[SCL] 'moderately' folded semantics

[Robert E. Kent]

Pat, John and other SCL folk,

In another forum today, John discussed the connections between various indexicals, such as pronouns, variables, and names.

John Sowa wrote:
For the Common Logic project, Pat Hayes suggested, and I quickly agreed, that we need not make any syntactic distinction between variables and proper names. If a character string is introduced by a quantifier, then it is a variable. Otherwise, it is assumed to be a name, which is treated logically in the same way as a variable introduced with an existential quantifier and having global scope (i.e., the entire text in which it occurs).

Linguistically, a proper name (noun) corresponds to an object (a specific individual), whereas a common name (noun) corresponds to a class or a relation. However, in the SCL there is no distinction between proper names and common names -- there is only names, and we can quantify over any name, no matter whether it represents an object, a class or a relation. As an example, the two expressions 'married(John, Abigail)' and '(exists (m) (exists (j) (exists (a) (m j a))))' should be equivalent. Note that the term 'married' is in relation position in the first expression, and the term 'm' is in relation position in the second expression. 

The SCL document suggests using as default the 'minimally' folded semantics that when computing contextual signatures, the assumption (for relation position) is that "a name which occurs only in relation position is not a denoting term. Such names are not required to denote individuals (although in the SCL semantics, they may do so)." But John's suggestion that in the SCL an unquantified name "is treated logically in the same way as a variable introduced with an existential quantifier and having global scope" seems to be more in keeping with a 'moderately' folded semantics, which makes the assumption that "a name which occurs in relation position also occurs in object position". This may simplify the SCL semantics. It is not the 'maximally' folded semantics, since we are only assuming that "all names denote individuals". We are not "associating every individual with both a relational and a functional extension". 

Robert E. Kent
rekent at ontologos.org
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