The only conceptualization of a partial definition that I have figured out in any detail can be summarized by the formula:
Partial Definition = Name of Concept System + Type of Relation in Concept System
E.g., for "Wristwatch"
Definition of "Wristwatch" = "A type of timepiece"
Obviously, this parallels the Aristoteialan formula of Definiton = Genus + Specific Difference. However, I think that Aristotle commits definitions to being only in a Concept System of generic relations (supertype-subtype to our data modeling friends). Other types of Concept System exist, e.g. partative (part-whole), and associative.
In a partial definition we provide information by locating the concept to be defined within a particular Concept System, giving context to the minds we are communicating with. Of course, we must expect that these minds know about the Concept System we name in the partial definition.
The Concept System does not have to be a proximate Genus, as Aristotle would like. It could be a much higher level generic concept, though this may broaden the context too much. In the above example, locating "Wristwatch" in the concept system "Timepiece" provides more precise context than if I said "A type of instrument", "instrument being a more generic concept containing "Timepiece". Obviously, there is skill required to choose the level appropriate to the mind being communicated with.
There is also the choice of Concept System to locate the concept in. For "Wristwatch" I could have alternative partial definitions such as "A fashion accessory", or "An item of jewelery". These identify different Concept Systems within which I wish to locate "Wristwatch" for whatever my purposes may be.
The Type of Relation in the Concept System in my formula above (e.g. "type", "part", "item") is one level of abstraction up from a description of the Concept System itself. I think it serves to reinforce the essence of the Concept System.
While full definitons are not something we work on every day, I think partial definitions are very common in everyday communication.
That's enough for now. To summarize (and these points may need further proof):
- Partial Definitions exist
- A common kind of Partial Definition is to locate a concept in a Concept System
- The Partial Defintion also describes the type of relation that predominates in the Concept System
- There is skill in selecting the Concept System as one concept can belong to many Concept Systems
- There is skill in selecting the level of generalization of the Concept System
- Partial Definitions are very common in everyday language (does that mean that everyone is an ontologist?)