Monotonicity in quantifier verification

Monotonicity is considered to be one of the key properties of languages both in logic and linguistics. In model theory it contributes to definability (see e.g. Väänänen and Westerståhl, 2002), in linguistics it is used, among other applications, to explain the phenomenon of negative polarity items (see e.g. Ladusaw, 1979). There are also strong links between monotonicity and learnability (see e.g. Tiede, 1999). Moreover, there are good reasons to believe that it is crucial for processing natural language expressions, as has already been suggested by psychologists (see e.g.Moxey et al., 2001), linguists and logicians (see e.g., Barwise and Cooper, 1981). In fact, Geurts (2003) shows that when it comes to reasoning in natural language downward monotone quantifiers, e.g., “No boy”, are more difficult than upward monotone quantifiers, e.g., “Every boy”.