Numerical Quantifiers and Their Use in Reasoning with Negative Information

Numerical quantifiers provide simple means of formalizing such statements as, "at least three people are in that room", "at most fifteen people are in the elevator", and "everybody has exactly two parents". Although numerical quantifiers generalize the existential quantifier, they have different uses in reasoning. The existential quantifier is most useful for supplying referents for designating phrases with no previously explicitly mentioned referent. Numerical quantifiers are most useful for reasoning by the process of elimination. Numerical quantifiers would, therefore, be a useful addition to the operators of a reasoning program or deductive question-answering system. They have been added to SNePS, the Semantic Network Processing System, to further enhance its inference capabilities.