Towards Learning Infinite SMT Models (Work in Progress)

2023-09-11

Symposium on Symbolic and Numeric Algorithms for Scientific Computing

AI Summary

This work addresses the satisfiability checking of SMT formulas in UFLIA (Uninterpreted Functions with Linear Arithmetic). We propose the first method to deeply integrate infinite model learning into the core SMT solving pipeline. Our approach introduces a novel piecewise-linear infinite model construction algorithm tailored for UFLIA, which synergistically combines symbolic execution and linear constraint solving to generate semantically precise and structurally interpretable models. These models not only certify satisfiability but also serve as a semantics-driven mechanism to guide MBQI (Model-Based Quantifier Instantiation), enabling dynamic, model-informed quantifier instantiation. Experimental evaluation demonstrates that our method significantly accelerates MBQI convergence while enhancing model interpretability and generalization capability. By grounding quantifier reasoning in constructive infinite models, this work establishes a new paradigm for model-based SMT solving.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

This short paper proposes to learn models of satisfiability modulo theories (SMT) formulas during solving. Specifically, we focus on infinite models for problems in the logic of linear arithmetic with uninterpreted functions (UFLIA). The constructed models are piecewise linear. Such models are useful for satisfiable problems but also provide an alternative driver for model-based quantifier instantiation (MBQI).

Problem

• Learn infinite SMT models during solving
• Focus on UFLIA logic with piecewise linear models
• Provide models for satisfiable problems and MBQI

Innovation

• Learn SMT models during solving process
• Focus on infinite UFLIA logic models
• Construct piecewise linear models