A learnable representation for syntax using residuated lattices
In: Conference on Formal Grammar, 25 -26 July 2009, Bordeaux, France.
We propose a representation for natural language syntax based on
the theory of residuated lattices: in particular on the Galois lattice between contexts and substrings, which we call the syntactic concept lattice.
The natural representation derived from this is a richly structured
context sensitive formalism that can be learned using a generalisation of distributional learning. In this paper we define the basic algebraic properties of the syntactic concept lattice,
together with a representation derived from this lattice and
discuss the generative power of the formalism. We establish some basic results which show that these representations, because they are defined language theoretically, can be inferred from information about the set of grammatical strings of the language.
We also discuss the relation to other grammatical formalisms notably categorial grammar and context free grammars.
We claim that this lattice based formalism is plausibly both learnable from evidence about the grammatical
strings of a language and may be powerful enough to represent natural languages, and thus presents a potential solution to the central problem of theoretical linguistics.