Expressing ignorance or indifference modal implicatures in bi-directional OT

The article presents a formal analysis in the framework of bi-directional optimality theory of the free choice, ignorance and indifference implicatures conveyed by the use of indefinite expressions or disjunctions. Ignorance is expressed by standard means of epistemic logic. To express indifference we use Groenendijk and Stokhof’s question meanings. To derive implicature, Grice’s conversational maxims, and an additional principle expressing preferences for minimal models, are formulated as violable constraints used to select optimal candidates out of a set of alternative sentence-context pairs. The implicatures of an utterance of φ are then defined as the sentences which are entailed by any optimal context for φ (but not by φ itself). Entailment is defined in a version of update semantics where contextual updates are derived by competition among contexts. Free choice and other modal implicatures of disjunctions and indefinites will follow, but also scalar implicatures and exhaustification.