Algebraic Methods in Language Processing AMiLP-3,

Head-driven Phrase Structure Grammar (HPSG, Pollard and Sag (1987, 1994)) is currently one of the most prominent linguistic theories. A grammar for HPSG is given by a set of abstract language universal principles, a set of language specific principles, and a lexicon. A sentence is grammatical, if it is compatible with all of the principles. The data structures underlying HPSG are so-called feature structures. These have always been considered as graphs. In this paper, we formalise feature structures as (hyper-) graphs and use monadic second-order logic (MS2) as a language to talk about these feature graphs. We indicate that HPSG grammar principles can be expressed as MS2-formulae over feature graphs. And we investigate the decidability properties of this framework. Doing so, we show that the MS2theory of HPSG feature graphs is undecidable. Since the general definition of feature graphs we present does not only lead to the undecidability result, but has also other linguistically undesirable properties, we propose to restrict the class of feature graphs to the subclass that can be generated by so-called hyperedge replacement grammars. Under this restriction, the MS2-theory of feature graphs becomes decidable.