Up to n: Pragmatic inference about an optimal lower bound

This paper focuses on English directional modified numerals up to n, which triggers opposite inference patterns in speaker-uncertainty and authoritative-permission contexts. I propose that these opposite inference patterns are due to pragmatic inference about an unspecified semantic lower bound of up to n, based on its similarities to gradable adjectives and vague characteristics. The value of the semantic lower bound in different contexts is predicted by a general pragmatic principle of interaction between informativity and applicability independently motivated in previous probabilistic models on gradable adjectives.