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3.4.2. Unification Grammars

Today, the predominant, formal models of grammar pertain to a class of linguistic formalisms that can be grouped under the name of "constraint-based grammars" or "unification grammars" [see Shieber (1992)]. More productive and flexible than Chomsky's models, they are characterized by the adoption of a very clean sort of denotational semantics, which allows the encoding of grammatical knowledge independently from the use of any particular processing algorithm ("declarative approach").

Within this general framework, a number of different formalisms exist: we can mention here Functional Unification Grammars (FUG), Head-Driven Phrase-Structure Grammars (HPSG), Lexical Functional Grammars (LFG), Categorial Unification Grammars (CUG), and Tree Adjunction Grammars (TAG). All these formalisms share two essential characteristics:

  1. All the grammatical units (words, phrases, sentences) are described by means of uniform formalisms based on the use of sets of attribute-value pairs, which are called "feature structures" (f-structures).
  2. 2. The formal characteristics of f-structures are exploited through the use of a basic mechanism for merging and checking the grammatical information, which is called "unification."

For comprehensibility's sake, f-structures can be introduced -- independently from any strict grammatical and syntactic consideration -- simply as an extension of the usual Artificial Intelligence, first-order terms formed by a predicate and its arguments. Each f-structure consists then, see the generic example of Figure 1, of two columns of entries enclosed in large square brackets. The elements ai of the left-hand column are the "attributes"; attributes are always atomic symbols, syntactic like "NP," "VP," or "object," but also semantic like "name" or "age," logic-oriented like "quantifier" or "logical-connective," discourse-oriented, etc. The elements vi of the right-hand column are the "values." Values can be atomic symbols or subordinate f-structures, as in the case of the value assumed by the attribute a14 in the example of Figure 1; i.e., f-structures can be nested. Values can be replaced by variables. Constraints under the form of "equality statements," see also Figure 5, can be expressed by associating with some variables the same numerical "coreference marker"; this means that the values assumed by those variables must be the same. Attributes and values are, obviously, paired, and the members of a pair are written on the same line; the order in which lines occur in an f-structure has no significance.

We can now transform the abstract framework of Figure 1 into a concrete example, see Figure 2; we will then assume that the above structure represents, in a "nested relations" style, something like: "There is a person whose name is Tom, who is 27 years old, and who is married to a girl named Lucy who is 23 years old." If we want now to introduce a simple constraint in the formulation of Figure 2, imposing, e.g., that "Tom can be married with any girl, but she must be exactly as old as he is," we will insert a free variable, [ ], as value of the attribute "name" in the enclosed f-structure, and another variable, labeled with the coreference marker "1," [1], as value of the attribute "age" in both the external and the internal f-structures.


FIGURE 1 Nested f-structures.


FIGURE 2 A concrete example of nested f-structures.

Let now examine briefly how this type of mechanism can be used for syntactic analysis. The main principle is that of utilizing the f-structure formalism to represent, at the same time, (1) the lexical entries; (2) the grammar rules; and (3) the analysis of the sentences. In particular, grammar rules specify how the words, represented by the lexical entries, can be combined with one another to give rise to the different elements of the analysis: these last f-structures are called "constituents." Examples of constituents are the classical "noun phrase" (NP) and "verb phrase" (VP) groups. In all the f-structures that represent lexical entries, grammar rules, or constituents, a particular attribute, "category," must always be present: its value indicates the (general) grammatical or syntactic category of that particular f-structure. We will make use here of a simple example, adapted from Knight (1989).

Suppose we want to analyze the sentence "the boy eats noodles." The lexical entry for "boy" is given in Figure 3.

To analyze this sentence according to the unification grammars approach, we will make use of "augmented rules" that correspond to a sort of "augmented context-free grammar" (see the previous subsection and, also, the ATN techniques in the next subsection). Accordingly, some classical rules in the S —> NP VP style will be "augmented" with constraints to be used both (1) to block the spurious developments of the analysis, and (2) to specify the details of the construction of the constituents. Using for the moment only context-free rules, we can now analyze the two symmetrical halves of the example, building up from the lexical entries associated with its words the NP and VP constituents represented, in a "unification" style, in Figure 4.


FIGURE 3 An example of lexical entry represented as f-structure.


FIGURE 4 f-structure representation of NP and VP constituents.


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