Deduction goes forward. Induction goes up. Abduction goes backward — and LLMs can't do it.
Abductive reasoning: given an observation, infer the most likely explanation. Unlike deduction (given premises, derive conclusions) and induction (given examples, derive rules), abduction requires generating hypotheses, evaluating their plausibility, and backtracking when evidence contradicts them. LLMs fail at this because the reasoning is non-monotonic — new evidence can invalidate previous conclusions — and the search space is underdetermined — multiple explanations are consistent with the same observations (arXiv:2603.21250).
The failure modes are specific: fabricated evidence (the LLM generates plausible-sounding support for a hypothesis that isn't grounded in the observations), context deterioration (long reasoning chains lose track of earlier constraints), failed backtracking (the model commits to an explanation and can't undo it), and premature stopping (declaring success before adequately testing alternatives).
Graph of States: a causal graph encodes logical dependencies between observations and hypotheses. A state machine governs valid transitions — what reasoning steps are allowed from each state. Multi-agent collaboration splits the reasoning across agents with different roles (hypothesis generation, evidence evaluation, consistency checking). The structured representation transforms unstructured exploration into directed, convergent search.
The structural insight: abduction is harder than deduction or induction because it requires managing belief states — what you currently think is true, what evidence supports it, and what would force a revision. LLMs process tokens, not belief states. The graph and state machine provide the belief management infrastructure that token prediction lacks. The reasoning ability isn't missing from the model — the representation for managing the reasoning is missing.