CATEGORIAL GRAPH GRAMMAR: A DIRECT APPROACH TO FUNCTOR-ARGUMENTOR-STRUCTURE
Klaus Robering · Theoretical Linguistics · 2000
Systems of categorial grammar usually define functor-argumentor-structure (FAS, for short) in terms of derivational history. Here a more direct approach is proposed. FASs of linguistic items are conceived of as graphs of a certain kind. Category assignment statements are used to classify these graphs into categories and grammatical rules are formulated as sequents relating such type assignment statements. A base grammar G is a natural deduction system whose rules are given by sequents of the kind described. These rules may also be interpreted as specifying the mapping behaviour of the basic functors of G. In order to endow G with its full combinatorial power, the meta-rules of a so-called framework F are used for the construction of more complex functors from the basic ones. From a logical point of view, these complex functors are just the derived rules of the system G. A full grammar F(G) is a sequent system for the production of these derived rules. Index constructors (like / and \), though theoretically suspensable in F(G), may be characterized within this systems by special rules. Given this definitional rules, the usual cancellation laws of categorial grammar may be derived.