It is a deep-seated tradition in science to view the use of natural languages in scientific theories as a manifestation of mathematical immaturity. The rationale for this tradition is that natural languages are lacking in precision. However, what is not recognized to the extent that it should, is that adherence to this tradition carries a steep price. In particular, a direct consequence is that existing scientific theories do not have the capability to operate on perception-based information exemplified by "Most Finns are honest." Such information is usually described in a natural language and is intrinsically imprecise, reflecting a fundamental limitation on the cognitive ability of humans to resolve detail and store information. Because of their imprecision, perceptions do not lend themselves to meaning-representation through the use of precise methods based on predicate logic. This is the principal reason why existing scientific theories do not have the capability to operate on perception-based information.
In a related way, the restricted expressive power of predicate-logic-based languages rules out the possibility of defining many basic concepts such as causality, resemblance, smoothness, and relevance in realistic terms. In this instance, as in many others, the price of precision is over-idealization and lack of robustness.
In a significant departure from existing methods, in the approach described in this work, the high expressive power of natural languages is harnessed by constructing what is called a precisiated natural language (PNL).
In essence, PNL is a subset of a natural language (NL)--a subset that is equipped with constraint-centered semantics (CSNL) and is translatable into what is called the Generalized Constraint Language (GCL). A concept that has a position of centrality in GCL is that of a generalized constraint expressed as X isr R, where X is the constrained variable, R is the constraining relation, and isr (pronounced as ezar) is a variable copula in which r is a discrete-valued variable whose value defines the way in which R constrains X. Among the principal types of constraints are possibilistic, veristic, probabilistic, random-set, usuality, and fuzzy-graph constraints.
With these constraints serving as basic building blocks, more complex (composite) constraints may be constructed through the use of a grammar. The collection of composite constraints forms the Generalized Constraint Language (GCL). The semantics of GCL is defined by the rules that govern combination and propagation of generalized constraints. These rules coincide with the rules of inference in fuzzy logic (FL).
A key idea in PNL is that the meaning of a proposition, p, in PNL may be represented as a generalized constraint that is an element of GCL. Thus, translation of p into GCL is viewed as an explicitation of X, R and r. In this sense, translation is equivalent to explicitation.
The concept of a precisiated natural language, the associated methodologies of computing with words, and the computational theory of perceptions open the door to a wide-ranging generalization and restructuring of existing theories, especially in the realms of information processing, decision, and control. In this perspective, what is very likely is that in coming years a number of basic concepts and techniques drawn from linguistics will be playing a much more important role in scientific theories than they do today.
* Professor in the Graduate School and Director, Berkeley Initiative in Soft Computing (BISC), Computer Science Division and the Electronics Research Laboratory, Department of EECS, Univeristy of California, Berkeley, CA 94720-1776; Telephone: 510-642-4959; Fax: 510-642-1712; E-Mail: firstname.lastname@example.org. Research supported in part by ONR Contract N00014-99-C-0298, NASA Contract NCC2-1006, NASA Grant NAC2-117, ONR Grant N00014-96-1-0556, ONR Grant FDN0014991035, ARO Grant DAAH 04-961-0341, and the BISC Program of UC Berkeley.