5 - The Formal and Computational Theory of Complex Constraint Solution

Abstract

This chapter reviews the formal and computational theory of complex constraint solution. Computational logic is an ideal paradigm for first order theories because it supports a direct mapping among grammars, seen as first order logic theories, and the first order theory of their implementation and at the same time provides a formally sound and efficient computational scheme. This paradigm is also well suited to simultaneously satisfy the main requirements put on computational grammar formalisms, namely, expressivity, formal soundness, and computational tractability. The choice of a computational logic framework is motivated by the fact that restricting the formal analysis to the static properties of formalisms does not do justice to the computational challenge posed by modern linguistic frameworks. It is not sufficient to design formalisms with a simple and sound denotational semantics and appropriate formal complexity characteristics. A finer analysis of the formal and computational properties of formalism is necessary to provide sound and adequate processing schemes for such formalisms, without which the main challenges facing modern grammatical formalism design are not addressed.