Definition
A specialization of MathematicalObject and the collection of all relations. Each instance of Relation is a relation that can hold among one or more things, depending on whether the relation is unary, binary, ternary, or whatever (see arity and relationalArity). A unary relation (such as unknownSentence) is a sort of degenerate case that holds of certain individual things (in this case, all sentences that are unknown to Cyc). A binary relation (such as likesAsFriend) relates one thing to another (in this case, it relates one sentient animal to another just in case the first likes the second). A ternary relation relates certain triples of things. And so on. There are also relations of no particular fixed arity; see VariableArityRelation.
Names of relations can be used to construct sentences and other formulas. More precisely, CycL terms that denote Relations can appear in the "0th" argument (or "arg0") position of a CycLFormula (q.v.), i.e. as the term immediately following the formula's opening parenthesis.
An important subcollection of Relation is TruthFunction (q.v.), whose instances are intimately related to truth-values, as reflected in the fact that the CycL expressions that denote truth-functions can appear in the arg0 position of a CycLSentence; and a sentence (if quantificationally closed; see CycLClosedSentence), will generally be either true or false (with respect to a given context or interpretation). The major subcollections of TruthFunction are Predicate, LogicalConnective, and Quantifier (qq.v.).
Another important subcollection of Relation is Function_Denotational (q.v.), the collection of all functions. A CycL term that denotes a function can appear in the arg0 position of a CycLNonAtomicTerm (q.v.).
See also relationExtension and relationHoldsAmong.
