Order Selection: The Logical Foundations of Exhaustivity

This thesis argues that exhaustive inferences in question/answer exchanges (A: Who purred? B: Frederick ⇝ not Gertrude) are systematically predictable on the basis of semantic content, without a supplementary theory of formal alternatives. An explicit recipe for calculating exhaustive inferences is developed and tested against a wide range of answers.

Chapter 1 surveys the descriptive properties of exhaustivity and argues that exhaustive inferences should be modeled using predicate circumscription: the assumption that an answer provides the “best” answer to a question, calculated using an order over possible worlds determined by the question that was asked. However, existing circumscription accounts only cover positive answers to questions, and do not make correct predictions about how negative and mixed answers are interpreted.

Chapter 2 shows that the exhaustive interpretation of negative and mixed answers can be accounted for using a novel order over possible worlds that simultaneously integrates positive and negative information. The chapter also argues that circumscription makes successful predictions about how exhaustivity interacts with semantic type.

Finally, chapter 3 develops a theory of order selection, arguing that which order a particular answer uses is guided by the interaction of a general preference for markedness reduction and a constraint on information preservation that requires an exhaustive answer to share a restriction with its literal counterpart. A markedness hierarchy over the orders is developed and grounded in the more general markedness of negation.