Treatment of Long Distance Dependencies in LFG and TAG: Functional Uncertainty in LFG is a Corollary in TAG

In this paper the functional uncertainty machinery in LFG is compared with the treatment of long distance dependencies in TAG. It is shown that the functional uncertainty machinery is redundant in TAG, i.e., what functional uncertainty accomplishes for LFG follows f~om the TAG formalism itself and some aspects of the linguistic theory instantiated in TAG. It is also shown that the analyses provided by the functional uncertainty machinery can be obtained without requiring power beyond mildly context-sensitive grammars. Some linguistic and computational aspects of these results have been briefly discussed also. 1 I N T R O D U C T I O N The so-called long distance dependencies are characterized in Lexical Functional Grammars (LFG) by the use of the formal device of functional uncertainty, as defined by Kaplan and Zaenan [3] and Kaplan and Maxwell [2]. In this paper, we relate this characterization to that provided by Tree ~,djoining Grammars (TAG), showing a direct correspondence between the functional uncertainty equations in LFG analyses and the elementary trees in TAGs that give analyses for "long distance" dependencies. We show that the functional uncertainty machinery is redundant in TAG, i.e., what functional uncertainty accomplishes for LFG follows from the TAG formalism itself and some fundamental aspects of the linguistic theory instantiated in TAG. We thus show that these analyses can be obtained without requiring power beyond mildly context-sensitive grammars. We also *Thi s work was par t ia l ly suppo r t ed (for the first author) by the D R R P A gran t N00014-85-K0018, A l tO gran t DAA29-84-9-0027, a n d NSF gran t IRI84-10413-A02. T h e first a u t h o r also benef i ted f rom some discuss ion wi th Mark Johnson a n d R on K a p l a n a t the Tit isee Workshop on Unif ication G r a m m a r s , March, 1988. briefly discuss the linguistic and computational significance of these results. Long distance phenomena are associated with the so-called movement. The following examples, 1. Mary Henry telephoned. 2. Mary Bill said that Henry telephoned. 3. Mary John claimed that Bill said that Henry telephoned. illustrate the long distance dependencies due to topicalization, where the verb telephoned and its object Mary can be arbitrarily apart. It is difficult to state generalizations about these phenomena if one relies entirely on the surface structure (as defined in CFG based frameworks) since these phenomena cannot be localized at this level. Kaplan and Zaenan [3] note that, in LFG, rather than stating the generalizations on the c-structure, they must be stated on f-structures, since long distance dependencies are predicate argument dependencies, and such functional dependencies are represented in the f-structures. Thus, as stated in [2, 3], in the sentences (1), (2), and (3) above, the dependencies are captured by the equations (in the LFG notation 1) by 1" T O P I C =T OBJ, T T O P I C =T C O M P OBJ, and 1" T O P I C =T C O M P C O M P OBJ, respectively, which state that. the topic Mary is also the object of tele. phoned. In general, since any number of additional complement predicates may be introduced, these equations will have the general form "f T O P I C =T C O M P C O M P ... OBJ Kaplan and Zaenen [3] introduced the formal device of functional unc'ertainty, in which this general case is stated by the equation 1 Because of lack of space, we will no t define the LFG nota t ion . We a s s u m e tha t the reader is famil iar wi th it.