Interpolation and Query Rewriting

2026-06-14

AI Summary

This study investigates the application of Craig interpolation and Beth definability to the simplification of logical expressions and database queries. By integrating model-theoretic preservation theorems with semantic-syntactic transformations, the work introduces a novel algorithmic framework that takes formal proofs as input to automatically generate interpolants or explicit definitions. Building on this foundation, it develops a new form of interpolation tailored to query rewriting in databases. The approach not only renders classical logical results effectively computable but also provides both theoretical grounding and practical algorithms for query optimization, thereby substantially expanding the applicability of interpolation and definability techniques in the database domain.

Abstract

We overview applications of Craig interpolation and Beth definability to simplifying logical expressions or database queries. From the perspective of the theory of interpolation and definability the results give a number of new angles. First, they give a different take on what it means to make definability or interpolation results effective, looking at algorithms that take a proof as input and return an interpolant or explicit definition as output. Secondly, they relate interpolation and definability to preservation theorems in model theory: interpolation and definability theorems are the basis for many "semantics-to-syntax" results, relating a semantic property of a formula to its equivalence with a certain syntactic form. Thirdly, they motivate new forms of interpolation and definability, focusing on syntactic forms that are of interest in databases.

Problem

• Craig interpolation
• Beth definability
• query rewriting
• preservation theorems
• database queries

Innovation

• Craig interpolation
• Beth definability
• query rewriting
• preservation theorems
• effective algorithms