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<Paper uid="J82-3003">
  <Title>Using Semantics in Non-Context-Free Parsing of Montague Grammar 1</Title>
  <Section position="4" start_page="0" end_page="0" type="metho">
    <SectionTitle>
6 TS Mr null
7 TE Mr null
7 r null Mary
</SectionTitle>
    <Paragraph position="0"> \[This computation continues and parses the second half of this sentence. Two parses are produced: (S11 ($4 Bill walk) ($4 Mary run)) and (S11 ($4 Bill walk) (S14,0 Mary ($4 he0 run))) After this, the execution method fails back to the FAKEPOP at PUSH 5, and another subtree from a bucket from PUSH 2 is FAKEPOPped.\] 1(5) &amp;Mr null (S14,0 Bill (he0 walk)) \[And the computation continues, eventually producing a total of ten parses for this sentence.\] (In the earlier example of Bill walks, these FAKEPOPs are done, but their computations immediately fail, because they are looking for a conjunction but are at the end of the sentence.)</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
128 American Journal of Computational Linguistics, Volume 8, Number 3-4, July-December 1982
David Scott Warren and Joyce Friedman Using Semantics in Non-Context-Free Parsing
Results of Parsing
</SectionTitle>
      <Paragraph position="0"> The sentence Bill walks and Mary runs has ten syntactic structures with respect to the PTQ grammar.</Paragraph>
      <Paragraph position="1"> The rules $4, Sll, and S14,i can be used in various orders. Figure 2 shows the ten different structures in the order they are produced by the syntactic parser.</Paragraph>
      <Paragraph position="2"> The nodes in the trees of Figure 2 that are in italics are the syntactic structures used for the first time.</Paragraph>
      <Paragraph position="3"> The nodes in standard type are structures used previously, and thus either are part of an execution path in common with an earlier parse, or are retrieved from a bucket in the recall table to be used again. Thus the number of italicized nodes measures in a crude way the amount of work required to find all the parses for this sentence.</Paragraph>
      <Paragraph position="4">  This sentence, Bill walks and Mary runs, is one for which semantic parsing is substantially faster. It is unambiguous; its only reduced extensionalized logical translation is &amp;quot;walk,'(b)&amp;run,'(m)&amp;quot;. In the directed process parser, all ten trees of Figure 2 are found.</Paragraph>
      <Paragraph position="5"> They will all have the same translation. In semantic parsing on'ly one is found. Here the method works to advantage because both parses of the initial string Bill walks result in the same environment for parsing Mary runs. These two parses go into the same bucket so only one needs to be used to construct larger structfires. We trace the example.</Paragraph>
      <Paragraph position="6">  \[This formula is the translation of the syntactic structure using S14,0 to substitute Bill into &amp;quot;he0 walks&amp;quot;. This is the same bucket and the same translation as obtained at the return from 1 after PUSH 3 above, so we do not POP (indicated by the 'n' in the final column), but instead fail back.\]</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="0" end_page="0" type="metho">
    <SectionTitle>
5 TS Bw&amp;Mr null
</SectionTitle>
    <Paragraph position="0"> \[FAKEPOP, since this is a repeat PUSH to this category with these parameters. There are two buckets: 1-&amp;Mrnull, which in syntactic parsing had two trees but now has only one translation, and bucket 1-&amp;Mr-(he0 B) with one translation. So we FAKEPOP 1-&amp;Mr-null.\]  This completes the trace of the semantic parse of the sentence.</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
Results of Parsing
</SectionTitle>
      <Paragraph position="0"> Figure 3 displays in graphical form the syntactic structures built during the semantic parsing of Bill walks and Mary runs traced above. A horizontal line over a particular node in a tree indicates that the translation of the structure duplicated a translation already in its bucket, so no larger structures were built using it. Only parse a) is a full parse of the sentence and thus it is the only parse returned. All the others are aborted when they are found equivalent to earlier partial results. These points of abortion in the computation are the points in the trace above at which a POP fails due to the duplication of a bucket and its contents. null</Paragraph>
      <Paragraph position="2"> Note that construction of parse c) is halted when a translation is built that duplicates the translation of the right $4 subtree of parse a). This corresponds to the failure due to duplicate bucket contents in bucket 6-E-null following PUSH 9 in the trace above. Similarly parse g) is aborted before the entire tree is built. This corresponds to the failure in the final line of the trace due to a duplicate translation in bucket 10-E-null. Semantic parses that would correspond to syntactic parses h), i), and j) of Figure 2 are not considered at all. This is because bucket 1-&amp;Mr-null contains two syntactic structures, but only one translation. Thus in semantic equivalence parsing we only do one FAKEPOP for this bucket for PUSH 5. In syntactic parsing the other parses are generated by the FAKEPOP of the other structure in this bucket.</Paragraph>
    </Section>
    <Section position="2" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
Reducing the Environment
</SectionTitle>
      <Paragraph position="0"> The potential advantage of semantic equivalence parsing derives from treating partial results as an equivalence class in proceeding. A partial result consists of a structure, its extensionalized reduced translation, and a set of parameters of the parse to that point.</Paragraph>
      <Paragraph position="1"> These parameters are the environment for parsing the phrase. Consider the sentence John loves Mary and its parses:  (1) ($4 John ($5 love Mary)) (2) ($4 John (S16,0 Mary ($5 love he0))) (3) (S14,0 John ($4 (he0 ($5 love Mary))) (4) (S14,0 John ($4 he0 (S16,1 Mary ($5 love hel))))  (plus 3 more) On reaching the phrase love Mary in parse (3) the parameters are not the same as they were at that point in parse (1), because the pair (he0 John) is in the environment. Thus the parser is not able to consult the recall table and immediately return the already parsed substructure. Instead it must reparse love Mary in the new context.</Paragraph>
      <Paragraph position="2"> This environment problem arises because the ATN is designed to follow PTQ in treating pronouns by the non-context-free substitution rules. We have also considered, but have not to this point implemented, alternative ways of treating variables to make partial results equal. One way would be not to pass variable bindings down into lower nets at all. Thus the PUSH environment would always be null. Since these bindings are used to find the antecedent for a pronoun, the way antecedents are determined would have to be changed. An implementation might be as follows: On encountering a pronoun during parsing, replace it by a new he-variable. Then pass back up the tree information concerning both the variable number used and the pronoun's gender. At a higher point in the tree, where the substitution rule is to be applied, a determination can be made as to which of the substituted terms could be the antecedent for the pronoun. The variable number of the pronoun can then be changed to agree with the variable number of its antecedent term by a variable-for-variable substitution. Finally the substitution rule can be used to substitute the term into the phrase for all occurrences of the variable. Note that this alternative process would construct trees that do have substitution rules to substitute variables for varia-American Journal of Computational Linguistics, Volume 8, Number 3-4, July-December 1982 133 David Scott Warren and Joyce Friedman Using Semantics in Non-Context-Free Parsing bles, contrary to the variable principle mentioned above. We also note that with this modification a pronoun is not associated with its antecedent when it is first encountered. Instead the pronoun is saved and at some later point in the parse the association is made. This revised treatment is related computationally to that proposed in Cooper 1975.</Paragraph>
      <Paragraph position="3"> Evaluation of Semantic Equivalence Parsing The question of the interaction of syntax and semantics in parsing was introduced early in computational linguistics. Winograd 1971 argued for the incorporation of semantics as early as possible in the recognition process, in order to reduce the amount of syntactic processing that would be needed. Partial parses that had no interpretation did not need to be continued. The alternative position represented by Woods's early work (Woods and Kaplan 1971) was basically the inverse: less semantic processing would be needed if only completed parses were interpreted.</Paragraph>
      <Paragraph position="4"> This argument is based on the idea of eliminating uninterpretable parses as soon as possible.</Paragraph>
      <Paragraph position="5"> This advantage, if it is one, of integrated syntactic and semantic procedures does not occur here because the semantic aspect does not eliminate any logical analyses. The translation of a structure to a formula is always successful, so no partial parse is ever eliminated for lack of a translation. What happens instead is that several partial parses are found to be equivalent because they have the same translation. In this case only a representative of the set of partial parses needs to be carried forward.</Paragraph>
      <Paragraph position="6"> A further expansion of equivalence parsing would be interpretation equivalence parsing. Sentence processing would take place in the context of a specified model. Two structures would be regarded as equivalent if they had the same denotation in the model. More partial structures would be found equivalent under the equivalence relation than under the reduceextensionalize relation, and fewer structures would need to be constructed. Further, with the interpretation equivalence relation, we might be able to use an inconsistent denotation to eliminate an incorrect partial parse. For example, consider a sentence such as Sandy and Pat are running and she is talking to him. In this case, since the gender of Sandy and Pat cannot be determined syntactically, these words would have to be marked in the lexicon with both genders. This would result in multiple logical formulas for this sentence, one for each gender assumption. However, during interpretation equivalence parsing, the referents for Sandy and Pat would be found in the model and the meaning with the incorrect coreference could be rejected.</Paragraph>
      <Paragraph position="7"> Logical normal forms other than the reduced, extensionalized form used above lead to other reasonable versions of equivalence parsing. For example, we could further process the reduced, extensionalized form to obtain a prenex normal form with the matrix in clausal form. We would use some standard conventions for naming variables, ordering sequences of the same quantifier in the prefix, and ordering the literals in the clauses of the matrix. This would allow the algorithm to eliminate, for example, multiple parses arising from various equivalent scopes and orderings of existential quantifiers.</Paragraph>
      <Paragraph position="8"> The semantic equivalence processor has been implemented in Franz Lisp. We have applied it to the PTQ grammar and tested it on various examples. For purposes of comparison the directed process version includes syntactic parse, translation to logical formula and reduction, and finally the reduction of the list of formulas to a set of formulas. The mixed strategy yields exactly this set of formulas, with one parse tree for each. Experiments with the combined parser and the directed parser show that they take approximately the same time for reasonably simple sentences. For more complicated sentences the mixed strategy usually results in less processing time and, in the best cases, results in about a 40 percent speed-up. The distinguishing characteristic of a string for which the method yields the greatest speed-up is that the environment resulting from parsing an initial segment is the same for several distinct parses.</Paragraph>
      <Paragraph position="9"> The two parsing method we have described, the sequential process and the mixed process, were obviously not developed with psychological modeling in mind. The directed process version of the system can be immediately rejected as a possible psychological model, since it involves obtaining and storing all the structures for a sentence before beginning to interpret any one of them. However, a reorganization of the programwould make it possible to interpret each structure immediately after it is obtained. This would have the same cost in time as the first version, but would not require storing all the parses.</Paragraph>
      <Paragraph position="10"> Although semantic equivalence parsing was developed in the specific context of the grammar of PTQ, it is more general in its applicability. The strict compositionality of syntax and semantics in PTQ is the main feature on which it depends. The general idea of equivalence parsing can be applied whenever syntactic structure is used as an intermediate form and there is a syntax-directed translation to an output form on which an equivalence relation is defined.</Paragraph>
    </Section>
  </Section>
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