Quantifying sequential subsumption (Q2326402)

The paper proposes to represent the concept intension of a sequence by its subsequences. A subsumption for a case where a concept (named sequential concept) can be represented as a sequence is analyzed. A 1-1 mapping between extensional subsumption and embedding of a sequential representation (using a function representation \(g\)) is established by Theorem 1. A grid algorithm (used for quantifying subsumption) is generalized by Theorem 3; two corollaries derived from this theorem study marching sequences under two types of linear warping. Efficient algorithms to calculate the size of three forms of set intersection and several experiments to evaluate the performance of some of the algorithms are presented in the last part of paper.