Structural Effects on Implicature Calculation

This paper provides an investigation of Ignorance Inferences by looking at the superlative modifier at least. The formal properties of these inferences are characterized in terms of the epistemic conditions that they impose on the speaker, thereby establishing how much can and must be inferred about what the speaker is ignorant about. The paper makes two main contributions. First, it argues that the form of these inferences depends solely on the structural properties of the expression that at least is modifying, which do not necessarily coincide with semantic entailment. Rather, rank and order seems to matter: with totally ordered associates, at least triggers Ignorance Inferences that may be formally different than those obtained with partially ordered associates (Mendia (2016b)). Second, it builds on neo-Gricean double alternative generation mechanisms (like Schwarz (2016)) arguing that one of them must be provided by focus.