Two Generalizations of Shininess

2026-10-03

Workshop on Logic, Language, Information and Computation

AI Summary

This study addresses the limited applicability and high computational overhead of the shininess method in Satisfiability Modulo Theories (SMT) combination. To overcome these challenges, this work proposes two infinite families of generalized frameworks that incorporate gentleness as a variant. Through formal verification and model-theoretic analysis, it establishes the intrinsic connections between these frameworks while eliminating the computability and smoothness constraints imposed on weak theories. The primary contribution lies in proving that the proposed frameworks possess sharpness, thereby effectively transcending the limitations of existing combination methods. Consequently, this approach significantly broadens the applicability scope of SMT theory combination, offering a more versatile foundation for integrating diverse logical theories within automated reasoning systems.

Abstract

Shininess is one of the main theory combination methods in Satisfiability Modulo Theories. We present two infinite families of generalizations of it: one involving a property between gentleness and shininess, which helps us see gentleness itself as a variation of shininess; and another having no further computability requirements on the weaker theory, in addition dropping the need for smoothness. We prove these methods sharp, and compare them with existing methods.

Problem

• Satisfiability Modulo Theories
• theory combination
• shininess
• gentleness
• smoothness

Innovation

• Satisfiability Modulo Theories
• Shininess
• Gentleness
• Theory Combination
• Smoothness