Relevance of Polarity for the Online Interpretation of Scalar Terms

Numeral determiners (such as two, three etc.) and scalar quantifiers (such as some) are known to have different interpretations. Under one interpretation, two and some have an upper bounded or strong meaning, where two means 'two and not more' (or 'exactly two') and some means 'some but not all'. Alternately these words can be interpreted with a lower bounded or weak meaning, where two means 'at least two' (or 'two or more') and some means 'at least some' (or 'some and possibly all'). For example, consider the following dialogue in which speaker (A) interrogates speaker (B) about the quantity of cupcakes eaten by Alan.