MetaPCR-LLM: Universal Proof-Carrying Reasoning Across Heterogeneous Logics for Large Language Model Validation

Large language models can combine inference steps governed by different logical semantics, so locally valid steps may still form an invalid reasoning chain. MetaPCR-LLM represents such chains as typed, labeled proof graphs and checks transfers between native validators. Across four constructed or transformed hallucination datasets, it improves pooled hallucination F1 from 0.77 to 0.83 relative to ValidLLP-style validation, while also improving step-validity and chain-certification decisions. On independently annotated ProcessBench, RAGTruth, and ProofWriter samples, it improves error detection, contextual hallucination detection, and query accuracy, respectively, over the matched ValidLLP-style comparator. In mixed-logic cases, disabling bridge checks reduces performance, indicating that locally accepted steps require explicit composition checks. Error analysis identifies decomposition, routing, and formalization as continuing sources of failure; specialist methods also retain advantages on some tasks. Validation incurs a modest latency increase. These findings support cross-logic composition checks in the evaluated settings, while formal guarantees remain conditional on encoded premises, supported fragments, and trusted checking procedures.