Pragmatic effects in processing superlative and comparative quantifiers

I present and discuss results of the experiment in which I investigate processing of so-called superlative quantifiers, such as at most n and at least n (where n represents a bare numeral), as well as their (presumably) logically equivalent though linguistically different forms, i.e. the disjunctive and the comparative form. Generalized Quantifier Theory (GQT ) defines those superlative quantifiers as equivalent to comparative quantifiers, i.e. fewer than n+1 and more than n-1 respectively. However, numerous differences have been observed between these presumably equivalent forms involving their linguistic use, as well as the inference patterns in which they occur, and their processing (Geurts, 2006), (Koster-Moeller et al., 2008), (Geurts et al., 2010), (Cummins and Katsos, 2010). For instance it has been shown that the logically valid (according to GQT ) inference in which from at most n A are B it is implied that at most n+1 A are B is, in general, not accepted by speakers (Geurts et al., 2010), (Cummins and Katsos, 2010). There is ample data concerning differences between processing of superlative and comparative quantifiers. For instance verification of sentences with superlative quantifiers requires supposedly more time than verification of sentences with respective comparative quantifiers (Koster-Moeller et al., 2008), (Geurts et al., 2010). Moreover, the processing of quantifiers is influenced by their monotonicity: Although the downward monotone quantifiers at most n and fewer than n take a longer time to be verified than the upward monotone quantifiers at least n and more than n, they are actually falsified faster (Koster-Moeller et al., 2008). To account for those data, Geurts (Geurts and Nouwen, 2007), (Geurts et al., 2010) proposes that whereas comparative quantifiers have a conventional meaning, superlative quantifiers have a modal component in their semantics, and hence both at most n A are B and at least n A are B logically imply that it is possible that there are exactly n A that are B. In contrast, Cummins and Katsos (Cummins and Katsos, 2010) propose that the considered linguistic phenomena can be better explained on pragmatic grounds. The authors show that people do not evaluate at most n and exactly n-1 as equally semantically incoherent as cases of obvious logical incoherence. Consequently, Cummins et al. agree with Geurts that at most n and at least n both imply it is possible that n but they claim that this is a pragmatic rather than a logical inference, namely a so-called clausal implicature. In order to test the predictions of the pragmatic and the semantic theory regarding the modal component in the meaning of superlative quantifiers, I conducted a sentence-picture verification experiment with reaction time measure. The experiment was designed to compare subjects’ correctness and processing effort (measured as a time taken to respond correctly) as depended on the the model in which the sentence is evaluated, i.e. whether it is pragmatically felicitous or not, and on the linguistic form in which the quantifier occurs. The predictions were as follows: If a sentence φ: At most n A are B logically implies ψ : It is possible that there are exactly n, then φ should be rejected in models in which there are fewer than n A that are B, since its logical consequence ψ is false about such models. If, however, ψ is a pragmatic inference from φ, then it should be defeasible and φ should remain true in the considered models. The presence of this kind of pragmatic inference (ψ) should, however, have some effect on subjects’ behavior. The hypothesis is that only in those models which are pragmatically less felicitous