"From Computing with Numbers to Computing with Words to Computation with Perceptions -- A Paradigm Shift"

1/28/2000: [time not recorded]
[location not recorded]

Abstract: One of the most deep-seated traditions in science has been and continues to be that of according much more respect to numbers than to words. The essence of this tradition was stated succinctly by Lord Kelvin in 1883: "I often say that when you can measure what you are talking about and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind." In a world that is changing as rapidly as ours, no tradition can have permanence and no dogma can remain beyond challenge forever. What Lord Kelvin did not foresee is the advent of the computer age and the ballistic ascent in the capability of computers to process huge volumes of information at high speed, low cost and high reliability. Paradoxically, it is this capability that reverses the direction of inequality in the respectability of words and numbers. This is the crux of the paradigm shift that is alluded to in the title of my talk. It is a truism that the quest for precision has led to brilliant successes. There is so much that we can do today that even Jules Verne could not have predicted. We have cellular phones and the Internet; we have eyeprint identification systems and the GPS; we can clone animals and transplant organs. But alongside the brilliant successes we see many problem-areas where progress has been slow and many problems which cannot be solved by any prolongation of existing theories, methodologies and technologies. A case in point is the problem of automation of driving in city traffic. This is easy for humans and an intractable problem for machines. Driving in city traffic is an example of the remarkable human capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Everyday examples of such tasks are parking a car, playing golf, deciphering sloppy handwriting and summarizing a story. Underlying this capability is the brain's crucial ability to reason with perceptions -- perceptions of time, distance, speed, force, direction, shape, intent, likelihood, truth and other attributes of physical and mental objects. In science, it is a long-standing tradition to deal with perceptions by converting them into measurements. But what is becoming increasingly evident is that, to a much greater extent than is generally recognized, conversion of perceptions into measurements is infeasible, unrealistic or counterproductive. With the vast computational power at our command, what is becoming feasible is a countertraditional move from measurements to perceptions. What this implies is a major enlargement of the role of natural languages in scientific theories. This is the essence of the paradigm shift which, in my view, is likely to take place in coming years. The theory which is put forth in my talk is focused on the development of what is referred to as the computational theory of perceptions (CTP) -- a theory which comprises a conceptual framework and a methodology for computing and reasoning with perceptions. The base for CTP is the methodology of computing with words (CW). In CW, the objects of computation are words and propositions drawn from a natural language. A typical problem in CW is the following. Assume that a function f, Y=f(X), is described in words as: if X is small then Y is small; if X is medium than Y is large; if X is large then Y is small, where small, medium and large are labels of fuzzy sets. The question is: What are the maximum and maximizing values of Y and X respectively? The point of departure in the computational theory of perceptions is the assumption that perceptions are described as propositions in a natural language, e.g., "Michelle is slim," "it is likely to rain tomorrow," "economy is improving," "it is very unlikely that there will be a significant increase in the price of oil in the near future." In this perspective, natural languages may be viewed as systems for describing perceptions. Furthermore, computing and reasoning with perceptions is reduced to computing and reasoning with words. To be able to compute with perceptions it is necessary to have a means of representing their meaning in a way that lends itself to computation. Conventional approaches to meaning representation cannot serve this purpose because the intrinsic imprecision of perceptions puts them well beyond the expressive power of predicate logic and related systems. In the computational theory of perceptions, meaning representation is based on what is referred to as constraint-centered semantics of natural languages (CSNL). A concept which plays a central role in CSNL is that of a generalized constraint. Conventional constraints are crisp and are expressed as X is C, where X is a variable and C is a crisp set. In a generic form, a generalized unconditional constraint is expressed as X isr R, where X is the constrained variable; R is the constraining (fuzzy) relation which is called the generalized value of X; and isr, pronounces as ezar, is a variable copula in which the value of the discrete variable r defines the way in which R constrains X. Among the basic types of constraints are the following: equality constraints (r:=); possibilistic constraints (r:blank); veristic constraints (r:v); probabilistic constraints (r:p); random set constraints (r:rs); usuality constraints (r:u); fuzzy graph constraints (r:fg); and Pawlak set constraints (r:ps). In constraint-centered semantics, a proposition, p, is viewed as an answer to a question, q, which is implicit in p. The meanings of p and q are represented as generalized constraints, which play the roles of canonical forms of p and q, CF(p) and CF(q), respectively. CF(q) is expressed as: X isr ?R, read as "What is the generalized value of X?" Correspondingly, CF(p) is expressed as: X isr R, read as "The generalized value of X isr R." The process of expressing p and q in their canonical forms plays a central role in constraint-centered semantics and is referred to as explicitation. Explicitation may be viewed as translation of p and q into expressions in GCL -- the Generalized Constraint Language. In the computational theory of perceptions, representation of meaning is a preliminary to reasoning with perceptions -- a process which starts with a collection of perceptions which constitute the initial data set (IDS) and terminates in a proposition or a collection of propositions which play the role of an answer to a query, that is, the terminal data set (TDS). Canonical forms of propositions in IDS constitute the initial constraint set (ICS). The key part of the reasoning process is goal-directed propagation of generalized constraints from ICS to a terminal constraint set (TCS) which plays the role of the canonical form of TDS. The rules governing generalized constraint propagation in the computational theory of perceptions coincide with the roles of inference in fuzzy logic. The principal generic rules are: conjunctive rule; disjunctive rule; projective rule; surjective rule; inversive rule; compositional rule; and the extension principle. The generic rules are specialized by assigning specific values to the copula variable, r, in X isr R. The principal aim of the computational theory of perceptions is the development of an automated capability to reason with perception-based information. Existing theories do not have this capability and rely instead on vconversion of perceptions into measurements -- a process which in many cases is infeasible, unrealistic or counterproductive. In this perspective, addition of the machinery of the computational theory of perceptions to existing theories may eventually lead to theories which have a superior capability to deal with real-world problems and make it possible to conceive and design systems with a much higher MIQ (Machine IQ) than those we have today.

Last updated: Mon Jun 19 17:44:06 2006