TENSA: Multi-Fidelity Neuro-Symbolic Reasoning over Temporal Hypergraphs with Configurable Fuzzy Semantics and Traceable Derivation

Large language models increasingly rely on structured knowledge graphs for grounding, but current systems treat epistemic states as flat scalars and explanations as post-hoc rationalisation. Both shortcuts are visible at the representation layer and propagate through every downstream reasoning step. We present TENSA, a neuro-symbolic reasoning system built on a bipartite temporal hypergraph, with three first-class contributions. First, multi-fidelity reasoning: every entity, situation, and attribution carries both a continuous confidence score and a discrete maturity lifecycle (Candidate ≺ Reviewed ≺ Validated ≺ GroundTruth), and reasoning traces propagate both jointly. Second, configurable fuzzy semantics: a fuzzy-logic layer exposes the four canonical t-norm families, OWA and Choquet-integral aggregation (with a supervised learning baseline for the Choquet measure), graded Allen relations, intermediate quantifiers, graded Peterson syllogisms, fuzzy formal concept analysis, Mamdani rule systems, and a scope-capped fuzzy-probabilistic hybrid surface — all selectable per query through TensaQL. Third, traceable derivation: every answer in debug mode is returned atomically with the TensaQL query and the data rows that produced it, providing auditable explanation by construction. This paper is a system description. The codebase is publicly available at https://github.com/arperon-labs/tensa under dual AGPL-3.0 + commercial licensing, and the release-tagged source tree is archived on Zenodo with the DOI registered for this record.