The Semantics of Resource Sharing in Lexical-Functional Grammar

The Semantics of Resource Sharing in Lexical-Functional Grammar Andrew Kehler" Aiken Computation Lab 33 Oxford Street Harvard University Cambridge, MA 02138 Mary Dalrymple t John Lamping t Vijay Saraswat t Xerox PARC 3333 Coyote Hill Road Palo Alto, CA 94304 Abstract We argue that the resource shar- ing that is commonly manifest in semantic accounts of coordination is instead appropriately handled in terms of structure-sharing in LFG f-structures. We provide an extension to the previous account of LFG seman- tics (Dalrymple et al., 1993a) accord- ing to which dependencies between f-structures are viewed as resources; as a result a one-to-one correspon- dence between uses of f-structures and meanings is maintained. The result- ing system is sufficiently restricted in cases where other approaches overgen- erate; the very property of resource- sensitivity for which resource sharing appears to be problematic actually provides explanatory advantages over systems that more freely replicate re- sources during derivation. 1 Introduction The resource-based approach to semantic compo- sition in Lexical-Functional Grammar (LFG) ob- tains the interpretation for a phrase via a logical deduction, beginning with the interpretations of its parts as premises (Dalrymple et al., 1993a). The resource-sensitive system of linear logic is used to compute meanings in accordance with relationships manifest in LFG f-structures. The properties of the system ensure that meanings are used exactly once, allowing coherence and com- pleteness conditions on f-structures (Kaplan and Bresnan, 1982, pages 211-212) to be maintained. However. there are cases where a single con- stituent appears to yield more than one contribu- tion to the meaning of an utterance. This is most *kehl er@das, harvard, edu t{dalrymple, i amping, saraswat }@parc. xerox, tom obvious in, but is not limited to, sentences involv- ing coordination. In example (1), for instant,'. NAFTA is the object of two different verbs: (1) Bill supported, and Hillary opposed, NAFTA. Since the hallmark of the linear logic approach is to ensure that f-structure contributions are uli- lized exactly once in a derivation, such construc- tions would at first glance appear to be problem- atic for the approach. We argue that the resource sharing that is commonly manifest in the treatment of coordi- nation in other approaches is appropriately han- dled by exploiting the structure-sharing in LF(', f-structures. We refine our previous analysis to account for cases where an f-structure is reached by multiple paths from an enclosing f-structure. Dalrymple et al. (199aa) provides an account of LFG semantics that represents the meaning of lexical items with linear logic formulas. These formulas manipulate basic assertions of the form f~,r'.~M, for f-structures f and meaning logzc terms M. Here (r is a mapping, the semantic pro- jectign, that relates f-structures to semantic struc- tures. To distinguish between multiple paths en- tering an f-structure, we now take cr to map from sets of paths in f-structures to semantic structures. Further, the paths between f-structures are made available in the semantic space as resources. This makes it possible for the semantic formulas to ex- ploit information about the multiple …

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