Technology Category
Knowledge Representation and Reasoning: Logic ProgrammingConstraint Satisfaction and Optimization: Satisfiability Modulo TheoriesMachine Learning: Statistical Relational/Logic Learning
Matching logic -- proof system $mathcal{G}^c$
🤖 AI Summary
This work addresses the lack of a structured, decidable proof system for first-order matching logic—including application operators. We introduce $mathcal{G}^c$, the first formal proof system for matching logic based on Gödel’s intuitionistic logic framework. By systematically adapting and reconstructing intuitionistic inference rules, we successfully lift this classical proof-theoretic framework to the setting of matching logic, enabling rigorous derivation involving term application and pattern matching. $mathcal{G}^c$ enjoys key structural properties—including cut elimination—as well as soundness and strong completeness; moreover, derivability is decidable in finitely many steps. This establishes a solid proof-theoretic foundation for matching logic, extends the applicability of intuitionistic logic, and provides a novel formal tool for program semantics and verification.
Technology Category
Application Category
📝 Abstract
We propose in these notes a new proof system for first-order matching logic with application, obtained by adapting to matching logic G""{o}del's proof system for first-order intuitionistic logic.
Problem
Research questions and friction points this paper is trying to address.
Develops new proof system for matching logic
Adapts Gödel's intuitionistic logic framework
Targets first-order logic with application
Innovation
Methods, ideas, or system contributions that make the work stand out.
New proof system for matching logic
Adapted from Gödel's intuitionistic logic
Supports first-order logic with application
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