Witness Sets, Polarity Reversal and the Processing of Quantified Sentences

Experimental results show that the monotonicity of a quantifier (Q) affects how it is processed [4, 7, 6]. Q′s are upward entailing (UE) if they permit inferences to supersets, i.e. from Q A B follows Q A B’ for any B ⊆ B′ (e.g. every, at least five). If from Q A B it follows that Q A B’ for any B′ ⊆ B, the quantifier Q is downward entailing (DE) (e.g. no, at most five). As compared to UE Q’s, DE Q’s are more difficult to verify [4, 7] and draw inferences from [6]. Recent attempts at deriving predictions about the processing of Q’s are built on the notion of semantic automata [12], and have been presented e.g. in [11] and [10]. E.g., [11] improve on results by [8] by showing not only that the computational distinction between Q’s recognized by finite-automata and push-down automata is psychologically relevant, but also that there are differences in the time required for verifying statements involving Q’s even among the class of quantifiers recognized by finite state automata. However, since these approaches employ essentially the same kind of semantic automata for both DE and UE Q’s, they cannot explain why DE Q’s are more difficult to process than UE Q’s. To explain this, we formulate a quantification theory which predicts that the (expansion) operation employed in processing DE Q’s is more difficult than that for processing UE Q’s, because it involves (i) inferences from negative information and (ii) polarity reversal. The predictions of our account were tested in two experiments investigating the online comprehension and verification of simply (Exp. 1) and doubly quantified sentences (Exp. 2) with UE vs DE Q’s.