Monotonicity and the Complexity of Reasoning with Quantifiers

AbstractWe present a natural logic for reasoning with quanti- fiers that can predict human performance in appro- priate 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 ac- count 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.

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