Download e-book for kindle: Attribute-value logic and the theory of grammar by Mark Johnson

By Mark Johnson

ISBN-10: 0937073377

ISBN-13: 9780937073377

Due to the ease in their implementation, attribute-value established theories of grammar have gotten more and more well known in theoretical linguistics in its place to transformational money owed and in computational linguistics. This ebook presents a proper research of attribute-value constructions, their use in a idea of grammar and the illustration of grammatical family in such theories of grammar. It offers a classical remedy of disjunction and negation, and explores the linguistic implications of alternative representations of grammatical kin. Mark Johnson is assistant professor in cognitive and linguistic sciences at Brown collage. He was once a Fairchild postdoctoral fellow on the Massachusetts Institute of know-how throughout the 1987-88 educational yr.

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Thus ~A must reduce to False. But if B reduces to B' then h B s B', so there exists a proof of ~A r> False, and thus a proof of A. Thus the axioms and inference rule of AVL are complete. 1 Reduced Forms In this section I define the reduced forms of A, wffs that are patently satisfiable on inspection of their syntactic form. I show then how to Decidability and Completeness of AVL 35 construct a model for any reduced form. This model is constructed from the terms and subterms of the reduced form itself.

Attribute-Value Logic 31 I now define the notion of 'proof in AVL. I use £ as a syntactical variable for a set of wffs. , An of wffs such that An is A and for each k, 1 < k < n, at least one of the following conditions is satisfied: (i) Ak is an axiom, (ii) Ak is a member of £. (iii) Ak follows by Modus Ponens from Aj and A:, where i

The following lemma shows that a model satisfies exactly the same formulae as its accessible submodel. Lemma 24: For all wffs A and models M,Mt= A. iff a(M) t= A. Proof: By induction on the structure of any term t, 03;*= [MacaoHence by an induction on the structure of any wff A, M 1= A iff A. D I now proceed to axiomatize the acyclically valid wffs. I do this by providing an additional axiom schemata called (A), and show that a wff A is acyclically valid if and only if there is a proof of A from the axioms of AVL and instances of axiom schema (A).

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Attribute-value logic and the theory of grammar by Mark Johnson

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