INDUCTION: Finite-Structure Concept Synthesis in First-Order Logic

2026-02-21

AI Summary

This work addresses the problem of inducing unified, concise, and generalizable first-order logic formulas to explain a target concept from labeled examples over finite relational structures. To this end, the authors introduce INDUCTION, a new benchmark comprising three settings—FullObs, CI, and EC—and incorporate a formula inflation penalty alongside exact model-checking validation. Their approach integrates formal first-order logic representations with contrastive learning, existential completion, and complexity control. Experimental results reveal a significant difficulty gradient across tasks and identify families of structures that are inherently hard to generalize over. The findings demonstrate that formulas with lower inflation exhibit superior generalization to unseen worlds, and that state-of-the-art models display fundamentally distinct inductive behaviors across the different benchmark settings.

Technology Category

Knowledge Representation and Reasoning: Computational Complexity of ReasoningConstraint Satisfaction and Optimization: Satisfiability Modulo TheoriesMachine Learning: Statistical Relational/Logic Learning

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingGraph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphsSemantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

We introduce INDUCTION, a benchmark for finite structure concept synthesis in first order logic. Given small finite relational worlds with extensionally labeled target predicates, models must output a single first order logical formula that explains the target uniformly across worlds, with correctness verified via exact model checking. The benchmark includes three regimes, FullObs, CI (contrastive), and EC (existential completion), nd penalizes formula bloat. We find sharp difficulty gradients, persistent hard structural families, and observe that low bloat formulas generalize far better on held out worlds. Elite recent models show qualitatively different behaviors across tasks and performance metrics, hinting to their different strategies of concept generalization.

Problem

• concept synthesis
• first-order logic
• finite structures
• relational reasoning
• formula generalization

Innovation

• concept synthesis
• first-order logic
• finite structures
• formula bloat
• model checking