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248 13 Local, Global and Glocal Knowledge Representation

indicates the simple and uninteresting ConceptNode grouping three objects owned by Ben
(note that the above-given Atoms don’t indicate the ownership relationship, they just link the
three objects with textual descriptions). In this example, the ConceptNode links transparently
to physical objects and English descriptions, but in general this won’t be the case – most
ConceptNodes will look to the human eye like groupings of links of various types, that link to
other nodes consisting of groupings of links of various types, etc.
There are Atoms referring to basic, useful mathematical objects, e.g. NumberNodes like
NumberNode #4
NumberNode #3.44

The numerical value of a NumberNode is explicitly referenced within the Atom.
A core distinction is made between ordered links and unordered links; these are handled
differently in the Atomspace software. A basic unordered link is the SetLink, which groups its
arguments into a set. For instance, the ConceptNode C defined by
ConceptNode C
MemberLink A C
MemberLink B C

is equivalent to
SetLink A B

On the other hand, ListLinks are like SetLinks but ordered, and they play a fundamental role
due to their relationship to predicates. Most predicates are assumed to take ordered arguments,
so we may say e.g.
EvaluationLink
PredicateNode eat
ListLink
ConceptNode cat
ConceptNode mouse

to indicate that cats eat mice.
Note that by an expression like
ConceptNode cat

is meant
ConceptNode C
ReferenceLink W C
WordNode W #cat

since it’s WordNodes rather than ConceptNodes that refer to words. (And note that the strength
of the ReferenceLink would not be 1 in this case, because the word "cat" has multiple senses.)
However, there is no harm nor formal incorrectness in the "ConceptNode cat" usage, since "cat"
is just as valid a name for a ConceptNode as, say, "C."
We’ve already introduced above the MemberLink, which is a link joining a member to the
set that contains it. Notable is that the truth value of a MemberLink is fuzzy rather than
probabilistic, and that PLN is able to inter-operate fuzzy and probabilistic values.
SubsetLinks also exist, with the obvious meaning, e.g.
ConceptNode cat
ConceptNode animal
SubsetLink cat animal

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