Polarized unification grammars

Abstract

This paper proposes a generic mathematical formalism for the combination of various structures: strings, trees, dags, graphs and products of them. The polarization of the objects of the elementary structures controls the saturation of the final structure. This formalism is both elementary and powerful enough to strongly simulate many grammar formalisms, such as rewriting systems, dependency grammars, TAG, HPSG and LFG.

Associative Grammar Combination Operators for Tree-Based Grammars

“…The grammar combination operation of PUG was indeed conjectured to be associative (Kahane and Lareau, 2005;Kahane, 2006). The present paper makes two main contributions: In the next section we show that the combination operation defined above is not associative.…”

“…The grammar combination operation of PUG was conjectured to be associative (Kahane and Lareau, 2005;Kahane, 2006). In this paper we show that it is not; even attaching polarities to objects does not render grammar combination order-independent.…”

“…To the best of our knowledge, no formal definition of PUG was published and the formalism is only discussed informally (Kahane and Lareau, 2005;Kahane, 2006). We therefore begin by defining the formalism and its combination operation, both with and without polarities, to establish a common notation.…”

“…This combination operation is extended by attaching polarities to nodes (Crabbé and Duchier, 2004;Perrier, 2000;Kahane, 2006). In a polarized framework, an extra condition for the identification of two nodes is that their polarities combine; in this case a new node (obtained by identifying two nodes) has a polarity which is the product of the polarities of the two identified nodes.…”

“…PUG is a powerful grammatical formalism that was shown to be capable of simulating various linguistic theories (Kahane, 2006). It can be instrumental for grammar engineering, and in particular for modular development of large-scale grammars, where grammar fragments are developed separately and are combined using the basic combination operation defined above.…”