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# The concept of protoform

The term "protoform" is an abbreviation of "prototypical form." Informally, a protoform, A, of an object, B, written as A = PF (B), is an abstracted summary of B (see Figure 6.6). Usually, B is a proposition, a system of propositions, question, command, scenario, decision problem, and so on. More generally, B may be a relation, system, case, geometrical form, or an object of arbitrary complexity. Usually, A is a symbolic expression, but, like B, it may be a complex object. The primary function of PF (B) is to place in evidence the deep semantic structure of B (see Figure 6.16).

Figure 6.16 Definition of protoform of p

• • Carol lives in a small city near San Francisco-? Residence(Carol) is
• ((city.near.SF) and small.city))

• Alan has severe back pain. He goes to see a doctor. The doctor tells him that there are two options: (1) do nothing; and (2) do surgery. In the case of surgery, there are two possibilities: (a) surgery is successful, in which case Alan will be pain free; and (b) surgery is not successful, in which case Alan will be paralyzed from the neck down. Question: Should Alan elect surgery?

• I am planning to drive from Berkeley to Santa Barbara, with stopover for lunch in Monterey. Usually, it takes about two hours to get to Monterey. Usually, it takes about one hour to have lunch. It is likely that it will take about five hours to get from Monterey to Santa Barbara. At what time should I leave Berkeley to get to Santa Barbara, with high probability, before about 6 p.m.?

Figure 6.17 Protoforms and PF-equivalence

Abstraction has levels, just as summarization does, including no summarization and/or no abstraction. For this reason, an object may have a multiplicity of protoforms (see Figure 6.17). Conversely, many objects may have the same protoform.

Such objects are said to be protoform-equivalent, or PF-equivalent, for short. For example, p: Most Swedes are tall, and q: Few professors are rich, are PF-equivalent.

A protoform may be extensional (e-protoform) or intensional (г-protoform). For example,

As in the case of meaning, an e-protoform is less informative than an i-protoform.

The concept of a protoform serves two important functions. First, it provides a basis for organization of knowledge, with PF-equivalent propositions placed in the same class. And second, in NL-computation the concept of a protoform plays a pivotal role in computation/deduction.

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