Citations of:
Language, Lambdas, and Logic
In R. Oehrle & J. Kruijff (eds.), Resource Sensitivity, Binding, and Anaphora (Studies in Linguistics and Philosophy 80). Dordrecht: Kluwer Academic Publishers. pp. 2354 (2003)
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This paper argues for the idea that in describing language we should follow Haskell Curry in distinguishing between the structure of an expression and its appearance or manifestation . It is explained how making this distinction obviates the need for directed types in typetheoretic grammars and a simple grammatical formalism is sketched in which representations at all levels are lambda terms. The lambda term representing the abstract structure of an expression is homomorphically translated to a lambda term representing its manifestation, (...) 

Many variants of categorial grammar assume an underlying logic which is associative and linear. In relation to left extraction, the former property is challenged by island domains, which involve nonassociativity, and the latter property is challenged by parasitic gaps, which involve nonlinearity. We present a version of type logical grammar including ‘structural inhibition’ for nonassociativity and ‘structural facilitation’ for nonlinearity and we give an account of relativisation including islands and parasitic gaps and their interaction. 

The ‘syntax’ and ‘combinatorics’ of my title are what Curry (1961) referred to as phenogrammatics and tectogrammatics respectively. Tectogrammatics is concerned with the abstract combinatorial structure of the grammar and directly informs semantics, while phenogrammatics deals with concrete operations on syntactic data structures such as trees or strings. In a series of previous papers (Muskens, 2001a; Muskens, 2001b; Muskens, 2003) I have argued for an architecture of the grammar in which ﬁnite sequences of lambda terms are the basic data structures, (...) 

This paper introduces λgrammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, λgrammars are multidimensional and their components are combined in a strictly parallel fashion. Grammatical representations are combined with the help of linear combinators, closed pure λterms in which each abstractor binds exactly one variable. Mathematically this is equivalent to employing linear logic, in use in LFG for semantic composition, but the method seems more practicable. 

This paper develops a detailed and unified analysis of semantics of the fromNtoN construction, based on a small number of ingredients, none of which are specific to this construction itself, but which are idiomatically packaged in this construction. Letting the construction uniformly apply to the product of the two nouns not only captures their strong relation, but it also obviates a role for a ‘reduplicative’ mechanism of some sort in this particular construction. 

Categorial grammar is wellknown for its elegant analysis of coordination enabled by the flexible notion of constituency it entertains. However, to date, no systematic study exists that examines whether this analysis has any obvious empirical advantage over alternative analyses of nonconstituent coordination available in phrase structurebased theories of syntax. This paper attempts precisely such a comparison. We compare the direct constituent coordination analysis of noncanonical coordinations in categorial grammar with an ellipsisbased analysis of the same phenomena in the recent HPSG (...) 