Neutrosophic Paraconsistent Logic: Evidence Degrees, Ontological Indeterminacy, and Scientific Evidence Synthesis

Maikel Leyva-Vázquez · Florentin Smarandache

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Classical logic prohibits contradiction as structural collapse: from a contradiction, anything follows (ex contradictione quodlibet). Two formal traditions have challenged this prohibition: da Costa's Annotated Paraconsistent Logic (LPA) [5,6], which tolerates contradictions without system collapse, and Smarandache's Neutrosophic Logic [1,2,3], which introduces genuine indeterminacy as an independent logical value. We show that LPA is algebraically a subset of neutrosophic logic via the embedding φ(A:(μ,λ)) = A:(T=μ, I=0, F=λ), which preserves all LPA operations under neutrosophic connectives. This result supports Smarandache's claim that neutrosophic logic subsumes paraconsistent logic structurally. Building on this foundation, we propose Neutrosophic Paraconsistent Logic (NPL), a development within the neutrosophic framework that adds an evidential layer: μ (favorable evidence) and λ (contrary evidence) as evidence degrees alongside the ontological I, enabling a formal distinction between epistemic contradiction (resolvable by evidence) and ontological contradiction (structurally irreducible). Nine formal propositions establish NPL's properties, including bounded paraconsistency under a defined annotated consequence relation _NPL. We formalize an Evidence Synthesis algorithm (NPL-ES) and apply it to a clinical controversy: prenatal paracetamol and autism spectrum disorder (N=17 studies), demonstrating that quality-weighted NPL annotation produces materially different and more actionable recommendations than raw vote-counting.