[UAI] The concept of cointensive precisiation     The message which follows is unconventional for UAI. It is intended
to draw attention of the UAI community to a concept which may shed some
light on why there are so many basic concepts for which operational
definitions do not exist. Among such concepts are those of causality,
relevance, summary, recession, pornography, mountain and many others.

    One of the principal objectives of AI is mechanization of reasoing
and question-answering. Reasoning involves knowledge. Much of human
knowledge is expressed in a natural language. What this implies is that,
in large measure, mechanization of reasoning and question-answering
reduces to mechanization of deduction from data expressed in a natural
language.

    A prerequisite to deduction from data expressed in a natural
language is precisiation of meaning. To illustrate, assume that the
datum is p: Most Swedes are tall, and the question is q: What is the
average height of Swedes? Clearly, to answer this question it is
necessary to precisiate the meaning of most and tall.

    How can a proposition, p, which is expressed in a natural language,
be precisiated? A key idea which is described in my paper "Precisiated
Natural Language (PNL)" AI Magazine, Vol. 25, No. 3, 74-91, 2004, is to
represent the meaning of p as a generalized constraint of the form X isr
R, where X is the constrained variable, R is a constraining relation and
r is an indexing variable whose value defines the modality of the
constraint, that is, its semantics. The principal constraints are
possibilistic (r=blank); veristic (r=v); probabilistic (r=p); usuality
(r=u); random set (r=rs); fuzzy graph (r=fg); bimodal (r=bm); and group
(r=g). The primary constraints are probabilistic, possibilistic and
veristic. The standard constraints, which are the constraints that
underlie standard logic and probability theory, are bivalent
possibilistic, bivalent veristic and probabilistic.

    A generalized constraint which precisiates the meaning of p is
referred to as a precisiand of p, denoted as GC(p). A point of basic
importance is that p may be precisiated in many different ways, giving
rise to precisiands GC1(p), ..., GCn(p). A precisiand, GC(p), is
cointensive with p if the intension of GC(p) is a close approximation to
that of p, with intension used in its technical sense as the meaning of
p. In this perspective, the problem of precisiation is that of picking a
generalized constraint whose intension (meaning) is close to the
intended intension (meaning) of p. To illustrate, for p: Speed limit is
65 mph, the precisiand GC(p): Speed of less than or equal to 70 mph is
allowed, and speed above 70 mph is not allowed, is not cointensive. A
cointesive precisiand would be GC(p): If speed is less than about 70
mph, probability of getting a ticket is very low; if speed is between
about 70 mph and about 80 mph, probability is medium; and over about 80
mph, probability is high.

    Definition of a concept, C, may be viewed as a precisiation of the
proposition X is C. If C is a fuzzy concept, that is, C is a matter of
degree, then, in general, there does not exist a cointensive precisiand
of p within the class of standard constraints. This is the reason why
one cannot find cointensive definitions of such concepts in the
literature. What this means is that cointensive definitions of concepts
such as causality, relevance, summary, recession, pornography and
mountain cannot be formulated within the conceptual structure of
standard logic and probability theory. If you do not agree with this
conclusion, try to define what is meant by a mountain.


