Empty-Set Effects in Quantifier Interpretation

Abstract

This paper proposes a novel, cognitively motivated theory of natural language quantification and presents experimental evidence for it. Taking into account recent findings from number cognition the theory readily explains (1) that the restrictor argument of natural language quantifiers universally has a domain-relativizing function and (2) that monotone decreasing quantifiers are often more difficult to process than increasing quantifiers. In the proposed theory, quantifiers that do not have the empty set as a witness set are simpler to evaluate than those that do (what we call empty-set quantifiers). This explains enhanced difficulty of monotone decreasing quantifiers because they are always empty-set quantifiers. Furthermore, quantificational complexity is predicted to be extraordinarily high if such an empty-set quantifier has to be evaluated in a situation in which its scope is empty (what we call empty-set situations). These predictions were tested in three experiments investigating the online comprehension and the verification of quantified sentences. The first experiment established empty-set effects, i.e., enhanced difficulty during the online interpretation and the evaluation of empty-set quantifiers relative to non-empty-set quantifiers, particularly during the evaluation of empty-set situations. The second experiment supports our claim that empty-set effects have to be distinguished from monotonicity effects. Empty-set effects were observed for the non-monotone Boolean combination of quantifiers none or three dots relative to one or three dots. The third experiment shows that the proposed theory of quantificational complexity is not limited to simply quantified sentences but can account for doubly quantified sentences, too. It was manipulated whether the first and/or the second quantifier were empty-set quantifiers. The experiment shows that the difficulty of empty-set quantifiers adds up in a cumulative fashion – a finding only expected under a ‘recursive’ version of the proposed theory.