Position: Logical Soundness is not a Reliable Criterion for Neurosymbolic Fact-Checking with LLMs

As large language models (LLMs) are increasing integrated into fact-checking pipelines, formal logic is often proposed as a rigorous means by which to mitigate bias, errors and hallucinations in these models' outputs. For example, some neurosymbolic systems verify claims by using LLMs to translate natural language into logical formulae and then checking whether the proposed claims are logically sound, i.e. whether they can be validly derived from premises that are verified to be true. We argue that such approaches structurally fail to detect misleading claims due to systematic divergences between conclusions that are logically sound and inferences that humans typically make and accept. Drawing on studies in cognitive science and pragmatics, we present a typology of cases in which logically sound conclusions systematically elicit human inferences that are unsupported by the underlying premises. Consequently, we advocate for a complementary approach: leveraging human-like reasoning tendencies of LLMs as a feature rather than a bug, and using these models to validate the outputs of formal components in neurosymbolic systems against potentially misleading conclusions.