What does "subset" mean as a verb?

Quoted from http://xml-tips.assistprogramming.com/sgml-xml-html-xhtml-all-together.html:

XHTML is the basis for a family of future document types that extend and subset HTML.

I understand subset here is a verb. Does it mean XHTML is a subset of HTML or HTML is a subset of XHTML?

Solution 1:

Both previous answers have pretended (implicitly) that the text read

XHTML […] subsets HTML.

But in fact, the sentence reads (again, only the relevant fragment):

… document types that … subset HTML.

It’s those document types that, each on its own, are subsets of HTML. This explains the apparent contradiction that XHTML both extends and subsets HTML: parts of XHTML extend HTML, whereas other parts are subsets of HTML. (As an example of an XHTML document type that extends HTML, consider XForms, and for a subset of HTML, consider XHTML 1.0 strict.)

Either way, the usage of “subset” as a verb is meant to mean “be a subset of”.

Solution 2:

It means that XHTML is a subset of HTML.

• XHTML is the basis for a family of future document types, therefore:
• XHTML is in this family of documents
• these documents extend and subset HTML, therefore:
• XHTML subsets HTML, therefore:
• XHTML is a subset of HTML