SBVR16 — Not all closed logical formulations formulate propositions

SBVR clause 21.3 (Logical formulations) says:

"Each meaning formulated by a closed logical formulation is a proposition".

This statement is false. If we assume the existence of a verb concept 'person is in location', then in a statement like: "John is in London on Tuesdays", the logical formulation of "John is in London" is closed – it contains no variables. But this usage is not intended to formulate a proposition. No assertion is made that "John is in London" is true or false, or that anyone cares. The 'meaning' that this closed logical formulation formulates is a concept – a category of 'state of affairs', whose instances are states in which John is in London.

By comparison, assuming that we also have 'state of affairs occurs on time interval', the whole sentence also has a closed logical formulation: For each Tuesday t, there is an instance of the concept "John is in London" that occurs on t. And that formulation IS intended to formulate a proposition.

When a closed logical formulation is used to represent a proposition, the interpretation as a proposition produces either 'true' or 'false', and the interpretation of the same closed logical formulation as a category of state of affairs produces a concept that corresponds to at most 1 actuality. So the SBVR statement that a true proposition corresponds to an actuality is consistent with both interpretations, and the idea that a false proposition does not correspond to an actuality is also consistent.

Now, SBVR asserts that a false proposition corresponds to a state of affairs that is not an actuality. But the closed logical formulation of a false proposition when it is interpreted as a category of state of affairs is simply a concept that does not correspond to any actuality. There is no need for it to correspond to some fictitious event or situation.

For "XYZCo needs to have an office in Miami", i.e., "XYZCo needs that XYZCo has an office in Miami", "XYZCo has an office in Miami" has a closed logical formulation that is not intended to represent a proposition, but rather a category of states of affairs. XYZCo does not need a fictitious instance of that category, it needs the category to correspond to an actuality. It is the nature of verbs like "needs" and "wants" to refer to a category with that intent. And it is no different from "XYZCo needs an XYZCo office in Miami" – "XYZCo office in Miami" refers to a concept with the intent that it should have at least one instance. There is no existing or fictitious 'XYZCo office in Miami' that XYZCo needs.

Similarly, if "Mary prevents Jimmy from playing with matches", what Mary prevents is "a 'playing with matches' by Jimmy", or equivalently, the situation 'Jimmy plays with matches'. The latter form is a closed logical formulation that is not intended to represent a proposition. It represents the same category of state of affairs that "a 'playing with matches' by Jimmy" does. Mary does not prevent one fictitious instance of that concept, but rather that the concept has any instances at all. It is the nature of "prevents" to refer to a category of states of affairs with that intent. In a similar way, one can "prevent forest fires". There is no need for the concept "forest fire" to have a fictitious instance that is prevented.

Technically, these latter usages mean is that the verb concept wording for "needs" should be:

thing1 needs thing2*

where the asterisk indicates an "intensional role" as described in SBVR A.2.6. And similarly for "prevents", "wants", etc. Similarly, the concept of occurrence should be worded:

state of affairs* occurs on time interval

The use of the intensional role makes it clear that when the thing2 or state of affairs role is played by a closed logical formulation, the intended interpretation is a concept, not a proposition.

Understanding this dual role of closed logical formulations (and the corresponding English and Structured English formulations) is critical to resolving a number of conflicts about states of affairs between SBVR and other OMG business specifications. It allows us to distinguish 'category of state of affairs' from 'state of affairs' in usages, and to recognize that 'state of affairs' and 'actuality' have exactly the same instances.