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<Paper uid="P06-2049">
  <Title>Sydney, July 2006. c(c)2006 Association for Computational Linguistics Transformation-based Interpretation of Implicit Parallel Structures: Reconstructing the meaning of vice versa and similar linguistic operators</Title>
  <Section position="4" start_page="377" end_page="377" type="metho">
    <SectionTitle>
2 Data Collected From Corpora
</SectionTitle>
    <Paragraph position="0"> In order to learn about cross-linguistic regularities in reconstructing the underlying form of propositions speci ed by vice versa or similar operators, we rst looked at several English and German corpora. These included, among others, the Negra, the Frankfurter Rundschau, the Europarl corpora and a corpus of tutorial dialogs on mathematics (Wolska et al., 2004). We also performed several internet searches. We looked at the German phrases andersrum and umgekehrt, and their English equivalents vice versa and the other way (a)round. We only considered instances where the parallel structure with a pair of items swapped is not stated explicitly. We excluded cases of the use of umgekehrt as a discourse marker, cases in which the transformation needed is of purely lexical nature, such as turning augment into reduce , and instances of andersrum as expressing a purely physical change, such as altering the orientation of an object (cf. the Bielefeld corpus1).</Paragraph>
    <Paragraph position="1"> The classi cation of vice versa utterances presented in Figure 1, re ects the role of the items that must be swapped to build the parallel proposition conveyed implicitly. The examples demonstrate that the task of reconstructing the proposition left implicit in the text may be tricky.</Paragraph>
    <Paragraph position="2"> The rst category concerns swapping two case role llers or Arguments of a predicate head. This may be applied to Agent and Patient dependents, as in (1), or to two directional roles as in (2). In the last example in this category, complications arise due to the fact that one of the arguments is missing on the surface and needs to be contextually inserted prior to building the assertions with exchanged directional arguments. Moreover, the swap can also work across clauses as in (3).</Paragraph>
    <Paragraph position="3"> Complex interrelations may occur when the llers themselves are composed structures, is in (4), which also makes swapping other pairs of items structurally possible. In this example, the need for exchanging the persons including their mentioned body parts rather than the mere body parts or just the persons requires world knowledge.</Paragraph>
    <Paragraph position="4"> The second category comprises swapping applied to modifiers of two arguments rather than the arguments themselves. An example is (5); the ut- null terance is ambiguous since, from a purely structural point of view, it could also be categorized as an Argument swap, however, given world knowledge, this interpretation is rather infelicitous. Similarly to (3), a contextually-motivated enhancement prior to applying a swapping operation is required in (6); here: a metonymic extension, i.e.</Paragraph>
    <Paragraph position="5"> expanding the strings to the strings' tones .</Paragraph>
    <Paragraph position="6"> The third category comprises occurrences of a mixed form of the rst two with a modi er substituted for an argument which, in turn, takes the role of the modi er in the reconstructed form. The rst example, (7), has already been discussed in the Introduction. The next one, (8), illustrates repeated occurrences of the items to be swapped.</Paragraph>
    <Paragraph position="7"> Moreover, swapping the items A and B must be propagated to the included formula. The next example, (9), is handled by applying the exchange on the basis of the surface structure: swapping the properties of a triangle for the reconstructed assertion. If a deeper structure of the sentence's meaning is built, this would amount to an implication expressing the fact that a triangle with two sides of equal length is a triangle that has two equal angles. For such a structure, the reconstruction would fall into the next category, exchange of the order of two propositions: here, reversing the implication. In (10), the lexeme Saxophonist needs to be expanded into Saxophone and Spieler ( player ), prior to performing the exchange.</Paragraph>
    <Paragraph position="8"> The fourth category involves a swap of entire Propositions; in the domain of mathematics, this may pertain to formulas. In (11), swapping applies to the sides of the equation descriptively referred to by the distributivity law. In (12), this applies to the arguments of the set inclusion relation, when the arguments are interpreted as propositions. The last example, (13), requires a structural recasting in order to apply the appropriate swapping operation. When the utterance is rebuilt around the RESULT relation, expressed as an optional case role on the surface, swapping the two propositions branching out of languages and geographical separation yields the desired result.</Paragraph>
  </Section>
  <Section position="5" start_page="377" end_page="380" type="metho">
    <SectionTitle>
3 The Interpretation Procedure
</SectionTitle>
    <Paragraph position="0"> In this section, we illustrate our technical contribution. It consists of three parts, each dealt with in a separate subsection: (1) the linguistic/semantic analysis, (2) de nitions of rules that support building parallel structures, and (3) the algorithm.</Paragraph>
    <Paragraph position="2"/>
    <Section position="1" start_page="379" end_page="379" type="sub_section">
      <SectionTitle>
3.1 Linguistic Analysis
</SectionTitle>
      <Paragraph position="0"> The linguistic analysis consists of semantic parsing followed by contextually motivated embedding and enhancements. We assume a deep semantic dependency-based analysis of the source text. The input to our reconstruction algorithm is a relational structure representing a dependency-based deep semantics of the utterance, e.g. in the sense of Prague School sentence meaning, as employed in the Functional Generative Description (FGD) at the tectogrammatical level (Sgall et al., 1986). In FGD, the central frame unit of a clause is the head verb which speci es the tectogrammatical relations (TRs) of its dependents (participants/modifications). Every valency frame speci es, moreover, which modi cations are obligatory and which optional. For example, the utterance (7) (see Figure 1.) obtains the interpretation presented in Figure 2.2 which, in the context of an informal verbalization of a step in a naive set theory proof, translates into the following formal statement: [?]x.x[?]A=x[?]K(B) .</Paragraph>
      <Paragraph position="1"> The meaning representations are embedded within discourse context and discourse relations between adjacent utterances are inferred where possible, based on the linguistic indicators (discourse markers). The nodes (heads) and dependency relations of the interpreted dependency structures as well as discourse-level relations serve as input to instantiate the reconstruction patterns. Contextual enhancements (e.g. lexical or metonymic extensions) driven by the reconstruction requirements may be carried out.</Paragraph>
      <Paragraph position="2"> Based on analysis of corpora, we have identi ed combinations of dependency relations that commonly participate in the swapping operation called for by the vice versa phrases. Examples of pairs of such relations at sentence level are shown in Figure 3.3 Similarly, in the discourse context, arguments in, for example, CAUSE, RESULT,  tions are likely candidates for a swapping operation. During processing, we use the association table as a preference criterion for selecting candidate relations to instantiate patterns. If one of the elements of a candidate pair is an optional argument that is not realized in the given sentence, we look at the preceding context to nd the rst instance of the missing element. Additionally, utterance (10) would call for more complex procedures to identify the required metonymic expansion.</Paragraph>
    </Section>
    <Section position="2" start_page="379" end_page="380" type="sub_section">
      <SectionTitle>
3.2 Interpretation Patterns
</SectionTitle>
      <Paragraph position="0"> In order to accomplish the formal reconstruction task, we de ne rules that encapsulate speci cations for building the implicit parallel text on the basis of the corresponding co-text. The rules consist of a pattern and an action part. Patterns are matched against the output of a parser on a text portion in question, by identifying relevant case roles, and giving access to their llers. Moreover, the patterns test constraints on compatibility of candidates for swapping operations. The actions apply recasting operations on the items identi ed by the patterns to build the implicit parallel text.</Paragraph>
      <Paragraph position="1"> Within patterns, we perform category membership tests on the representation. Assuming x referring to a semantic representation, Pred(x) is a logical function that checks if x has a Predfeature, i.e., it is an atomic proposition. Similarly, Conj(x) and Subord(x) perform more speci c tests for complex propositions: coordination or subordination, respectively. Moreover, Pred1(x,x1) accesses the rst proposition and binds it to x1, while Pred2(x,x2) does the same for the second one. Within a proposition, arguments and modi ers are accessed by Case(x,y), where y speci es the ller of Case in x, and indices express constraints on identity or distinctiveness of the relations. Case+ is a generalization of Case for iterative embeddings, where individual cases in the chain are not required to be  identical. In addition to access predicates, there are test predicates that express constraints on the identi ed items. The most basic one is Typecompatible(x,y), which tests whether the types of x and y are compatible according to an underlying domain ontology. A more speci c test is performed by Exchangeable(Case1,Case2) to access the associations speci ed in the previous section. The action part of the patterns is realized by Swap(x,y,z,xp) which replaces all occurrences of x in z by y and vice-versa, binding the result to xp. Different uses of this operation result in different instantiations of y and z with respect to the overarching structure x.</Paragraph>
      <Paragraph position="2"> There are patterns for each category introduced in Section 2 (see Figure 4). All patterns are tested on a structure x and, if successful, the result is bound to xp. For Argument swap there are two patterns. If the scope of the swap is a single clause (1a), two arguments (case roles) identi ed as exchangeable are picked. Their llers must be compatible in types. If the swapping overarches two clauses (1b), the connecting relation must be a conjunction and subject to swapping are arguments in the same relations. For Modifier swap (2), type compatible modi ers of distinct arguments are picked. For Mixed swap (3), a depen- null dent is picked, as in (1a) and a type-compatible modi er of another argument, as in (2). Proposition swap (4) inverts the order of the two clauses. In addition to the the pattern matching tests, the Argument and the Proposition swap operations undergo a feasibility test if knowledge is available about symmetry or asymmetry of the relation (the Pred feature) whose cases are subject to the swapping operation: if such a relation is known as asymmetric, the result is considered implausible due to semantic reasons, if it is symmetric, due to pragmatic reasons since the converse proposition conveys no new information; in both cases such a swapping operation is not carried out.</Paragraph>
      <Paragraph position="3"> To extend the functionality of the patterns, we de ned a set of recasting rules (Figure 5) invoked to reorganize the semantic representation prior to testing applicability of a suitable reconstruction rule. In contrast to inserting incomplete information contextually and expanding metonymic relations the recasting operations are intended purely to accommodate semantic representations for this purpose. We have de ned three recasting rules (numbered accordingly in Figure 5):</Paragraph>
    </Section>
  </Section>
  <Section position="6" start_page="380" end_page="381" type="metho">
    <SectionTitle>
1. Lexical recasting
</SectionTitle>
    <Paragraph position="0"> The semantics of some lexemes con ates the meaning of two related items. If one of them is potentially subject to swapping, it is not accessible for the operation without possibly af- null fecting the other so closely related to it. The representation of such lexemes is expanded, provided there is a sister case with a ller that is type compatible.</Paragraph>
  </Section>
  <Section position="7" start_page="381" end_page="381" type="metho">
    <SectionTitle>
2. Case recasting
</SectionTitle>
    <Paragraph position="0"> The dependency among items may not be reected by the dependencies in the linguistic structure. Speci cally, a dependent item may appear as a sister case in overarching case frame. The purpose of this operation is to build a uniform representation, by removing the dependent case role ller and inserting it as a modi er of the item it is dependent on.</Paragraph>
  </Section>
  <Section position="8" start_page="381" end_page="382" type="metho">
    <SectionTitle>
3. Proposition recasting
</SectionTitle>
    <Paragraph position="0"> Apart from expressing a discourse relation by a connective, a proposition lling a subordinate relation may also be expressed as a case role (argument). Again, uniformity is obtained through lifting the argument (case ller) and expressing the discourse relation as a multiple clause construct.</Paragraph>
    <Paragraph position="1"> Additional predicates are used to implement recasting operations. For example, the predicate Lex[?]Expand(y,u,Case,v) re-expresses the semantics of y by u, accompanied by a Case role lled by v. Type(x,y) associates the type y with x. The type information is used to access Recastable(t1,C1,t2,C2) table to verify whether case C1 with a t1-type ller can also be expressed as case C2 with type t2. Build(x) creates a new structure x. Remove(x,y) is realized as a function, deleting occurrences of y in x, and Add(x,y) expands x by an argument y.</Paragraph>
    <Section position="1" start_page="381" end_page="382" type="sub_section">
      <SectionTitle>
3.3 The Structure Building Algorithm
</SectionTitle>
      <Paragraph position="0"> In this section, we describe how we build implicitly conveyed parallel structures based on the definitions of swapping operations with optional incorporation of recasting operations if needed. The procedure consists of two main parts (see Figure 6). In the rst part, the scope for applying the swapping rules de ned in Figure 4 is determined, and in the second part, the results obtained by executing the rules are collected. Due to practical reasons, we introduce simpli cations concerning the scope of vice-versa in the current formulation of the procedure. While the effect of this operator may range over entire paragraphs in some involved texts, we only consider single sentences with at most two coordinated clauses or one subordinated clause. We feel that this restriction is not severe for uses in application-oriented systems.</Paragraph>
      <Paragraph position="1"> The procedure Build-Parallel-Structure takes the last input sentence x, examines its clause structure, and binds potential scopes to variable Scopes. For composed sentences, the entire sentence (x) as well as the second clause (Case2(x,z)) is a potential scope for building parallel structures.</Paragraph>
      <Paragraph position="2"> In the second part of the procedure, each swapping pattern is tested for the two potential scopes, and results are accumulated in Structures. The call &lt; X [?] swap(Scope1) &gt;, with X being either Case, Argument, Mixed, or Prop expresses building a set of all possible instantiations of the pattern speci ed when applied to Scope1.</Paragraph>
      <Paragraph position="3"> Some of these operations are additionally invoked with alternative parameters which are accommodated by a recasting operation tting to the pattern used, that call being &lt; X [?] swap(Y [?] recast(Scope1)) &gt;, where Y is Case, Lex, or Prop. Finally, if multiple readings are generated, they are ranked according to the following priori- null tized criteria: 1. The nearest scope is preferred; 2. Operations swapping duals , such as left-right, are given priority; 3. Candidate phrases are matched against the corpus;  items with higher bigram frequencies are preferred. Linguistic analysis, structure reconstruction patterns, recasting rules, and the algorithms operating on top of these structures are formulated in a domain-independent way, also taking care that the tasks involved are clearly separated. Hence, it is up to a concrete application to elaborate lexical  semantic de nitions required (e.g. for a saxophonist to capture example (10) in Figure 1) to de ne the tables Exchangeable and Recastable, and to enhance preference criteria.</Paragraph>
    </Section>
  </Section>
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