We present a new method for characterizing the interpretive possibilities generated by elliptical constructions in natural language. Unlike previous analyses, which postulate ambiguity of interpretation or derivation in the full clause source of the ellipsis, our analysis requires no such hidden ambiguity. Further, the analysis follows relatively directly from an abstract statement of the ellipsis interpretation problem. It predicts correctly a wide range of interactions between ellipsis and other semantic phenomena such as quantifier scope and bound anaphora. Finally, although the analysis itself is stated nonprocedurally, it admits of a direct computational method for generating interpretations. This article is available through the Computation and Language E-Print Archive as cmp-lg/9503008, and also appears in Linguistics and Philosophy 14(4):399–452. cmp-lg/9503008 Ellipsis and Higher-Order Unification 1

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Abstract We investigate the notion of "logicality " for arbitrary categories of linguistic expression, viewed as a phenomenon which they can all possess to a greater or lesser degree. Various semantic aspects of logicality are analyzed in technical detail: in particular, invariance for permutations of individual objects, and respect for Boolean structure. Moreover, we show how such properties are systematically related across different categories, using the apparatus of the typed lambda calculus. 315 / The range of logicality Philosophical discussions of the nature of logical constants often concentrate on the connectives and quantifiers of standard predicate logic, trying to find out what makes them so special. In this paper, we take logicality in a much broader sense, including special predicates among individuals such as identity ("be") or higher operations on predicates such as reflexivization ("self"). One convenient setting for achieving the desired generality is that of a standard Type Theory, having primitive types e for entities and t for truth values, while forming functional compounds (a,b) out of already available types a and b. Thus, e.g., a one-place predicate of individuals has type (e,t) (assigning truth values to individual entities), whereas a two-place predicate has type (e, (e, t)). Higher types occur, among others, with quantifiers, when regarded in the Fregean style as denoting properties of properties: ((e,t)9t). For later reference, here are some types, with categories of expression taking a corresponding denotation: e entities proper names / truth values sentences (t,t) unary connectives sentence operators

Many theories of grammar and styles of grammar specification have stemmed from mathematical logic, computer science, and computational linguistics, and have been used for describing natural languages. By a series of constructions, we relate categorial, attribute and logic grammars via (axiomatic) labelled deductive systems, and extend this relation to accommodate unification-based grammars and so-called Montague Grammar. The axioms of a labelled deductive system can also be used to constrain the proof search by automatically generating an LR parser from them; we describe the implementation of such a parser-generator. Furthermore, we show how a modification of the LR parsing algorithm, plus the (meta-level) information contained in the axioms, can be used to parse a grammar specification which is based on procedural rather than combinatorial properties of the language. 1 Introduction Many theories of grammar have been proposed in theoretical linguistics, computational linguistics, com...