Context localization for generalized level-based evaluation in knowledge-based systems
TL;DR
The main theorem shows that 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 $B$.
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.
