Categorial Grammar: Logical Syntax, Semantics, and - download pdf or read online

By Glyn V. Morrill

ISBN-10: 0199589852

ISBN-13: 9780199589852

ISBN-10: 0199589860

ISBN-13: 9780199589869

This ebook presents a state of the art advent to categorial grammar, one of those formal grammar which analyzes expressions as features or based on a function-argument courting. The book's concentration is on linguistic, computational, and psycholinguistic facets of logical categorial grammar, i.e. enriched Lambek Calculus. Glyn Morrill opens with the historical past and notation of Lambek Calculus and its program to syntax, semantics, and processing. Successive chapters expand the grammar to a few major syntactic and semantic houses of average language. the ultimate half applies Morrill's account to numerous present matters in processing and parsing, thought of from either a mental and a computational standpoint. The ebook bargains a rigorous and considerate examine of 1 of the most strains of analysis within the formal and mathematical conception of grammar, and should be compatible for college kids of linguistics and cognitive technological know-how from complicated undergraduate point upwards.

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16. Natural deduction for the Lambek calculus with semantic annotation If we annotate natural deduction assumptions with (distinct) variables, the semantic annotation built up at the root of a proof represents its derivational semantics. However, in natural deduction we may annotate open assumptions with their lexical semantics and then build up (and possibly normalize) semantics as we work from leaves to root. For example: (30) John N:j loves Mary (N\S)/N : love N:m N\S : (love m) S : ((love m) j) (31) the E\ cat N/CN : È CN : cat N : (È cat) E/ slept N\S : slept S : (slept (È cat)) (32) E/ loves E\ himself John (N\S)/N : love ((N\S)/N)\(N\S) : ÎxÎy((x y) y) N:j N\S : (ÎxÎy((x y) y) love) = Îy((love y) y) S : (Îy((love y) y) j) = ((love j) j) E\ E\ 44 lambek categorial grammar Categorial grammar handles subcategorization, that is the classification of the categorial contexts in which expressions expect to find themselves, quite naturally.

Logical constants constant type constraint ¬ ∧ ∨ → = ∀ ∃ È t→t t → (t → t) t → (t → t) t → (t → t) e → (e → t) (e → t) → t (e → t) → t (e → t) → e f (¬)(m) = m{∅} f (∧)(m)(m ) = m ∩ m f (∨)(m)(m ) = m ∪ m f (→)(m)(m ) = m{∅} ∪ m f (=)(m)(m ) = {∅} if m = m else ∅ f (∀)(m) = m ∈d(e) m(m ) f (∃)(m) = m ∈d(e) m(m ) f (È)({m}) = m |x| = x for individual variable x |a| = a for individual constant a | f (t 0 , . . , t n )| = (· · · ( f |t 0 |) · · · |t n |) |P t 1 . . 13. 1. There is the translation | · | given in Fig.

Z n )] where T (X) = Ù1 → · · · → Ùn → t. Something further would be required for group readings of conjunction, and there are complications with agreement in subject noun phrase coordination in, for example, John (m) or Mary (f) arrived and John (sg) and Mary (sg) are/*is arriving, but we leave these issues aside here. As is also well-known, this generalized coordination extends automatically in combinatory categorial grammar to coordination of non-standard constituents as in right node raising (John likes and Mary dislikes linguistics) and left node raising (John saw Bill yesterday and Mary today) (Steedman 1985; 1987; Dowty 1988).

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Categorial Grammar: Logical Syntax, Semantics, and Processing by Glyn V. Morrill


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