Monotonicity and the Complexity of Reasoning with Quantifiers

We present a natural logic for reasoning with quantifiers that can predict human performance in appropriate reasoning tasks. The model is an extension of that in (Geurts, 2003) but allows for better fit with data on syllogistic reasoning and is extended to account for reasoning with iterated quantifiers. We assign weights to inference rules and operationalize the complexity of a reasoning pattern as weighted length of proof in our logic – this results in a measure of complexity that outperforms other models in their predictive capacity and allows for the derivation of empirically testable hypotheses.