A Concept of Derivation for LFG

In this paper a version of LFG will be developed, which has only one level of representation and is equivalent to the modified version of [2], presented in [3]. The structures of this monostratal version are f-structures, augmented by additional information about the derived symbols and their linear order. For these structures it is possible to define an adequate concept of direct derivability by which the derivation proeess becomes more efficient, as the f-description solution algorithm is directly simulated during the derivation of these structures, instead of being postponed. Apart from this it follows from tiffs redueability that LFG as a theory in its present form does not make use of the c-structure information that goes beyond the mere linear order of the derived symbols. 1 .Introduction* The derivation process of sentences in LFG as defined in [2] is very complex, because an additional filter has to be applied to derived c-structures. Within this filter component the fstructures are constructed. An f-structure can be regarded as a special kind of labelled directed acyclic graph (DAG), which represents a structure of partial functions (i.e. the labels of the edges leaving each node have to be different). 1) A terminal string (x) is wellformed if it satisfies the following conditions: i. There is a e-structure for x that can be generated by the contextfree (of) base of the grammar. ii. There is an f-structure d and a mapping f from the set of nodes of c to the set of subDAGs of d such that d is a unique minimal f-structure that satisfies the annotations associated with the c-structure nodes (f and d are constructed by the fdescription solution algorithm, for short KB-algorithm). iii. d satisfies all constraints in the f-description. iv. d is complete and coherent. The derivation process is performed by checking these conditions in the order i. < ii. < iii.,iv.. This kind of derivation has several theoretical and practical disadvantages: a. A parser/generator that works in accordance witb this derirational process is not very efficient, because usually many strings are parsed completely or many c-structures are generated completely, although the strings themselves are not wellformed and therefore rejected by the filter (ii.-iv.). b. The process is formally not very transparent and complicates a comparison wlth other formalisms. c. The grammar is multistratal. It has two levels of representation (c-structures, f-structures), although it can be shown that the c-structure information, which goes beyond the linear order of the derived symbols is not exploited in the present version of the theory ([2],[3]) at all. 2) In the following it will be demonstrated that for each LFG a monostratal version can be constructed, which describes the same language with the monostratal concept of derivation. The entities of these derivations are augmented f-structures which are constructed along the following lines: In the KB version the c-structure derivation of a wellformed terminal string is a sequence of annotated c-structures, where each c-structure results from the application of an annotated cf rule to a terminal node of the preceding c-structure. If one applies the KB-algorithm to each annotated c-structure then it constructs a minimal f-structure and a mapping from the e-structure nodes to the substructures of the f-structure. The augmented f-structures are then constructed by attaching the occurrences of the derived string, represented by the labelled terminal nodes of the c-structure tree, as additional labelled edges to the start nodes of those subDAGs, which are the values of the mapping for the corresponding c-structure nodes. An example: NP VP ~ ~"~ #7 \~ =>