Counterfactual Neuro-Symbolic Proof-Carrying Memory for Auditable Multi-Hop Reasoning on Unstructured Data

Knowledge-intensive language understanding suffers a structural reliability bottleneck: fluent answers can be produced without logically sufficient support, especially in multi-hop question answering and dynamic knowledge graphs where edge drift degrades retrieval. We introduce Counterfactual Neuro-Symbolic Proof-Carrying Memory (CNS-PCM), a backbone-agnostic neuro-symbolic harness that decouples frozen neural representations from inspectable symbolic verification checks. Candidate reasoning chains are discovered via ontology-constrained beam search (Γ) and compiled into a compact proof-carrying memory carrying crisp domain validity flags (κk), NLI-derived contradiction scores (ρk), and textual support confidences (αk). At inference time, a counterfactual verifier stress-tests prediction stability across a targeted pool of J=12 graph interventions sampled via betweenness centrality, requiring O(J·K·d) localized re-scoring operations over the K≤16 retained proofs (or O(J·d) at fixed memory capacity K, where empirical proof depth satisfies d≤3 for >94% of retained paths under a search ceiling mmax=6, bounding verifier latency overhead to ≈45 ms per query), and abstains when evidence is unstable. Rather than invasive early token fusion or prompt linearization, CNS-PCM externalizes verification into an inspectable audit record while training lightweight adapter heads using task, logical-consistency, intervention-invariance, and differentiable Brier calibration objectives. Evaluated on official public splits of HoVer, HotpotQA, and FEVEROUS with headline F1 scoring ABSTAIN as incorrect, CNS-PCM achieves test F1 scores of 80.6%, 75.2%, and 79.0%, outperforming LLaMA-2-7B + CoT (72.4%/67.1%/70.2%), GraphRAG (78.5%/73.8%/77.4%), and unthresholded Logic-LM (79.1%/74.1%/77.9%). Specifically, CNS-PCM reduces total gold-unsupported accepted assertions on the validation splits by up to 2.4 percentage points (lowering total unsupported rate from 16.4% to 14.7%, and correct-but-ungrounded assertions from 6.8% to 5.3%) and reduces Expected Calibration Error (ECE) to 6.5%, maintaining 95.2% final test coverage via a bounded re-try feedback loop (R¯=0.471 re-tries). Component ablations confirm that training invariance and inference gating provide complementary gains, while sensitivity analyses identify Stage-2 entity linking as the primary reliability lever.