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Type-theoretical semantics with coercive subtyping
- Semantics and Linguistic Theory 20 (SALT20
, 2010
"... Abstract In the formal semantics based on modern type theories, common nouns are interpreted as types, rather than as functional subsets of entities as in Montague grammar. This brings about important advantages in linguistic interpretations but also leads to a limitation of expressive power because ..."
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Abstract In the formal semantics based on modern type theories, common nouns are interpreted as types, rather than as functional subsets of entities as in Montague grammar. This brings about important advantages in linguistic interpretations but also leads to a limitation of expressive power because there are fewer operations on types as compared with those on functional subsets. The theory of coercive subtyping adequately extends the modern type theories with a notion of subtyping and, as shown in this paper, plays a very useful role in making type theories more expressive for formal semantics. In particular, it gives a satisfactory treatment of the type-theoretic interpretation of modified common nouns and allows straightforward interpretations of interesting linguistic phenomena such as copredication, whose interpretations have been found difficult in a Montagovian setting. We shall also study some type-theoretic constructs that provide useful representational tools for formal lexical semantics, including how the so-called dot-types for representing logical polysemy may be expressed in a type theory with coercive subtyping.
Formal semantics in modern type theories with coercive subtyping
- Linguistics and Philosophy
"... Abstract. In the formal semantics based on modern type theories, common nouns are interpreted as types, rather than as predicates of entities as in Montague's semantics. This brings about important advantages in linguistic interpretations but also leads to a limitation of expressive power beca ..."
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Cited by 9 (4 self)
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Abstract. In the formal semantics based on modern type theories, common nouns are interpreted as types, rather than as predicates of entities as in Montague's semantics. This brings about important advantages in linguistic interpretations but also leads to a limitation of expressive power because there are fewer operations on types as compared with those on predicates. The theory of coercive subtyping adequately extends the modern type theories and, as shown in this paper, plays a very useful role in making type theories more expressive for formal semantics. It not only gives a satisfactory solution to the basic problem of 'multiple categorisation' caused by interpreting common nouns as types, but provides a powerful formal framework to model interesting linguistic phenomena such as copredication, whose formal treatment has been found difficult in a Montagovian setting. In particular, we show how to formally introduce dot-types in a type theory with coercive subtyping and study some type-theoretic constructs that provide useful representational tools for reference transfers and multiple word meanings in formal lexical semantics.
doi: 10.3765/sp.3.8 Varieties of conventional implicature ∗
"... This paper provides a system capable of analyzing the combinatorics of a wide range of conventionally implicated and expressive constructions in natural language via an extension of Potts’s (2005) LCI logic for supplementary conventional implicatures. In particular, the system is capable of analyzin ..."
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This paper provides a system capable of analyzing the combinatorics of a wide range of conventionally implicated and expressive constructions in natural language via an extension of Potts’s (2005) LCI logic for supplementary conventional implicatures. In particular, the system is capable of analyzing objects of mixed conventionally implicated/expressive and at-issue type, and objects with conventionally implicated or expressive meanings which provide the main content of their utterances. The logic is applied to a range of constructions and lexical items in several languages.
