Semantics

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By Mark Johnson

As a result of ease in their implementation, attribute-value dependent theories of grammar have gotten more and more well known in theoretical linguistics as a substitute to transformational debts and in computational linguistics. This publication offers a proper research of attribute-value constructions, their use in a idea of grammar and the illustration of grammatical family members in such theories of grammar. It offers a classical therapy of disjunction and negation, and explores the linguistic implications of alternative representations of grammatical family. Mark Johnson is assistant professor in cognitive and linguistic sciences at Brown college. He used to be a Fairchild postdoctoral fellow on the Massachusetts Institute of expertise throughout the 1987-88 educational yr.

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The reduction algorithm terminates only when the wff has been rewritten to False or a reduced form. Because each rewriting step decreases the norm of the wff, the reduction algorithm must terminate. Thus any wff A reduces ultimately to False if A is unsatisfiable, and reduces ultimately to some reduced form R if A is satisfiable. This result together with the Soundness Theorem just established shows that the satisfiability and validity problems in AVL are decidable. Finally, I show completeness.

That I call reduced forms, which I prove are all satisfiable. Reduced forms are characterized in terms of their syntactic form alone, and there is an algorithm for determining whether a given wff of %. is a reduced form or not. Second, I prove a series of theorem schemata of the form L s R, whose instances are theorems of AVL. Third, I define a positive integer valued norm || A || on terms and wffs of A. This norm has the property that for any terms tv t2, II tj || = II t2 II iff tj = t2. Moreover, I establish that for any instance L' s R' of these theorem schemata, ||R' || < ill/ ||.

Thus if A is satisfiable then A has a finite model, and hence A is Fin-satisfiable. Now for any wff B, B is valid/Fin-valid iff ~B is satisfiable/Fi«satisfiable respectively. But since ~B is Fin-satisfiable iff ~B is satisfiable it follows that B is valid iff B is Fin-valid. 2 Discernible Attribute-Value Structures Another restriction that can be placed on attribute-value structures is that any two distinct non-constant elements must differ on the value they take on some attribute. Recall that in an attribute-value structure (F,C,<5) two elements /j,/ 2 in F - C are indiscernible iff for every g in F, 5(fltg) is defined iff S(f2,g) is defined, and for all g such that S(flrg) is defined, S(flfg) = S(f2,g).

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