Bounds

2026-09-21

AI Summary

本文提出了一种新的结构映射算法SMTB，它比现有方法SME快5-15倍，并在大型嵌套领域中寻找映射的能力提高了约50%，通过最大化关系连接性而非优先考虑高阶关系来解决结构映射问题。

Abstract

Structure-mapping forms analogies by aligning systems of relationally connected elements based on shared structure instead of surface features. We introduce a new structure-mapping algorithm: Structure-Mapping with Tight Bounds (SMTB) that is 5--15x faster than the structure-mapping engine (SME) and about 50\% better at finding mappings in large nested domains. SMTB is part of the broader Cognitive Rule Engine (CRE) project, a flexible multi-language-compatible framework with an accessible Python interface to state-of-the-art C++ implementations of core algorithms commonly used in cognitive systems such as pattern matching, planning, and structure-mapping. CRE and SMTB are designed to work with a wide range of representation choices. Unlike SME, which biases higher-order correspondences in tree-like predicate logic, SMTB maximizes relational connectivity without privileging higher-order relations. This allows SMTB to work just as well over arbitrary relational graphs as it does in tree-like domains of nested predicate logic. We discuss situations where privileging "higher-orderness" in structure-mapping can cause issues, and illustrate how SMTB avoids failure modes that SME would encounter in these situations. We also provide an evaluation comparing SMTB to SME v4 over 5845 domain pairs from the SME corpus.

Problem

• structure-mapping
• relational connectivity
• nested domains
• higher-order relations
• algorithm speed

Innovation

• Structure-Mapping with Tight Bounds (SMTB)
• Cognitive Rule Engine (CRE)
• relational connectivity
• arbitrary relational graphs
• higher-order relations