Inductive First-Order Formula Synthesis by ASP: A Case Study in Invariant Inference

2026-01-07

Electronic Proceedings in Theoretical Computer Science

AI Summary

Synthesizing first-order logic invariants from examples is hindered by an enormous search space and the limited scalability of existing approaches. This work proposes a unified framework based on Answer Set Programming (ASP) that systematically encodes and categorizes current methods for first-order invariant synthesis. Central to this framework is an innovative orthogonal slicing technique that partitions the formula search space into manageable subsets, enabling two complementary incremental candidate pruning strategies. The approach not only substantially accelerates state-of-the-art algorithms for inferring invariants in distributed systems but also uncovers new optimization opportunities through cross-framework composition.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Distributed Search
• Multiagent Systems: Distributed Problem Solving

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We present a framework for synthesising formulas in first-order logic (FOL) from examples, which unifies and advances state-of-the-art approaches for inference of transition system invariants. To do so, we study and categorise the existing methodologies, encoding techniques in their formula synthesis via answer set programming (ASP). Based on the derived categorisation, we propose orthogonal slices, a new technique for formula enumeration that partitions the search space into manageable chunks, enabling two approaches for incremental candidate pruning. Using a combination of existing techniques for first-order (FO) invariant synthesis and the orthogonal slices implemented in our framework FORCE, we significantly accelerate a state-of-the-art algorithm for distributed system invariant inference. We also show that our approach facilitates composition of different invariant inference frameworks, allowing for novel optimisations.

Problem

• first-order logic
• invariant inference
• formula synthesis
• transition systems
• distributed systems

Innovation

• orthogonal slices
• first-order logic synthesis
• answer set programming
• invariant inference
• formula enumeration