[SCL] question about composite terms in relation/function position

[Robert E. Kent]

I am trying to understand the nature of the composite terms that occur in function or relation position. Let us concentrate on relation position here. These terms must represent relations of some arities. Must they be built using relational operators such as the "union" operator below, or can they be expressed as "ordinary" terms; that is, terms that express a relation but whose arguments are not relations. Here are two examples of possible SCL atomic sentences.

((union equal-to less-than) 3 4)

((less-than (square-root (first z)) (times (first z) (second z))) (pair 4 1))

Since the second atom has a free variable, perhaps this is not allowed. This means that we cannot express terms by implicitly using embedded first order logic interpretations. For example the second atomic sentence above elaborated as: 

(= complex-relation (less-than (square-root (first z)) (times (first z) (second z))))
(complex-relation (pair 4 1))

If only the first kind of atom is allow, perhaps this answers my question about the nature of the composite relational position terms. But then a second question crops up: in the first atom do I need to relegate the names "equal-to" and "less-than" to relational position, since they are relations which evaluate to the "less-than-equal-to" relation?

Robert E. Kent
rekent at ontologos.org
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