Authors' ORCIDs
Rana Muhammad Zulqarnain: https://orcid.org/0000-0002-2656-8679
Saalam Ali: https://orcid.org/0009-0009-2615-5207
Article Type
Research Article
Abstract
Persistent AI agents increasingly convert interaction histories into long-lived memory, making memory transformation not retrieval alone—a central reliability problem. NMIC (Neutrosophic Memory-Integrity Calculus) formalizes the integrity of write, merge, consolidation, revision, and retrieval operations over persistent memory. Each proposition is represented through an evidence ledger carrying independent truth, indeterminacy, and falsity degrees together with reliability, provenance, temporal validity, contextual applicability, and inter-evidence dependence. A dependence-normalized hazard aggregation preserves simultaneous support and opposition while making the resulting state invariant to exact evidence duplication. Pure consolidation is governed by five integrity conditions: no support invention, no opposition invention, no manufactured certainty, contradiction retention, and provenance coverage. At retrieval time, visibility is separated from assertability so that relevant contradictory memories remain accessible without being promoted to uncontested facts. Seven propositions establish boundedness, independent-evidence reduction, exact-duplicate invariance, temporal non-inversion, manufactured-certainty detectability, contradiction retention, and provenance closure. A fixed-seed synthetic stress benchmark evaluates five mechanism-level failure modes. NMIC preserves conflict/ignorance separation, yields zero duplicate-inflation error, prevents duplicate-driven decision flips, detects 92.22% of randomized manufactured-certainty transformations at tolerance 0.05 with 100% precision, and resolves the benchmark's bi-temporal queries exactly. The resulting calculus provides an auditable mathematical layer for persistent-memory transformations and can be placed beneath existing vector, graph, or language-model memory architectures.
Keywords
Neutrosophic logic, Persistent AI memory, Memory integrity, Contradiction, Indeterminacy, Provenance, Belief revision, LLM agents, Memory poisoning, Temporal validity
How to Cite
Zulqarnain, Rana Muhammad and Ali, Saalam
(2026)
"A Neutrosophic Memory-Integrity Calculus for Contradiction-Preserving Persistent AI Agents,"
Neutrosophic Systems with Applications: Vol. 26:
Iss.
9, Article 3.
DOI: https://doi.org/10.63689/2993-7159.1369
