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Sigma KEE - totalOrderingOn
?REL is a total ordering on a
only if it is a partial ordering for which either (?REL ?INST1 ?INST2) or (?REL ?INST2 ?INST1) for every ?INST1 and ?INST2 in the
Properties or qualities as distinguished from any particular embodiment of the properties/qualities in a physical medium. Instances of Abstract can be said to exist in the same sense as mathematical objects such as sets and relations, but they cannot exist at a particular place and time without some physical encoding or embodiment.
?REL is an
if for distinct ?INST1 and ?INST2, (?REL ?INST1 ?INST2) implies not (?REL ?INST2 ?INST1). In other words, for all ?INST1 and ?INST2, (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST1) imply that ?INST1 and ?INST2 are identical. Note that it is possible for an
to be a
is asymmetric if and only if it is both an
relating two items - its valence is two.
s are relations that are true only of pairs of things.
s are represented as slots in frame systems.
The universal class of individuals. This is the root node of the ontology.
The class of
s whose properties can be inherited downward in the class hierarchy via the
?REL is irreflexive iff (?REL ?INST ?INST) holds for no value of ?INST.
is a sentence-forming
. Each tuple in the
is a finite, ordered sequence of objects. The fact that a particular tuple is an element of a
is denoted by '(*predicate* arg_1 arg_2 .. arg_n)', where the arg_i are the objects so related. In the case of
s, the fact can be read as `arg_1 is *predicate* arg_2' or `a *predicate* of arg_1 is arg_2'.
of relations. There are two kinds of
s both denote sets of ordered n-tuples. The difference between these two
es is that
s cover formula-forming operators, while
s cover term-forming operators.
Belongs to Class
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