Knowledge Vault - Please explain the local closed world assumption

Background

I'm currently reading a paper on the google knowledge vault here : http://www.cs.cmu.edu/~nlao/publication/2014.kdd.pdf.

I'm having trouble with the Local Closed World Assumption (LCWA).

My understanding of LCWA in layman's terms :

• a) If a candidate triple has the same value as contained in its knowledge base then it's labelled as true.

• b) If a candidate triple has a different value than contained in the knowledge base, it is labelled as false.

• c) If the subject and predicate are not in the knowledge base, the triple is thrown out from the test and training set.

Problem with my understanding

In Section 3.1, LCWA is used to create a labelled training set for text extractors. According to my understanding of LCWA,triples with new predicates or subjects would fall into c) and would not be used to create and train extractors.

Question

Is my understanding of LCWA correct? If so how are new facts extracted if c) causes those triples to be thrown out?

Explanation from section 2.2 of the paper

Explanation of LCWA:

Define O(s, p) as the set of existing object values for a given s and p. This set will be a singleton for functional (single-valued) predicates such as place of birth, but can have multiple values for general relations, such as children; of course, the set can also be empty. Now, given a candidate triple (s, p, o), we assign its label as follows: if (s, p, o) ∈ O(s, p), we say the triple is correct; if (s, p, o) 6∈ O(s, p), but |O(s, p)| > 0, we say the triple is incorrect (because we assume the KB is locally complete for this subject-predicate pair); if O(s, p) is empty, we do not label the triple, and we throw it out of our training / test set.