A Coalgebraic Modelling of Head-Driven Phrase Structure Grammar

This paper provides a coalgebraic modelling of Head-Driven Phrase Structure Grammar. HPSG is a licensing theory in the sense that grammaticality is defined in terms of abstract grammar principles, well-formedness conditions on linguistic analyses rather then by a set of rules that would explicitely generate an analysis. Since coalgebras are very well suited for modelling licensing theories, we provide a conceptually particularly adequate formalisation for HPSG by showing that HPSG can indeed be modeled with coalgebras. We also show that the category of grammar models contains a final coalgebra. This final coalgebra we propose as the model of an HPSG grammar, because it models the analyses of the structurally different readings of all and only those utterances licensed by the grammar while eliminating spurious ambiguities.