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ASSOCIATION WITH FOCUS (MONTAGUE GRAMMAR, SEMANTICS, ONLY, EVEN)
Suppose John introduced Bill and Tom to Sue and performed no other introductions. Then (i) John only introduced Bill to SUE is true, while (ii) John only introduced BILL to Sue is false, where capitalization symbolizes a focus marked by a phonetic prominence. Two analyses of this phenomenon of association with focus are considered. The scope theory posits a logical form in which the focused phrase and a lambda abstract with a bound variable in the position of the focused phrases are arguments of only . According to the domain selection theory I propose, (i) and (ii) have a function-argument structure mirroring the syntax. The translation of only has two arguments, the VP translation and the translation of the subject NP; (i) expresses a quantification over properties. Focus contributes to the meaning of (i) by delimiting the domain of quantification to properties of the form \u27introduce Bill to y\u27, where y is an individual. This yields an assertion: if John has a property of the form \u27introduce Bill to y\u27, then it is the property \u27introduce Bill to Sue\u27. This is similar in truth conditions to the assertion produced by the scope theory, namely \u27if John introduced Bill to y, then y is Sue\u27. This idea is executed by including a recursive definition of the sets which will serve as domains of quantification in a Montague grammar. It is argued that the domain selection theory is superior in several ways. In particular, no bound variable in the position of the focused phrase is postulated; the relation between only (or even ) and a focused phrase violates structural conditions on bound variables. Chomsky\u27s crossover argument for assigning scope to focused phrases is answered. The proposal is extended to cases where only and even modify NP and various other categories by means of a crosscategorial semantics analogous to the crosscategorial semantics for conjunction proposed by Gazdar and others. Other constructions discussed are association of focus with adverbs of quantification (MARY always takes John to the movies, Mary always takes JOHN to the movies), clefts (it is JOHN\u27s father who came, it is John\u27s FATHER who came), and conditionals
Negation, Polarity, and Deontic Modals
Universal deontic modals may vary with respect to whether they scope over or under negation. For instance, English modals like must and should take wide scope with respect to negation; modals like have to and need to take narrow scope. Similar patterns have been attested in other languages. In this article, we argue that the scopal properties of modals with respect to negation can be understood if (a) modals that outscope negation are positive polarity items (PPIs); (b) all modals originate in a position lower than I[superscript 0]; and (c) modals undergo reconstruction unless reconstruction leads to a PPI-licensing violation
Gestural agreement
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