Informal semantics, atype shifter is aninterpretation rule that changes an expression'ssemantic type. For instance, theEnglish expression "John" might ordinarilydenote John himself, but a type shifting rule calledLift can raise its denotation to afunction which takes a property and returns "true" if John himself has that property. Lift can be seen as mapping an individual onto theprincipal ultrafilter that it generates.[1][2][3]
Type shifters were proposed byBarbara Partee andMats Rooth in 1983 to allow for systematic typeambiguity. Work of the period assumed thatsyntactic categories corresponded directly with semantic types, and researchers thus had to "generalize to the worst case" when particular uses of particular expressions from a given category required an especially high type. Moreover, Partee argued that evidence, in fact, supported expressions having different types in different contexts. Thus, she and Rooth proposed type shifting as a principled mechanism for generating the ambiguity.[1][2][3]
Type shifters remain a standard tool in formal semantic work, particularly incategorial grammar and related frameworks. Type shifters have also been used to interpret quantifiers in object position and to capturescope ambiguities. In that regard, they serve as an alternative to syntactic operations such asquantifier raising used in mainstreamgenerative approaches to semantics.[4][5] Type shifters have also been used to generate andcompose alternative sets without the need to fully adopt analternative-based semantics.[6][7]
