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We automate deep step-by step reasoning in an LLM dialog thread byrecursively exploring alternatives (OR-nodes) and expanding details (AND-nodes)up to a given depth. Starting from a single succinct task-specific initiator westeer the automated dialog thread to stay focussed on the task by synthesizinga prompt that summarizes the depth-first steps taken so far.  Our algorithm is derived from a simple recursive descent implementation of aHorn Clause interpreter, except that we accommodate our logic engine to fit thenatural language reasoning patterns LLMs have been trained on. Semanticsimilarity to ground-truth facts or oracle advice from another LLM instance isused to restrict the search space and validate the traces of justificationsteps returned as answers. At the end, the unique minimal model of a generatedHorn Clause program collects the results of the reasoning process.  As applications, we sketch implementations of consequence predictions, causalexplanations, recommendation systems and topic-focussed exploration ofscientific literature.

Full Automation of Goal-driven LLM Dialog Threads with And-Or Recursors and Refiner Oracles