Computational verb theory

Computational verb theory, which was invented by then-University of California, Berkeley visiting scholar Tao Yang in 1997, is the theory of how to implement verbs and relative verbal phenomena in any natural languages into computers. The building block of the computational verb theory is computational verbs. The basic mathematical concept in the computational verb theory is the computational verb set(verb set, for short), which corresponds to set in Classical mathematics and fuzzy set in fuzzy theory. The following statement constitutes a verb set: “All people will go to the States”. While a fuzzy set or a classical set is most likely to state as follows: “All people (BE) in the States”. A computational verb set is more “irrational” than its classical or fuzzy counterpart. The logic in computational verb theory is called computational verb logic.

Another important mathematical concept in computational verb theory is computational verb number(verb number, for short). While a real number, an interval number and a fuzzy number can respectively represented as “3”, “[2,4]”, and “close to 3”, a computational verb number has the form such as “increase to 3”, “become old” and “remain high”. Computational verb number give numbers dynamic lives. Many operations between dynamic processes associated with numbers can be computed by applying computational verb numbers.

In the computational verb theory, the relation between adverbs (adverbials) and verbs are mathematically modeled by using a mathematical concept called operators. In this theory, each computational verb is modeled by a dynamical process of which the dynamics can be modified by either adverbs or operating verb such as “must”, “will” and “be”.

Theory

The theory of computational verb consists of the following aspects.

Mathematic Theory of Computational Verbs

The researches in this aspect of computational verbs are addressing the following issues.

  • The mathematical operations between computational verbs and other kinds of words. For example, the relation between an adverb and a verb can be defined by mathematical operators.
  • The dynamical models of computational verbs and their relations.

Physical Theory of Computational Verbs

  • How to measure the outer systems and the inner systems of computational verbs.
  • How to construct experiments for observing complex computational verbs.

Biological Theory of Computational Verbs

  • The brain dynamics for computational verbs.
  • The neural basis for constructing computational verbs in brains.

Psychological Theory of Computational Verbs

  • The cognitive basis for computational verbs.
  • The cognitive models for computational verbs.

Applications

The applications of computational verbs are:

Image Processing

Computational verb theory has been successfully applied to many dynamics-related image processing applications such as: intelligent traffic control systems (ITCS), visual flame detection, card counting and homeland security. The advantages of applying computational verbs to image processing are

  • Reduce the demand of computational resources.
  • Robust to spatio-temporal fluctuation and noise.
  • Reduce the cost of image processing platform by using low-end DSP chips and video camera.
  • Fast and reliable development of new vision products.

Some representative products based on computational verb image processing technolofies are: CardSeer card and paper sheet counting system, FaceID Webcam Face Login System for biometrics password, and FlameSky flame detecting systems.

Industrial Controllers

The control rules and experiences of human experts can be used to design different intelligent controllers, among them are fuzzy controllers. The fuzzy controllers can be further expanded into computational verb controllers. A typical fuzzy control rule is given by

  • IF the temperature HIGHT, THEN the control FAST.

This rule is in face a concise form of the following rule:

  • IF the temperature “is” HIGHT, THEN the control “is” FAST.

One should note that the only verb used in fuzzy control rule is BE. If we expand BE into any kinds of verbs such as BECOME, GO, INCREASE, FEEL, we have computational verb rules such as

  • IF the temperature “increases to” HIGHT, THEN the control “becomes” FAST.
  • IF the temperature “stays” HIGHT, THEN the control “decreases to” FAST.

Observe that the space of computational verb rules is much bigger than that of fuzzy rules.

Computational verb fuzzy controllers becomes a part of the standard course(EE6452 Introduction to Fuzzy Informatics and Intelligent Systems) for undergraduates at City University of Hong Kong. Please refer to G. Chen's homepage for the information of the instructor.

Paths

When Tao Yang invented computational verbs in 1997, he might not realize that this is the second step in science to implement a measurable linguistics, or to make linguistics as a natural sciences with a system of metrics just like that used in physics. The first step was fuzzy theory invented by L.A. Zadeh in 1965. The physical linguistics is such a theory for building the measurable linguistics. Physical linguistics leads a path to a universal theory of mind and physical world called the Theory of the Unicogse.