The concept of a generalized constraint - a bridge from natural languages to mathematics

The concept of a generalized constraint was introduced close to two decades ago. For a number of years, it lay dormant and unused. But then, in the mid-nineties, it found an important application as a basis for the methodology of computing with words (CW). More recently, an idea which began to crystallize is that the concept of a generalized constraint may serve an important function as a bridge from natural languages to mathematics. In the role, it may find many applications, ranging from formalization of legal reasoning to enhancement of Web intelligence and natural language understanding. The basis for the expectation is that as we move further into the age of machine intelligence and mechanized reasoning, the problem of natural language understanding looms larger and larger in importance and visibility. Traditional approaches to natural language understanding are based on classical, Aristotelian, bivalent logic. So far, use of traditional approaches has met with limited successes. The principal problem is that, basically, natural languages are systems for describing perceptions, and as such are intrinsically imprecise in ways that put them beyond the reach of bivalent logic and probability theory.