Graduation and granulation are keys to computation with information described in natural language

Abstract

Graduation and granulation play essential roles in human cognition. Both are concomitants of the bounded ability of human sensory organs, and ultimately the brain, to resolve detail and store information. Graduation relates to unsharpness of boundaries or, equivalently, fuzziness. Granulation involves clumping, with a granule being a clump of attribute values drawn together by indistinguishability, similarity, proximity or functionality. Graduation and granulation underlie the concept of a linguistic variable—a concept which plays a pivotal role in fuzzy logic and its applications. What is the connection between graduation, granulation and natural languages? Basically, a natural language is a system for describing perceptions. Perceptions are intrinsically imprecise, reflecting—as do graduation and granulation—the bounded ability of human sensory organs, and ultimately the brain, to resolve detail and store information. Imprecision of perceptions is passed on to natural language. Seen in this perspective, semantic imprecision of natural language is closely linked to graduation and granulation. Imprecision of natural language is a major obstacle to application of conventional methods of computation to computation with information described in natural language. What is computation with information described in natural language? Here are simple examples. I am planning to drive from Berkeley to Santa Barbara, with stopover for lunch in Monterey. It is about 10 am. It will probably take me about two hours to get to Monterey and about an hour to have lunch. From Monterey, it will probably take me about five hours to get to Santa Barbara. What is the probability that I will arrive in Santa Barbara before about six pm? Another simple example: A box contains about twenty balls of various sizes. Most are large. What is the number of small balls? What is the probability that a ball drawn at random is neither small nor large? Another example: A function, f, from reals to reals is described as: If X is small then Y is small; if X is medium then Y is large; if X is large then Y is small. What is the maximum of f? Another example: Usually the temperature is not very low, and usually the temperature is not very high. What is the average temperature? Another example: Usually most United Airlines flights from San Francisco leave on time. What is the probability that my flight will be delayed? Computation with information described in natural language, or NL-computation for short, is a problem of intrinsic importance because much of human knowledge is described in natural