Showing papers by "Chris Mellish published in 1988"

Implementing systemic classification by unification

Abstract: The \"system networks\" of Systemic Grammar provide a notation for declaring how combinations of properties may imply or be inconsistent with other combinations. Partial information about a linguistic entity can be recorded as a set of known properties, and a system network then enables one to infer which other properties follow from this and which other properties are incompatible with this. The possible descriptions allowed by a system network are partially ordered by the relationship of subsumption, where a description subsumes any description that is more specific than it, given the background constraints declared by the network. Given this partial ordering, the set of descriptions can be seen as forming a lattice with least upper bound and greatest lower bound operations. In a class of applications (such as parsing and generation) that require incremental description refinement, we are only really interested in forming new conjunctions (greatest lower bounds) and testing subsumption relationships. If one factors out the complexity of variable renaming and introduces special top and bottom elements, the set of logical terms also forms a lattice (the lattice of Generalised Atomic Formulae \" G A F lattice\") under the partial ordering relation \"is equally or more instantiated than\" (Reynolds (1970)). In this lattice, the greatest lower bound operation is unification (Robinson (1965)). Unification is a primitive operation in most logic programming systems and is also the basis of various grammatical formalisms. It is therefore a relatively well understood operation and can be efficiently implemented. In this paper, we investigate to what extent it is possible to find structure-preserving mappings from the description spaces defined by system networks to sublattices of the GAF lattice. Where this is possible, we can use a fixed mapping from property names to logical terms to create terms that represent conjunctive descriptions (by unification) and to test subsumption (by testing \"less instantiated than\"). Incompatibility of descriptions is also indicated by unification failure. There are a number of reasons why it is interesting to investigate these possibilities: