Algebras for Boolean Presuppositions

Abstract

We present an algebraic approach to the semantics of presuppositions in dynamic semantics: preconditions are introduced explicitly as separate components in the semantic algebra. The approach is worked out for a propositional language that is interpreted in a Boolean setting. We provide several (meta-)mathematical results about the example- some completeness issues are discussed and a decision method is presented- and we compare the approach with the presupposition-as-preconditions approach, the major alternative treatment of presuppositions in dynamic semantics. It turns out that our way of introducing presuppositions into a presuppositionless semantics gives satisfactory results for the examples inside its range.