ALBI: LLM-Guided Inductive Logic Programming via Iterative Generate-Test-Constrain Refineme

We introduce ALBI (Agent for Learning By Induction), a neuro-symbolic ILP framework that replaces the ASP-based hypothesis generator in the Learning from Failures (LFF) paradigm with a Large Language Model (LLM), while retaining SWI-Prolog as a formal verifier. ALBI implements an iterative generate-test-constrain loop: the LLM proposes candidate hypotheses from structured prompts; Prolog tests each candidate; and diagnostic feedback drives refinement. We further introduce semantic anonymization, a metamorphic testing methodology, to distinguish structural symbolic induction from surface-level pattern matching on predicate names. Experiments on 30 standard ILP benchmarks show that ALBI achieves 100% success across three frontier LLMs (Gemini 3.1 Pro, GPT 5.4 Pro, Claude Opus 4.6), matching Popper while requiring only 1.4-1.7 iterations on average. Under anonymization, all models maintain 100% success with a moderate iteration increase (1.36-1.67 times), providing evidence of robust symbolic reasoning.