Presuppositions are a central problem in natural language semantics, which centers around two main questions:
- Triggering Problem: why are the inferences triggered by some expressions treated as presuppositions rather than, say, at-issue entailments?
- Projection Problem: how are the presuppositions of complex sentences inherited from the presuppositions of their component parts and the way they are put together?
Most research has centered on the Projection Problem. In the 1980’s, the analysis of ‘presupposition projection’ led to the development of a new and more powerful type of semantics, called ‘dynamic semantics’. In recent years, various alternatives (some of them pragmatic, some of them not) were developed within non-dynamic semantics. We will provide an introduction to this debate, first by developing an explicit dynamic semantics for presuppositions, and then by considering various alternatives to it, including ones developed within bivalent or trivalent logics. The database will include traditional data, experimental data, and also gestural inferences that enrich the debate (they pertain to presupposition-like inferences that are arguably triggered by co-speech gestures).