Monotonicity has only a relative effect on the complexity of quantifier verification

Abstract

We discuss a computational model of quantifier verification. It predicts that there is no effect of monotonicity on the verification of numerical quantifiers but only the interaction of monotonicty and sentential truth-values. Moreover, it predicts no monotonicity or interaction with truth-values effects for proportional quantifiers. We present an experimental study supporting the predictions of the computational model. We argue that the role of the interaction between monotonicty and sentential truth-values as well as the differences between various quantifier classes (numerical vs. proportional) have been regularly overlooked in the literature.