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This paper advances theoretical foundations in knowledge-based systems by establishing structural conditions for context localization within generalized level-based evaluation frameworks. The work provides rigorous mathematical criteria ensuring consistency between filtering scores and localizing admissible contexts, which is critical for stabilizing non-additive support evaluation in complex AI reasoning tasks. By interpreting these results as stability criteria for evidence selection, the research directly contributes to the robustness of machine learning models operating under context-dependent constraints.
Context Localization for Generalized Level-Based Evaluation in Knowledge-Based Systems
arXiv:2608.27482v1 Announce Type: new Abstract: We study context localization for generalized level-based evaluation in knowledge-based systems. The framework models situations where a structured nonnegative score, defined on facts, rules, cases, criteria or evidence units, is evaluated through conditional aggregation tests on admissible knowledge contexts. The generalized level measure maximizes a monotone set function over all contexts whose aggregated support reaches a prescribed level. We characterize when filtering the score by a context $B$ is equivalent to localizing the admissible contexts by intersection with $B$. The main theorem shows that this consistency holds for all monotone set functions if and only if two structural conditions are satisfied: monotonicity with respect to contexts and a reduction property excluding positive localized support outside $B$. We analyze pointwise and block-generated mechanisms producing the reduction property, extend the result to parameterized systems, and interpret it as a stability criterion for context-dependent evidence selection, non-additive support evaluation and level-based knowledge aggregation.
Abstract:We study context localization for generalized level-based evaluation in knowledge-based systems. The framework models situations where a structured nonnegative score, defined on facts, rules, cases, criteria or evidence units, is evaluated through conditional aggregation tests on admissible knowledge contexts. The generalized level measure maximizes a monotone set function over all contexts whose aggregated support reaches a prescribed level. We characterize when filtering the score by a context $B$ is equivalent to localizing the admissible contexts by intersection with $B$. The main theorem shows that this consistency holds for all monotone set functions if and only if two structural conditions are satisfied: monotonicity with respect to contexts and a reduction property excluding positive localized support outside $B$. We analyze pointwise and block-generated mechanisms producing the reduction property, extend the result to parameterized systems, and interpret it as a stability criterion for context-dependent evidence selection, non-additive support evaluation and level-based knowledge aggregation.
Artificial Intelligence (cs.AI)
arXiv:2608.27482 [cs.AI]
(or arXiv:2608.27482v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2608.27482 Focus to learn more arXiv-issued DOI via DataCite
https://doi.org/10.1016/j.knosys.2026.116832 Focus to learn more DOI(s) linking to related resources
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