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Download Categorial Grammar: Logical Syntax, Semantics, and by Glyn Morrill PDF

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By Glyn Morrill

This ebook presents a state of the art advent to categorial grammar, a kind of formal grammar which analyzes expressions as features or in line with a function-argument courting. The book's concentration is on linguistic, computational, and psycholinguistic features of logical categorial grammar, i.e. enriched Lambek Calculus. Glyn Morrill opens with the background and notation of Lambek Calculus and its software to syntax, semantics, and processing. Successive chapters expand the grammar to a couple of major syntactic and semantic houses of usual language. the ultimate half applies Morrill's account to a number of present matters in processing and parsing, thought of from either a mental and a computational viewpoint. The booklet deals a rigorous and considerate research of 1 of the most strains of analysis within the formal and mathematical thought of grammar, and should be compatible for college students of linguistics and cognitive technology from complex undergraduate point upwards.

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Extra info for Categorial Grammar: Logical Syntax, Semantics, and Processing

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Fig. 18 shows the transitive verb phrase coordination of likes with the non-standard constituent will love. Fig. 19 shows coordination of prepositional ditransitive verbs. Fig. 20 shows coordination of subjects. Observe the subject type lifting necessary in order to predicate sings of both disjuncts. In the analysis of John loves Mary and himself in Fig. 21 we see object coordination, which also requires derivational type lifting in general, but in this case the second conjunct is a reflexive pronoun which already has the lifted type lexically.

N ) for variables x 1 , . . , x n (of types Ù1 , . . , Ùn ) in a term ˆ is the result of simultaneously replacing by ¯i every free occurrence of x i in ˆ, 1 ≤ i ≤ n. We say that ¯ is free for x in ˆ if and only if no free variable in ¯ becomes bound in ˆ{¯/x}. Renaming of variables (·-conversion) may be required to ensure that substitutions are free in this sense. The laws of lambda conversion in Fig. 4 obtain. 3. 4. Laws of lambda-conversion When we apply the laws of lambda-conversion from left to right we speak of lambda-reduction, evaluation, or normalization.

Each term or formula ˆ receives a semantic value [ˆ]g relative to an interpretation (D, F ) and an assignment g as shown in Fig. 12. A formula A entails a formula B, or B is a logical consequence of A, if and only if [A]g ⊆ [B]g in every interpretation and assignment. First-order logic is semidecidable but not decidable: there exist algorithms that determine for all pairs of formulas whether they stand in the entailment relation in the case that they do, but there is no algorithm that does so and also always terminates in the negative case.

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