Learning Context Free Grammars with the Syntactic Concept Lattice

Abstract

The Syntactic Concept Lattice is a residuated lattice based on the distributional structure of a language; the natural representation based on this is a context sensitive formalism. Here we examine the possibility of basing a context free grammar (cfg) on the structure of this lattice; in particular by choosing non-terminals to correspond to concepts in this lattice. We present a learning algorithm for context free grammars which uses positive data and membership queries, and prove its correctness under the identification in the limit paradigm. Since the lattice itself may be infinite, we consider only a polynomially bounded subset of the set of concepts, in order to get an efficient algorithm. We compare this on the one hand to learning algorithms for context free grammars, where the non-terminals correspond to congruence classes, and on the other hand to the use of context sensitive techniques such as Binary Feature Grammars and Distributional Lattice Grammars. The class of cfgs that can be learned in this way includes inherently ambiguous and thus non-deterministic languages; this approach therefore breaks through an important barrier in cfg inference.