What Was Said, Not What Was 'Thought': Type-6 Logic for CoT Verification

arXiv:2609.38420v1 Announce Type: cross Abstract: We introduce Type-6 logic, a variant of dynamic epistemic logic augmented with two operators (uncertainty and recurrence), designed to model the inferential dynamics of contemporary large language model (LLM) chain-of-thought (CoT) reasoning. Type-6 accounts for common LLM reasoning pathologies such as unlicensed revision, enthymemes, loopbacks, and unverifiable/incorrect claims. We propose a verifier based on Type-6 logic that builds a graph out the trace, and checks it against Type-6's axioms and inference rules. We evaluate our framework on LLM-generated CoTs four splits spanning formal and informal reasoning. Our verifier detects structurally unsound reasoning steps that surface-level heuristics miss, and allows for easy visualisation of the model's reasoning process. In our corpus, our verifier shows that derived contradiction is the most common hard-fail category in CoT, and that only about 3\% of the propositions of a trace have impact on the final derivation. Ablation studies show that other verification methods (LLMs-as-judges, other neurosymbolic approaches, etc.) cannot be considered interchangeable: for example, agreement between LLMs-as-judges and LINC is $\kappa \approx 0.034$, and this persists within a method across underlying models. Type-6, however, is the most agreed-with method amongst the ones we tested. We prove our verifier runs on average-case linear time; and release our logic specification and artefacts.

Abstract:We introduce Type-6 logic, a variant of dynamic epistemic logic augmented with two operators (uncertainty and recurrence), designed to model the inferential dynamics of contemporary large language model (LLM) chain-of-thought (CoT) reasoning. Type-6 accounts for common LLM reasoning pathologies such as unlicensed revision, enthymemes, loopbacks, and unverifiable/incorrect claims. We propose a verifier based on Type-6 logic that builds a graph out the trace, and checks it against Type-6's axioms and inference rules. We evaluate our framework on LLM-generated CoTs four splits spanning formal and informal reasoning. Our verifier detects structurally unsound reasoning steps that surface-level heuristics miss, and allows for easy visualisation of the model's reasoning process. In our corpus, our verifier shows that derived contradiction is the most common hard-fail category in CoT, and that only about 3\% of the propositions of a trace have impact on the final derivation. Ablation studies show that other verification methods (LLMs-as-judges, other neurosymbolic approaches, etc.) cannot be considered interchangeable: for example, agreement between LLMs-as-judges and LINC is $\kappa \approx 0.034$, and this persists within a method across underlying models. Type-6, however, is the most agreed-with method amongst the ones we tested. We prove our verifier runs on average-case linear time; and release our logic specification and artefacts.

Logic in Computer Science (cs.LO); Artificial Intelligence (cs.AI); Computation and Language (cs.CL)

arXiv:2609.38420 [cs.LO]

(or arXiv:2609.38420v1 [cs.LO] for this version)

https://doi.org/10.48550/arXiv.2609.38420 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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What Was Said, Not What Was 'Thought': Type-6 Logic for CoT Verification

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