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By Chris Cummins

This booklet considers how expressions regarding quantity are utilized by audio system and understood through hearers. A speaker's number of expression could be a advanced challenge even in particularly simple-looking domain names. with regards to numerical expressions, there are frequently many decisions that will be semantically appropriate: for example, if 'more than two hundred' is correct, then so is 'more than 199', 'more than 150', and 'more than 100', between others. A speaker doesn't make a choice from those strategies arbitrarily but in addition doesn't constantly keep on with any uncomplicated rule. The hearer is not only in what has been stated but additionally in any more inferences that may be drawn.

Chris Cummins deals a suite of standards that separately effect the speaker's number of expression. the method of selecting what to claim is then handled as an issue of a number of constraint delight. This method allows a number of diversified issues, drawn from ideas of semantics, philosophy, psycholinguistics and the psychology of quantity, at the same time to be built-in inside a unmarried coherent account. This constraint-based version deals novel predictions approximately utilization and interpretation which are borne out experimentally and in corpus study. It additionally explains complex facts in numerical quantification that experience formerly been dealt with by means of extra stipulative capacity, and provides a possible line of assault for addressing the matter of the speaker's selection in additional common linguistic environments.

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Technically, this means that we are casting the informativeness constraint as a faithfulness constraint, in that it governs the relation between the speaker’s knowledge state and the utterance, rather than applying to the utterance in isolation. That is to say, if, in some situation, a speaker knows that ‘more than ’ is the case, then the candidate utterance ‘more than ’ will incur a violation of this constraint. However, if the speaker’s best knowledge runs to ‘more than ’, then the utterance ‘more than ’ incurs no violation of informativeness, even if the real-world situation is just the same as in the previous example.

We might also posit that more prolix forms such as ‘give or take’ or ‘plus or minus m’ incur additional violations of the simplicity constraint, although the latter in particular might be favoured on the grounds of informativeness (or even considered to be double-bounded). ). Within the ‘single-bounded’ category, things are potentially more interesting, because there are several productive ways to express this type of quantification. These include ‘more/fewer/less than’, ‘at least/ most’, and ‘no(t) more/fewer/less than’.

Moreover, whatever the underlying cognitive representations, round numbers are expressed in few words (given their magnitude), which makes them especially efficient in oral communication. ) might acquire particular psychological prominence. For these reasons, I posit a constraint requiring the speaker to use a round number. However, in order to define and quantify violations of this constraint, we need to adopt a specific measure of roundness. This is not a completely straightforward matter. For instance, we cannot just appeal to the divisibility properties of a number in order to determine how round it is.

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