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While reading this paper (section 3.3) I came across an unfamiliar notation:

"Given an expanded query set Q, we extract $Q_s |q_i \nsubseteq q_j|q_i,q_j \in Q_s $ "

Here Q is a set of elements. Can someone please explain what the notation means? My inference is that $q_i$ is not a subset of $q_j$ but, that doesn't make sense because $q_i$ and $q_j$ are elements in a set.

Especially Lime
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Ashoka Lella
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  • “that doesn't make sense because $q_i$ and $q_j$ are elements in a set.” — Just because they are elements in a set does not imply they aren't sets themselves (I didn't look in the paper, so I can't tell whether a subset relation makes sense in this specific case; my point is that your argument is not sound). – celtschk Nov 18 '17 at 16:33
  • @celtschk the elements themselves are not sets – Ashoka Lella Nov 18 '17 at 16:38

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The notation is nonstandard and rather confusing, but the subsequent example makes it clear. While the elements are not sets, they are strings, and the authors seem to be (ab)using subset notation between two strings to represent being a substring (i.e. one string appears as a contiguous section of the other). So $Q_s$ is the subset of all elements in $Q$ which are not substrings of any other element. Equivalently it is the smallest subset of $Q$ such that everything in $Q$ is a substring of (or equal to) something in $Q_s$

Especially Lime
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