By Mark Johnson
End result of the ease in their implementation, attribute-value dependent theories of grammar have gotten more and more renowned in theoretical linguistics as a substitute to transformational money owed and in computational linguistics. This publication presents a proper research of attribute-value buildings, their use in a idea of grammar and the illustration of grammatical relatives in such theories of grammar. It presents a classical remedy of disjunction and negation, and explores the linguistic implications of other representations of grammatical family. 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 expertise through the 1987-88 educational yr.
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Additional info for Attribute-value logic and the theory of grammar
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). I show this by first proving that a model satisfies every instance of (A) if and only if its accessible submodel cc(;M) is acyclic.
Tj = t2 A t = t) s ta « t2 for t a subterm of ^ or t2. 40 Attribute-Value Structures Example 11: If \\a\\ = 1, II b \\ = 2, \\x \\ = 3 and \\y\\ = 4, then (i) IUfl) II =58, (ii) IU(«) = y|| =124, and (iii) || x(a) ^ y II = 2124 or approximately 1037. Finally, note that the norm just defined has the property that for all of the theorems L s R that are instantiations of the group 1 theorem schemata of the previous subsection || R || Const,Var = II L II Const/Var' and for all of the theorems L s R that are instantiations of the group 2 theorem schemata it is the case that || R || const,Var < II L II const,Var' where Const is any set of constant symbols containing all of the constant symbols appearing in L and Var is any set of variables containing the variables appearing in L.
The completeness theorem is considerably more complex than the soundness theorem. To prove it I use several intermediate results. Decidability of the satisfiability and validity problems follows from the techniques I use to prove completeness. First, I define a set of wffs of A. 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.
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