SBVR — Meaning of fact-type formulation and fact type projection

Doc: dtc/06-03-02
Date: March 2006
Version: Interim Convenience Document
Chapter: 9.1.1.9
Pages:
Nature: Editorial
Severity: minor

Description:

In 9.1.1.9, 'fact type formulation' is defined as:
"projecting formulation of a referent fact type whose intension is formulated in a particular projection"

I don't know what this means. There is no referent fact type. If the formulation is closed, then it defines a fact-type. And there is no reference to the bindable target.

Is this intended to mean:
"definition of a fact type by a projection that formulates its intension"?
If that is the intent, the fact type formulation should have a referent (text?) constant, which is its name. And it introduces a set of variables corresponding to the roles of the fact type. And the intension is represented by a logical formulation in which each of those variables is free, and no other variable is free. Note that this description does not involve a projection, because there is no "set" involved. The definiens has the same syntactic structure as a projection (except that the bound variables are associated with the roles of the fact type and not with the projection per se), but the definiens means the logical formulation (the intension), while the projection means the "set" (of things that satisfies it – the extension).

If this is the intent, I would also say a fact-type formulation is not a 'logical formulation' in the usual sense – it is a definition, and cannot be substituted for 'logical formulation' in other uses.

Note also that the 'referent fact type' must be a constant, not a variable, and therefore not a 'bindable_target'. (If one allows the definition of variable fact types, it creates problems with the Henken semantics model in clause 10 – the fact types of a given SBVR model might not be enumerable.)

Now the above is all guesswork, because I don't understand the definition, and the example doesn't identify any part of it as the fact type formulation.

In the Example, the interpretation of "drinking and driving violates the rental agreement" is:
For any person such that p is-renter, IF p drinks AND p drives, THEN p violates-rental-agreement.
I don't see where any projection fits in here, except possibly for p is-renter.

In 9.1.1.10 'projection' (whose definition appears to be "some operation that results in a set"), the concept of formulating a fact type appears in the Note:
"A projection’s result can be taken in multiple ways. Which way depends on how the
projection is used. When used in an aggregating formulation or as defining a concept other
than a fact type, the result elements are simply the referents of the variable in the projection.
When used to define a fact type, each result element is taken as an actuality that involves the
referents of the variables in the projection."

This supports the idea above that 'projection' has more than one semantic interpretation, and the interpretations are only loosely consistent. And that means it fails as a "structure of meaning". It is a structure, but the meaning is imposed by something else.

Now, to define a fact type, the referents of the variables in the projection would have to be assigned to "roles", so the presumption must be that the different variables represent different roles. A "result element" must then be a tuple of referents, one for each variable, in which each 'position' corresponds to a role. Since no verb is associated with the tuple, such a tuple can be "taken as an actuality" only in the sense that the collection of referents in the tuple is related by satisfying the logical formulation that constrains the projection. But relating a variable that ranges over actualities (states of affairs) to such a tuple would be very difficult. You can only get the tuple by having a fact-type to interpret the actuality. (As Antoine says, a fact is an actuality interpreted by a fact-type.)

'Fact type formulation' appears to fill a theoretical hole in structuring meanings of natural language statements, but no good example of its use has been produced. Therefore, the resolution is to remove 'fact type formulation'.