By Mark Johnson

ISBN-10: 0937073377

ISBN-13: 9780937073377

End result of the ease in their implementation, attribute-value dependent theories of grammar have gotten more and more renowned in theoretical linguistics instead to transformational money owed and in computational linguistics. This ebook offers a proper research of attribute-value buildings, their use in a conception 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 other representations of grammatical relatives. Mark Johnson is assistant professor in cognitive and linguistic sciences at Brown college. He was once a Fairchild postdoctoral fellow on the Massachusetts Institute of expertise through the 1987-88 educational yr.

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**Example text**

Since I A ^ False, we can show I- A. Thus all valid formulae are theorems of AVL. 6 Compactness of A. In this section I show that the languages A. are compact, and use this to obtain a generalized completeness result. Definition 14: A set of wffs £ is FINITELY SATISFIABLE iff every finite subset of £ is satisfiable. Theorem 15 (Compactness Theorem): A set £ of wffs of A. is satisfiable if and only if £ is finitely satisfiable. 46 Attribute-Value Structures Proof: The proof from left to right is trivial.

Of A in the propositional calculus. [pn/Bn] is a theorem of AVL for 1 < i < n. D The Transitive Law of Implication and the Deduction Theorem hold in AVL, just as in first-order logic. , Andrews 1986). , An of AVL. Deduction Theorem: // Eu{ A } t- B, then E h A r> B for arbitrary wffs A, B of AVL. The equality axioms characterize the properties of equality in this system. Axiom schemata (El) through (E4) present pairs of terms that are necessarily equal or unequal. I show immediately below that axiom schemata (E6) allows the substitution of equals for equals.

AvB||= || A || + ||B||+I. ||B||. (vi) ||~A||=2lA'. Decidability and Completeness of AVL 39 Group 1 Theorem Schemata: I- ((A v B) v C) a (A v (B v C) \- ((A A B) A C) s (A A (B A C)) Associativity I-(A vB) s (B v A) h (A A B) s (B A A) Commutativity Group 2 Theorem Schemata: h (A A (B v C)) s ((A A B) v (A A C)) Distributivity \- ~(A v B) g ~A A ~B h ~(A A B) s ~A v ~B De Morgan I- —A s A Double Negation One and Zero I- (A v True) s True I- (A A True) s A (- (A v Fafee) s A h- (A A False) x False Symmetry of Equality (t, = tj) s (fc, = t t ) where ||tj> Substitutivity of Equality h (tj - tz A A) a (t, - 12 A Alia/t,]) where || tj || < || t2 || and A contains an occurrence of t2.

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