Computational verb systems: Verb numbers

In this paper the concepts of(computational) verb number and arithmetical operations of verb numbers are presented. A verb number is a kind of special computational verb, which is derived from structures of(host) verb + (real, interval, fuzzy) number. From the linguistic point of view, a verb number is a computational verb with contexts defined by (real, interval, fuzzy) numbers. Verb numbers can be classified into three basic types based on the outer systems of host verbs. The arithmetic for verb numbers and its rules are presented and proved. If host computational verbs degrade to BE, then verb numbers collapse to real numbers, interval numbers, fuzzy numbers (sets), or other numbers. The set of all verb numbers can be a metric space. The distance between verb numbers can be defined based on the collapses of verb numbers. The cases when verb numbers collapse to triangular fuzzy numbers, trapezoidal fuzzy numbers, and interval numbers are presented and proved. (C) 2001 John Wiley & Sons, Inc.