7. Parsing in functional unification grammar

Han gi-deuc

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Contents

7.1 Functional unification grammar– 7.1.1 Compilation– 7.1.2 Attributes and values– 7.1.3 Unification– 7.1.4 Patterns and constituent sets– 7.1.5 Grammar

7.2 The parser– 7.2.1 The General Syntactic Processor– 7.2.2 The parsing grammar

7.3 The compiler 7.4 Conclusion

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7.1 functional unification grammar

The claim that this theory makes on the word “functional” in its title is therefore supported in three ways.– 1. It gives primary status to those aspects of language that have

often been called functional; logical aspects are not privileged– 2. It describes linguistic structures in terms of the function that a

part fills in a whole, rather than in terms of parts of speech and ordering relations

– 3. Most important for this paper, it requires its grammars to function; that is, they must support the practical enterprises of language generation and analysis.

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7.1.1 Compilation

This paper will concentrate on how this translation is actually carried out; it will, in short, be about machine translation between grammatical formalisms.

This kind of translation to be explored here is known in computer science as compilation, and the computer program that does it is called a compiler.

The term “compilation” almost always refers to a process that translates a text produced by a human into a text that is functionally equivalent, but not intended for human consumption.

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7.1.2 Attributes and values

Functional unification grammar knows things by their functional descriptions, (FDs). A simple FD is a set of descriptors and a descriptor is a constituent set, a pattern, or an attribute with an associated value.

The list of descriptors that make up an FD is written in square brackets, no significance attaching to the order. The attributes in an FD must be distinct from one another so that if an FD F contains the attribute a, it is always possible to use the phrase “the a of F” to refer unambiguously to a value.

An attribute is a symbol, that is, a string of letters. A value is either a symbol or another FD

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7.1.2 Attributes and values

The sentence “He saw her”

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7.1.3 Unification

A string of atoms enclosed in angle brackets constitutes a path and there is at least one that identifies every value in an FD.

The path <a1 a2 … ak> identifies the value of the attribute ak in the FD that is the value of <a1 a2 … ak-1>. It can be read as The ak of the ak-1 … of the a1.

Paths are always interpreted as beginning in the largest FD that encloses them.

A pair consisting of a path in an FD and the value that the path leads to is a feature of the object described.

If the value is a symbol, the pair is a basic feature of the FD

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7.1.3 Unification

The sentence “He likes writing books”

Example of Path

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7.1.3 Unification

The union of a pair of FDs in not, in general, a well-formed FD.

The reason is this: The requirement that a given attribute appear only once in an FD implies a similar constraint on the set of features corresponding to an FD.

A path must uniquely identify a value.

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7.1.3 Unification

When two or more simple FDs are compatible, they can be combined into one simple FD describing those things that they both describe, by the process of unification.

Unification is the same as set union except that it yields the null set when applied to incompatible arguments.

The “=“ sign is used for unification, so that α = β denotes the result of unifying α and β.

Unification is the fundamental operation underlying the analysis and synthesis of sentences using functional unification grammar.

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7.1.3 Unification

Example of Unification

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7.1.4 Patterns and constituent sets

The value of SUBJ is the FD of a constituent of the sentence, whereas the value of ASPECT is not

The purpose of constituent sets and patterns is to identify constituents and to state constraints on the order of their occurrence

The value of the C-set attribute covers all constituents.

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7.1.4 Patterns and constituent sets

Each pattern is a list whose members can be– 1. A path. The path may have as its value

a. An FD. As in the case of the constituent set, the FD describes a constituentb. A pattern. The pattern is inserted into the current one at this point

– 2. A string of dots. This matches any number of constituents– 3. The symbol #. This matches any one constituent– 4. An FD. This will match any constituent whose description is unifiable

with it. The unification is made with a copy of the FD in the pattern, rather than with the FD itself, because the intention is to impute its properties to the constituent, but not to unify all the constituents that match this part of the pattern

– 5. An expression of the form (* fd), where fd is an FD. This matches zero or more constituents, provided they can all be unified with a copy of fd.

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7.1.4 Patterns and constituent sets

Expressions of pattern

The pattern (16) requires exactly one constituent to have the property [TRACE=NP]; all others must have the property [TRACE=NONE];

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7.1.5 Grammar

A functional unification grammar is a single FD

Example (19) shows a simple grammar, corresponding to a context-free grammar containing the single rule (20)

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7.2 The Parser

7.2.1 The General Syntactic Processor– The input is an FD that constitutes the

specification of a sentence to be uttered– There are two principal data structures, the

chart and the agenda– The chart is a directed graph each of whose

edges maps onto a substring of the sentence being analyzed

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7.2.1 The General Syntactic Processor

Chart– K+1 vertices for a sentence of k words– Each word in the sentence to be parsed is represented by an edge l

abeled with an FD obtained by looking that word up in the lexicon– If the word is ambiguous, that is, if it has more than one FD, it is r

epresented by more than one edge.– All the edges for the i-th word clearly go from vertex

i – 1 to vertex i The label on an active edge has two parts, an FD describin

g what is known about the putative phrase, and a procedure that will carry the recognition of the phrase one step further forward

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7.2.1 The General Syntactic Processor

Parsing proceeds in a series of steps in each of which the procedure on an active edge is applied to a pair of FDs, one coming from that same active edge, and the other from an inactive edge that leaves the vertex where the active edge ends.

If a and i are an active and an inactive edge respectively, a being incident to the vertex that i is incident from, the step consists in evaluating Pa(fa,fi) , where fa and fi are the FDs on a and i, and Pa is the procedure

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7.2.1 The General Syntactic Processor

This process carried out for every pair consisting of an active followed by an inactive edge that comes to be part of the chart. Each successful step leads to the introduction of one new edge, but this edge may result in several new pairs.

Each new pair produced therefore becomes a new item on the agenda which serves as a queue of pairs waiting to be processed

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7.2.2 The parsing grammar

The parsing grammar, as we have seen, takes the form of a set of procedures, each of which operates on a pair of FDs

One of these FDs, the matrix FD, is a partial description of a phrase, and the other, the constituent FD, is as complete a description as the parser will ever have of a candidate for inclusion as constituent of that phrase

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7.2.2 The parsing grammar

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7.3 The compiler

The compiler has two major sections. The first part is a straightforward application of the generation program to put the grammar, effectively, into disjunctive normal form. The second is concerned with actually building the procedures

If F is grammar, or indeed any complex FD, it is always possible to recast it in the form F1 ˇ F2 … Fn, where the Fi (1 ≤ i ≤ n) each contain no alternations

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7.3 The compiler

The process of generation from a particular FD, ƒ, effectively selects those members of F1 … Fn that can be unified with ƒ, and then repeats this procedure recursively for each constituent. F is, in general, a conjunct containing some atomic terms and some alternations.

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7.3 The compiler

Ignoring patterns for the moment, the procedure is as follows– 1. Unify the atomic terms of F with ƒ. If this fails, the procedure as

a whole fails. Some number of alternations now remain to be considered. In other words, that part of F that remains to be unified with ƒ is an expression F' of the form (a1.1 ˇ a1.2 … a1.k1

) ˆ (a2.1 ˇ a2.2 … a2.k2

) … (an.1 ˇ an.2 … an.kn)

– 2. Rewrites as an alternation by multiplying out the terms of an arbitrary alternation in F', say the first one. This give an expression F" of the form (a1.1 ˆ (a2.1 ˇ a2.2 … a2.k2

) ˆ (an.1 ˇ an.2 … an.kn)) ˇ (a1.2 ˆ

(a2.1 ˇ a2.2 … a2.k2) ˆ (an.1 ˇ an.2 … an.kn

)) ˇ … (a1.k1 ˆ (a2.1 ˇ a2.2 … a2.k2) ˆ

(an.1 ˇ an.2 … an.kn))

– 3. Apply the whole procedure (steps 1-3) separately to each conjunct in F"

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7.3 The compiler

It remains to spell out the alternatives that are implicit in the patterns

The basic idea is to generate all permutations of the constituent set of the FD and to eliminate those that do not match all the patterns

The result of this phase of the compilation is a list of simple FDs, containing no alternations, and having either no pattern, or a single pattern that specifies the order of constituents uniquely

Those that have no pattern become lexical entries and they are of no further interest to the compiler

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7.3 The compiler

The second phase of the compiler centers around a procedure which, given a list of simple FDs, and an integer n, attempts to find an attribute, or path, on the basic of which the nth constituent of those FDs can be distinguished

The result of this process is (1) a path A, (2) a set of values for A, each associated with the subset of the list of FDs whose nth constituent has that value of A, and (3) a residual subset of the list consisting of FDs whose nth constituent has no value of the attribute A

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7.3 The compiler Second process

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7.4 Conclusion

Two things can be said to mitigate this to some extent. First, the parsing and generation grammars do indeed describe exactly the same languages, so that much of the work involved in testing prototype grammars can be done with a generator that works directly and efficiently off the competence grammar. The second point is this: the compiler behaves as though any attribute-value pair in the grammar that did not mention CAT was not there at all.

The resulting set of parsing procedures clearly recognizes at least all the sentences of the language intended, though possibly others in addition.