Context Localization for Generalized Level-Based Evaluation in Knowledge-Based Systems

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.