David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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In this paper we address an important issue in the development of an adequate formal theory of underspeciﬁed semantics. The tension between expressive power and computational tractability poses an acute problem for any such theory. Generating the full set of resolved scope readings from an underspeciﬁed representation produces a combinatorial explosion that undermines the eﬃciency of these representations. Moreover, Ebert (2005) shows that most current theories of underspeciﬁed semantic representation suﬀer from expressive incompleteness. In previous work we present an account of underspeciﬁed scope representations within Property Theory with Curry Typing (PTCT), an intensional ﬁrst-order theory for natural language semantics. We review this account, and we show that ﬁlters applied to the underspeciﬁed-scope terms of PTCT permit expressive completeness. While they do not solve the general complexity problem, they do signiﬁcantly reduce the search space for computing the full set of resolved scope readings in non-worst cases. We explore the role of ﬁlters in achieving expressive completeness, and their relationship to the complexity involved in producing full interpretations from underspeciﬁed representations.
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Chris Fox & Shalom Lappin (forthcoming). Type-Theoretic Logic with an Operational Account of Intensionality. Synthese:1-22.
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