Making linguistic theory is like specifying a programming language...

This paper is geared towards compiling and motivating the objects and principles we need for a semantic analysis of subclausal quotations such as (1), in which the quoted expressions pick out linguistic objects but also have the usual semantics of their quotation-free counterparts (here, apricot). (1) (a) When in Santa Cruz, Peter orders “[eI]pricots ” at the local market. (b) When in Amherst, Peter orders “[æ]pricots ” at the local market. The danger lurking around these examples is that we will derive a meaning that has Peter ordering up linguistic objects. We must avoid this pitfall, but we must also preserve the meaning difference: (1a) istrueinadifferent class of situations than (1b).Itwillnotdotostripoff the quotation marks and gesture at a “metalinguistic ” theory to explain why speakers easily find situations in which Peter orders “[ei]pricots ” is semantically distinct from Peter orders “[æ]pricots”. The two sentences have clearly contrasting entailments. This is therefore clearly a semantic issue. My analysis capitalizes on the insight that “[ei]pricots ” and “[æ]pricots” (with their quotation marks) have a dual semantics: they are natural language objects as well as properties. The sentences containing them in turn express two distinct propositions. In the case of (1a), we have at least the following: ∗ MariaBittner’scommentaryonmypresentationattheBrownWorkshoponDirectCompositionality led to a complete overhaul of the original version of this paper. I am indebted to her for the commentary and extensive conversation before and after it. My thanks also to Polly Jacobson for organizing the workshop and, through her work, helping me to see things afresh. For conversation

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Categorial Grammars'. Section 4 then continues with a closer look at possible ways to set up a particular Lambda Grammar, lling in some design choices. In particular we will opt for a three dimensional grammar there; one component will deal with dominance and precedence, one with semantics, and one with syntactic features. These choices bring us in close contact with the traditional architecture of Lexical-Functional Grammar (LFG, (Kaplan and Bresnan 1982), for further connections with LFG see (Oehrle 1999) and (Muskens 2001a), which is based upon the present system) and indeed the LFG architecture inspires our answer to question 4 above. Section 4 also works out the logics of the three grammatical components in some detail and thus illustrates one possible set of answers to question 3. For the semantic component we choose a standard type logic with possible worlds; for the feature component a type logic over the rst-order theory of features ((Johnson 1991)); and the multimodal approach to grammar that is found in most modern versions of the Lambek Calculus (see (Moortgat 1997) and references therein) will serve as a basis of the component dealing with dominance and precedence. The multimodal approach is thus moved from the general level of combing signs to one of the special dimensions of the grammar, another illustration of the modularity of the set-up. The chapter ends with a short conclusion.

The compositional, bottom-up computation of alternative sets was first introduced by Hamblin (1973) into Montague grammar to treat in-situ wh-questions. In the thirty years since then, alternative sets have found their way into theories of focus (Rooth 1985), indeterminate pronouns (Shimoyama 2001), and free-choice indefinites (Kratzer and Shimoyama 2002). These theories often position alternatives as a scope-taking mechanism that operates separately from Quantifier Raising (May 1977), Quantifying In (Montague 1974), or some other scope-taking mechanism for “genuine ” quantifiers like most. On these theories, then, it is not surprising that (say) in-situ who takes scope differently from most, as is empirically observed. In particular, if “genuine ” scope requires syntactic movement but alternative scope does not, then constraints on movement apply only to the former, and we predict— correctly—that the scope of most is more restricted than the scope of in-situ who. (1) Who denied that who left? ‘Which x and y are such that x denied that y left?’ (2) Who denied that most people left?

Here I will develop a formulation of LFG’s ‘glue semantics ’ that I hope might be more accessible to syntacticians than the standard ones are. Before starting out, I want to emphasize the point that the ‘intuitionistic implicational linear logic ’ (IILL) that glue is based on is a mathematical system that can be presented in many superficially different but essentially equivalent ways; the motivation for the present version is accessibility to people with certain kinds of backgrounds, rather than an attempt to make any kind of empirical claim. The basic idea of this approach is to treat meaning-constructors as introducing prefab pieces of logical forms, which are then assembled by means of some simple rules. Technically, this is a version of ‘proof nets’, the format for IILL proofs that was devised by Girard (the inventor of linear logic) as the preferred format for proofs, for those logics where they work well. But the beginner is not supposed to have to know anything about this in order to master basic use of the system. We will however have to spend some time on the standard format of meaning-constructors, and its relationship to the present approach.

I present a strictly compositional semantics of interrogatives in English that accounts for these properties. Specifically, in my analysis, � there is no covert movement or wh-raising between surface syntax and denotational semantics (contra Epstein’s (1992) economy account), yet a single denotation suffices for both raised and in-situ appearances of each wh-phrase. Moreover, � as a natural consequence of the denotation of wh-phrases and the rules of the grammar, only in-situ wh-phrases can take scope ambiguously. I describe my system below as one where, roughly speaking, interrogative clauses denote functions from answers to propositions (an old idea). However, such denotations are not crucial for my purposes—the essential ideas in my analysis carry over easily to a system where interrogative clauses denote say sets of propositions instead. Hence this paper bears not so much on what interrogatives denote, but how. My analysis builds upon Barker’s (2000a, 2000b) use ofcontinuations to characterize quantification in natural language. In Section 2, I introduce continuation

A unified explanation for crossover and superiority in a theory of binding by generalized predicate abstraction We introduce a theory of quantificational binding in which the relationship between a binder and a bindee is established by covert (i.e., semantic) movement of the bindee to a position adjacent to the binder. This theory requires little of the semantic interpretation machinery beyond the standard assumption (Heim and Kratzer 1998) that movement corresponds to semantic abstraction. By relating binding to movement, our theory unifies crossover effects in the domain of quantificational binding and superiority effects in the domain of wh-movement. To spell out what we mean by generalized predicate abstraction (henceforth “GPA”), suppose that one element α moves to adjoin to another element β, forming β ′ as in (1). The semantic type of α must be of the form (τ → ω) → ω ′ , where τ, ω, and ω ′ are types. At the tail of its chain, α is interpreted as a variable of type τ, over which β denotes a λ-abstraction of type τ → ω. At the head of the chain, α is interpreted a functional of type (τ → ω) → ω ′ , and combines with β by function application to give β ′ , which has semantic type ω ′. For example, quantifier raising, as shown in (2), is a special case of GPA where the types τ, ω,

1.95> J\PhiM 1 ) think(x 2 ; [(8x 3 \Delta \Pi X 1 ) x 2 6= x 3 ) like(x 2 ; x 3 )]) Here the lower universal quantifier is contributed by the remnant part of the reciprocal (e 2 other ), which is assumed to raise locally. (The symbol \Delta\Pi stands for proper-atomic-part-of ). This solution works because the dependent pronoun ranges over the elements of the matrix subject. Indeed, since reciprocals are subject to Binding Principle A, it is necessary to stipulate that such "long-distance" reciprocals are only possible when the embedded subject is bound by the distributor of the matrix subject. For example, sentence (4) does not have a long-distance interpretation (or any other, since the embedded subject is singu

This is a collection of papers from a one-day symposium, Theory and