Abstract
This article reviews the set of possible paths from a semantics based on Simple Type Theories (STTs) toward one based on Rich Type Theories (RTTs) and the motivations behind the move from one to the other. The main elements of this review are threefold. First, it provides a systematic overview of different STTs, including options for what to include as members of the set of basic types, and whether to assume type constructors additional to the one for constructing functional types. Second, this review discusses the main differences between STTs and RTTs, namely, that in RTTs but not in STTs, types are part of the object language. That is, one can refer to and reason with and about types. In turn, this makes available an alternative account of propositions to the one assumed in semantics in the Frege–Church–Montague tradition: Instead of being characterized as sets of possible worlds, propositions can be treated themselves as types, that is, as structured semantic objects. Third and finally, this review provides an outline of some of the main applications of RTTs, including hyperintensionality, quantification, anaphora, polysemy, and modification.
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