Lexical Functional Grammar (LFG) is a theory of the structure of natural language and how different aspects of linguistic structure are related. The name of the theory expresses two ways in which it differs from other theories of linguistic structure and organization. LFG is a lexical theory: relations between linguistic forms, such as the relation between an active and passive form of a verb, are generalizations about the structure of the lexicon, not transformational operations that derive one form on the basis of another one. And LFG is a functional theory: GRAMMATICAL RELATIONS such as subject and object are basic, primitive constructs, not defined in terms of phrase-structure configurations or of semantic notions such as agent or patient.
Two aspects of syntactic structure are copresent in the LFG analysis of a sentence or phrase. The concrete, perceptible relations of dominance, precedence, and phrasal grouping are represented by a phrase structure tree, the constituent structure or c-structure. More abstract functional syntactic information such as the relation of subjecthood or objecthood is represented by an attribute-value matrix, the functional structure or f-structure. Each node of the constituent structure is related to its corresponding functional structure by a functional correspondence φ, illustrated in Figure 1 by dotted lines. This functional correspondence induces equivalence classes of structural positions that can be related to a particular grammatical function. There may be functional structures that are not related to any constituent structure node (that is, the φ correspondence function is not onto); for example, in so-called pro-drop languages, a verb may appear with no overtly expressed arguments. In such a case, the verb's arguments are represented at functional structure but not at constituent structure.
Figure 1. Simplified constituent structure and functional structure for the prepositional phrase with a book.
Information about the constituent structure category of each word as well as its functional structure is contained in the LEXICON, and the constituent structure is annotated with information specifying how the functional structures of the daughter nodes are related to the functional structure of the mother node. The functional structure must also obey the well-formedness conditions of completeness and coherence: all grammatical functions required by a predicate must be present, and no other grammatical functions may be present. For example, a transitive verb requires the presence of a subject and an object (completeness) and no other grammatical functions (coherence). Thus, the universally applicable principles of completeness and coherence together with a language-specific lexicon and principles for phrase-structure annotation provide the criteria for determining the constituent-structure tree and the functional structure that corresponds to it for a sentence or phrase of a language.
LFG adheres to the lexical integrity principle, which states that morphological composition does not interact with syntactic composition: the minimal unit analyzed by the constituent structure is the word, and the internal morphological structure of the word is not accessible to syntactic processes (Bresnan and Mchombo 1995). However, it is possible for words and phrases to have similarly articulated functional structure: a verb with a morphologically incorporated pronominal object may have the same functional structure as a verb phrase with a verb and an independent pronoun. A number of apparent paradoxes are explained by distinguishing between syntactic phenomena at the two different syntactic levels.
Distinguishing the outer, crosslinguistically variable constituent structure from the functional structure, which encodes relations that hold at a more abstract level in every language, allows for the incorporation of a comparative assessment of grammatical structures as proposed in OPTIMALITY THEORY (Bresnan 1997; Choi 1996).
The formal generative properties of LFG grammars are fairly well described. Like context-free languages, LFG languages are closed under union, concatenation, and Kleene closure (Kelly Roach, unpublished work). The recognition problem (whether a given string is in the language generated by a given LFG grammar) was shown to be decidable by Kaplan and Bresnan (1982). The emptiness problem (whether a given LFG grammar generates a nonempty set of strings) was shown to be undecidable in further unpublished work by Roach. A synopsis of Roach's results is given by Dalrymple et al. (1995).
The efficient processing of LFG grammars, both from a psycholinguistic and a computational standpoint, is a central concern of the theory. It has been shown that LFG recognition is NP-complete (Berwick 1982): for some string (not necessarily a string in any natural language) and some LFG grammar, no known algorithm exists to determine in polynomial time whether that string is in the language generated by that grammar. Kaplan (1982) proposes that the NP-complete class is actually a psycholinguistically plausible one for a linguistic model: the exponentially many candidate analyses of a string can be heuristially winnowed, and subsequent verification of the correct analysis can be accomplished very quickly. Strategies can also be devised to optimize the distribution of processing work between the two syntactic structures (Maxwell and Kaplan 1993). In recent unpublished work, Ronald M. Kaplan and Rens Bod explore the Data-Oriented Parsing approach within the LFG framework; this approach assumes that LANGUAGE ACQUISITION proceeds by forming generalizations over fragments of constituent structures and functional structures of previously encountered utterances and by inducing the most likely structure of newly encountered utterances based on these generalizations.
Besides constituent structure and functional structure, LFG assumes other structures for other aspects of linguistic form. These structures are generally assumed to be related by functional correspondence to the constituent structure, the functional structure, and/or one another (Kaplan 1987). Argument structure encodes the THEMATIC ROLES of the arguments of predicates and plays an important role in LFG's linking theory, principles for how the thematic role of an argument affects its grammatical function and realization in the functional structure (Bresnan and Kanerva 1989; Alsina 1994). The meaning of a phrase or sentence is represented at semantic structure (Halvorsen 1983), related directly to functional structure and indirectly to other linguistic structures. The relation between semantic structures and their corresponding functional structures is exploited in recent deductive accounts of the SYNTAX-SEMANTICS INTERFACE; syntactic relations established at functional structure interact with lexically specified information about the meaning of individual words in a logical deduction of the meaning of larger phrases and sentences (Dalrymple, Lamping, and Saraswat 1993).
Further information about LFG, including a continually updated bibliography, is available at http://clwww.essex.ac. uk/LFG/.
Alsina, A. (1994). Predicate Composition: A Theory of Syntactic Function Alternations. Ph.D. diss., Stanford University.
Berwick, R. (1982). Computational complexity and Lexical Functional Grammar. American Journal of Computational Linguistics 8:97-109.
Bresnan, J. (1997). The emergence of the unmarked pronoun: Chichewa pronominals in Optimality Theory. Paper presented at the BLS 23 Special Session on Syntax and Semantics in Africa. http://www-csli.stanford.edu/bresnan/jb-bls-roa.ps.
Bresnan, J., and J. Kanerva. (1989). Locative inversion in Chichewa: A case study of factorization in grammar. Linguistic Inquiry 20(1):1-50. Reprinted in T. Stowell and E. Wehrli, Eds., Syntax and Semantics No. 26: Syntax and the Lexicon. New York: Academic Press, pp. 53 - 101.
Bresnan, J., and S. A. Mchombo. (1995). The lexical integrity principle: Evidence from Bantu. Natural Language and Linguistic Theory 13(2):181-254.
Choi, H.-W. (1996). Optimizing Structure in Context: Scrambling and Information Structure. Ph.D. diss., Stanford University.
Dalrymple, M., R. M. Kaplan, J. T. Maxwell, and A. Zaenen. (1995). Mathematical and computational issues. In M. Dalrymple, R. M. Kaplan, J. T. Maxwell, and A. Zaenen, Eds., Formal Issues in Lexical Functional Grammar. Stanford, CA: CSLI Publications, pp. 331-338.
Dalrymple, M., J. Lamping, and V. Saraswat. (1993). LFG semantics via constraints. Proceedings of the 6th Meeting of the European Association for Computational Linguistics, University of Utrecht, April. ftp://ftp.parc.xerox.com/pub/nl/eacl93-lfg-sem.ps.
Halvorsen, P.-K. (1983). Semantics for Lexical Functional Grammar. Linguistic Inquiry 14(4):567-615.
Kaplan, R. M. (1982). Determinism and nondeterminism in modelling psycholinguistic processes. Paper presented to the Conference on Linguistic Theory and Psychological Reality Revisited, Princeton University.
Kaplan, R. M. (1987). Three seductions of computational psycholinguistics. In P. Whitelock, M. McGee Wood, H. L. Somers, R. Johnson, and P. Bennett, Eds., Linguistic Theory and Computer Applications. London: Academic Press, pp. 149-181. Reprinted in M. Dalrymple, R. M. Kaplan, J. Maxwell, and A. Zaenen, Eds., Formal Issues in Lexical Functional Grammar. Stanford, CA: CSLI Publications, pp. 337 - 367.
Kaplan, R. M., and J. Bresnan. (1982). Lexical Functional Grammar: A formal system for grammatical representation. In J. Bres nan, Ed., The Mental Representation of Grammatical Relations. Cambridge, MA: MIT Press, pp. 173-281. Reprinted in M. Dalrymple, R. M. Kaplan, J. Maxwell, and A. Zaenen, Eds., Formal Issues in Lexical Functional Grammar. Stanford, CA: CSLI Publications, pp. 29 - 130.
Maxwell, J. T., III, and R. M. Kaplan. (1993). The interface between phrasal and functional constraints. Computational Linguistics 19(4):571-590. Reprinted in M. Dalrymple, R. M. Kaplan, J. Maxwell, and A. Zaenen, Eds., Formal Issues in Lexical Functional Grammar. Stanford, CA: CSLI Publications, pp. 403 - 429.
Alsina, A. (1992). On the argument structure of causatives. Linguistic Inquiry 23(4):517-555.
Alsina, A. (1996). The Role of Argument Structure in Grammar: Evidence from Romance. Stanford, CA: CSLI Publications.
Andrews, A. D. (1990). Unification and morphological blocking. Natural Language and Linguistic Theory 8(4):507-557.
Andrews, A., and C. Manning. (1993). Information spreading and levels of representation in LFG. Technical Report CSLI - 93-176 Stanford, CA: CSLI Publications.
Bresnan, J., Ed. (1982). The Mental Representation of Grammatical Relations. Cambridge, MA: MIT Press.
Bresnan, J. (1994). Locative inversion and the architecture of universal grammar. Language 70(1):2-31.
Bresnan, J., and L. Moshi. (1990). Object asymmetries in comparative Bantu syntax. Linguistic Inquiry 21(2):147-185. Reprinted in S. A. Mchombo, Ed., Theoretical Aspects of Bantu Grammar 1. Stanford: CSLI Publications, pp. 47 - 91.
Bresnan, J., and S. A. Mchombo. (1987). Topic, pronoun, and agreement in Chichewa. Language 63(4):741-782. Reprinted in M. Iida, S. Wechsler, and D. Zec, Eds., Working Papers in Grammatical Theory and Discourse Structure: Interactions of Morphology, Syntax, and Discourse. Stanford, CA: CSLI Publications, pp. 1 - 59.
Bresnan, J., and A. Zaenen. (1990). Deep unaccusativity in LFG. In K. Dziwirek, P. Farrell, and E. M. Bikandi, Eds., Grammatical Relations: A Cross-Theoretical Perspective. Stanford CA: CSLI Publications/Stanford Linguistics Association, pp. 45-57.
Butt, M. (1995). The Structure of Complex Predicates in Urdu. Stanford, CA: CSLI Publications.
Dalrymple, M. (1993). The Syntax of Anaphoric Binding. Stanford, CA: CSLI Publications. CSLI Lecture Notes, no. 36.
Dalrymple, M., R. M. Kaplan, J. T. Maxwell, and A. Zaenen, Eds. (1995). Formal Issues in Lexical Functional Grammar. Stanford, CA: CSLI Publications.
Fenstad, J.-E., P.-K. Halvorsen, T. Langholm, and J. van Benthem. (1987). Situations, Language, and Logic. Dordrecht: Reidel.
Johnson, M. (1988). Attribute-Value Logic and the Theory of Grammar. Stanford, CA: CSLI Publications. CSLI Lecture Notes, no. 16.
King, T. H. (1995). Configuring Topic and Focus in Russian. Stanford, CA: CSLI Publications.
Kroeger, P. (1993). Phrase Structure and Grammatical Relations in Tagalog. Stanford, CA: CSLI Publications.
Laczko, T. (1995). The Syntax of Hungarian Noun Phrases: A Lexical Functional Approach. Frankfurt am Main: Peter Lang GmbH.
Levin, L. (1986). Operations on Lexical Forms: Unaccusative Rules in Germanic Languages. Ph.D. diss., Massachusetts Institute of Technology.
Levin, L. S., M. Rappaport, and A. Zaenen, Eds. (1983). Papers in Lexical Functional Grammar. Bloomington, IN: Indiana University Linguistics Club.
Matsumoto, Y. (1996). Complex Predicates in Japanese: A Syntactic and Semantic Study of the Notion "Word". Stanford and Tokyo: CSLI Publications and Kuroiso Publishers.
Mohanan, K. P. (1983). Functional and anaphoric control. Linguistic Inquiry 14(4):641-674.
Neidle, C. (1988). The Role of Case in Russian Syntax. Dordrecht: Kluwer.
Pinker, S. (1984). Language Learnability and Language Development. Cambridge, MA: Harvard University Press.
Simpson, J. (1991). Warlpiri Morphology and Syntax: A Lexicalist Approach. Dordrecht: Reidel.
Zaenen, A. (1994). Unaccusativity in Dutch: Integrating syntax and lexical semantics. In J. Pustejovsky, Ed., Semantics and the Lexicon. Dordrecht: Kluwer, pp. 129-161 .
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