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<Paper uid="P90-1007">
  <Title>TRANSFORMING SYNTACTIC GRAPHS INTO SEMANTIC GRAPHS* Hae-Chang Rim</Title>
  <Section position="5" start_page="48" end_page="48" type="metho">
    <SectionTitle>
SYNTACTIC GRAPHS
</SectionTitle>
    <Paragraph position="0"> In the previous paper we argued that the syntactic graph supported by an exclusion matrix would provide all and &amp;quot;only&amp;quot; the information given by a parse forest. 1 Let us first review an example of a syntactic graph for the following sentence: Exl) John saw a man on the hill with a telescope. null There are at least five syntactic interpretations for Exl from a phrase structure grammar. The syntactic graph is represented as a set of dominator-modifier triples 2 as shown in the middle of Figure 1 for Exl. Each triple consists of a label, a head-word, and a modifier-word.</Paragraph>
    <Paragraph position="1"> Each triple represents an arc in a syntactic graph in the left of Figure 1. An arc is drawn from the head-word to the modifier-word. The label of each triple, SNP, VNP, etc. is uniquely determined according to the grammar rule used to generate the triple. For example, a triple with the label SNP is generated by the grammar rule, SNT --+ NP + VP, VPP is from the rule VP --+ VP / PP, and PPN from PP ---+ Prep/ NP, etc.</Paragraph>
    <Paragraph position="2"> We can notice that the ambiguities in the graph are signalled by identical third terms (i.e., the same modifier-words with the same sentence position) in triples because a word cannot modify two different words in one syntactic interpretation. In  streams.&amp;quot; a graph, each node with multiple in-arcs shows an ambiguous point. There is a special arc, called the root are, which points to the head word of the sentence. The arc (0) of the syntactic graph in Figure 1 represents a root arc. A root arc contains information (not shown) about the modalities of the sentence such as voice: passive, active, mood: declarative or wh-question, etc. Notice that a sentence may have multiple root arcs because of syntactic ambiguities involving the head verb.</Paragraph>
    <Paragraph position="3"> One interpretation can be obtained from a syntactic graph by picking up a set of triples with no repeated third terms. In this example, since there are two identical occurrences of on and three of with, there are 2.3 = 6 possible sentence interpretations in the graph represented above. However, there must be only five interpretations for Exl.</Paragraph>
    <Paragraph position="4"> The reason that we have more interpretations is that there are triples, called exclusive triples, which cannot co-occur in any syntactic interpretation. In this example, the triple (vpp saw on) and (npp man with) cannot co-occur since there is no such interpretation in this sentence. 3 That's why a syntactic graph must maintain an exeluslon matrix.</Paragraph>
    <Paragraph position="5"> An exclusion matrix, (Ematrix), is an N * N matrix where N is the number of triples. If Ematrix(i,j) = 1 then the i-th and j-th triple 3Once the phrase &amp;quot;on the hill&amp;quot; is attached to saw, &amp;quot;with a telescope&amp;quot; must be attached to either hill or saw, not m0~n.</Paragraph>
    <Paragraph position="6"> cannot co-occur in any reading. The exclusion matrix for Exl is shown in the right of Figure 1. In Exl, the 'triples 5 and 9 cannot co-occur in any interpretation according to the matrix. Trivially exclusive triples which share the same third term are also marked in the matrix. It is very important to maintain the Ematrix because otherwise a syntactic graph generates more interpretations than actually result from the parsing grammar.</Paragraph>
    <Paragraph position="7"> Syntactic graphs and the exclusion matrix are computed from the chart (or forest) formed by an all-paths chart parser. Grammar rules for the parse are in augmented phrase structure form, but are written to minimize their deviation from a pure context-free form, and thus, limit both the conceptual and computational complexity of the analysis system. Details of the graph form, the grammar, and the parser are given in (Seo and Simmons 1989).</Paragraph>
  </Section>
  <Section position="6" start_page="48" end_page="53" type="metho">
    <SectionTitle>
COMPUTING SEMANTIC
GRAPHS FROM SYNTACTIC
GRAPHS
</SectionTitle>
    <Paragraph position="0"> An important test of the utility of syntactic graphs is to demonstrate that they can be used directly to compute corresponding semantic graphs that represent the union of acceptable case analyses. Nothing would be gained, however, if we had to extract one reading at a time from the syntactic graph, transform it, and so accumulate the union of case analyses. But if we can apply a set of rules</Paragraph>
    <Paragraph position="2"> directly to the syntactic graph, mapping it into the semantic graph, then using the graph can result in a significant economy of computation.</Paragraph>
    <Paragraph position="3"> We compute a semantic graph in a two-step process. First, we transform the labeled dependency triples resulting from the parse into functional notation, using labels such as subject, object, etc.</Paragraph>
    <Paragraph position="4"> and transforming to the canonical active voice.</Paragraph>
    <Paragraph position="5"> This results in a functional graph as shown in Figure 3. Second, the functional graph is transformed into the semantic graph of Figure 5. During the second transformation, filtering rules are applied to reduce the possible syntactic interpretations to those that are semantically plausible.</Paragraph>
  </Section>
  <Section position="7" start_page="53" end_page="53" type="metho">
    <SectionTitle>
COMPUTING FUNCTIONAL GRAPHS
</SectionTitle>
    <Paragraph position="0"> To determine SUB, OBJ and IOBJ correctly, the process checks the types of verbs in a sentence and its voice, active or passive. In this process, a syntactic triple is transformed into a functional triple: for example, (snp X Y) is transformed into (subj X Y) in an active sentence.</Paragraph>
    <Paragraph position="1"> However, some transformation rules map several syntactic triples into one functional triple. For example, in a passive sentence, if three triples, (voice X passive), (vpp X by), and (ppn by Y), are in a syntactic graph and they are not exclusive with each other, the process produces one functional triple (subj X Y). Since prepositions are used as functional relation names, two syntactic triples for a prepositional phrase are also reduced into one functional triple. For example, 50 (vpp lives in) and (ppn in jungles) are transformed into (in lives jungles). These transformations are represented in Prolog rules based on general inference forms such as the following:</Paragraph>
    <Paragraph position="3"> When the left side of a rule is satisfied by a set of triples from the graph, the exclusion matrix is consulted to ensure that those triples can all co-occur with each other.</Paragraph>
    <Paragraph position="4"> This step of transformation is fairly straighttoward and does not resolve any syntactic ambiguities. Therefore, the process must carefully transform the exclusion matrix of the syntactic graph into the exclusion matrix of the functional graph so that the transformed functional graph has the same interpretations as the syntactic graph has 4.</Paragraph>
    <Paragraph position="5"> Intuitively, if a functional triple, say F, is produced from a syntactic triple, say T, then F must be exclusive with any functional triples produced from the syntactic triples which are exclusive with T. When more than one syntactic triple, say T\[s are involved in producing one functional triple, say F1, the process marks the exclusion 4At a late stage in our research we noticed that we could have written our grammar to result directly in syntactic-functional notation; but one consequence would be increasing the complexity of our grammar rules, requiring frequent tests and transformations, thus increasing conceptual and computational complexities.</Paragraph>
    <Paragraph position="6"> N : the implausible triple which will be removed.</Paragraph>
    <Paragraph position="7"> The process starts by calling remove-all-Dependent-arcs(\[N\]). remove-all-dependent-arcs(Arcs-to-be-removed) for all Arc in Arcs-to-be-removed do  matrix so that F1 can be exclusive with all functional triples which are produced from the syntactic triples which are exclusive with any of T/~s. The syntactic graph in Figure 2 has five possible syntactic interpretations and all and only the five syntactic-functional interpretations must be contained in the transformed functional graph with the new exclusion matrix in Figure 3. Notice that, in the functional graph, there is no single, functional triple corresponding to the syntactic triples, (~)-(8), (11) and (13). Those syntactic triples are not used in one-to-one transformation of syntactic triples, but are involved in many-to-one transformations to produce the new functional triples, (50)-(55), in the functional graph.</Paragraph>
  </Section>
  <Section position="8" start_page="53" end_page="53" type="metho">
    <SectionTitle>
COMPUTING SEMANTIC GRAPHS
</SectionTitle>
    <Paragraph position="0"> Once a functional graph is produced, it is transformed into a semantic graph. This transformation consists of the following two subtasks: given a functional triple (i.e., an are in Figure 3), the process must be able to (1) check if there is a semantically meaningful relation for the triple (i.e., co-occurrence constraints test), (2) if the triple is semantically implausible, find and remove all functional triples which are dependent on that triple.</Paragraph>
    <Paragraph position="1"> The co-occurrence constraints test is a matter of deciding whether a given functional triple is semantically plausible or not. 5 The process uses a type hierarchy for real world concepts and rules that state possible relations among them. These relations are in a case notation such as agt for agent, ae for affected-entity, etc. For example, the 5 Eventually we will incorporate more sophisticated tests as suggested by Hirst(1987) and others, but our current emphasis is on the procedures for transforming graphs.</Paragraph>
    <Paragraph position="2">  subject(I) arc between lives and monkey numbered (1) in Figure 3 is semantically plausible since animal can be an agent of live if the animal is a subj of the live. However, the subject arc between and and monkey numbered (15) in Figure 3 is semantically implausible, because the relation conjvp connects and and streams, and monkey can not be a subject of the verb streams. In our knowledge base, the legitimate agent of the verb streams is a flow-thing such as a river.</Paragraph>
    <Paragraph position="3"> When a given arc is determined to be semantically plausible, a proper case relation name is assigned to make an arc in the semantic graph.</Paragraph>
    <Paragraph position="4"> For example, a case relation agt is found in our knowledge base between monkey and lives under the constraint subject.</Paragraph>
    <Paragraph position="5"> If a triple is determined to be semantically implausible, then the process removes the triple.</Paragraph>
    <Paragraph position="6"> Let us explain the following definition before discussing an interesting consequence.</Paragraph>
    <Paragraph position="7"> Definition 1 A triple, say T1, is dependent on another triple, say T2, if every interpretation which uses 7&amp;quot;1 always uses T2.</Paragraph>
    <Paragraph position="8"> Then, when a triple is removed, if there are any triples which are dependent on the removed triple, those triples must also be removed. Notice that the dependent on relation between triples is transitive.</Paragraph>
    <Paragraph position="9"> Before presenting the algorithm to find dependent triples of a triple, we need to discuss the following property of a functional graph.</Paragraph>
    <Paragraph position="10"> Property 1 Each semantic interpretation derived from a functional graph must contain every node in each position once and only once.</Paragraph>
    <Paragraph position="11">  Here the position means the position of a word in a sentence. This property ensures that all words in a sentence must be used in a semantic interpretation once and only once.</Paragraph>
    <Paragraph position="12"> The next property follows from Property 1.</Paragraph>
    <Paragraph position="13"> Property 2 Ira triple is determined to be semantically implausible, there must be at least one triple which shares the same modifier-word. Otherwise, the sentence is syntactically or semantically illformed. null Lemma 1 Assume that there are n triples, say 7&amp;quot;1 .... , Tn, sharing a node, say N, as a modifier-word (i.e. third term) in a functional graph. If there is a triple, say T, which is exclusive with T1,..., T/-1, Ti+ l ..... Tn and is not exclusive with T~, T is dependent on Ti.</Paragraph>
    <Paragraph position="14"> This lemma is true because T cannot co-occur with any other triples which have the node N as a modifier-word except T/in any interpretation. By Property 1, any interpretation which uses T must use one triple which has N as a modifier-word.</Paragraph>
    <Paragraph position="15"> Since there is only one triple, 7~ that can co-occur with T, any interpretations which use T use T/.\[3 Using the above lemma, we can find triples which are dependent on a semantically implausible triple directly from the functional graph and the corresponding exclusion matrix. An algorithm for finding a set of dependent relations is presented in  For example, in the functional graph in Figure 3, since monkey cannot be an agt of streams, the triple (15.) is determined to be semantically  implausible. Since there is only one triple, (1), which shares the same modifier-word, monkey, the process finds triples which are exclusive with (1). Those are triples numbered (14), (15), (16), and (17). Since these triples are dependent on (16), these triples must also be removed when (16) is removed. Similarly, when the process removes (14), it must find and remove all dependent triples of (14). In this way, the process cascades the remove operation by recursively determining the dependent triples of an implausible triple.</Paragraph>
    <Paragraph position="16"> Notice that when one triple is removed, it removes possibly multiple ambiguous syntactic interpretations--two interpretations are removed by removing the triple (16) in this example, but for the sentence, It is transmitted by eating shellfish such as oysters living in infected waters, or by drinking infected water, or by dirt from soiled fingers, 189 out of 378 ambiguous syntactic interpretations are removed when the semantic relation (rood water drinking) is rejected, e This saves many operations which must be done in other approaches which check syntactic trees one by one to make a semantic structure. The resulting semantic graph and its exclusion matrix derived from the functional graph in Figure 3 have three semantic interpretations and are illustrated in Figure 5. This is a reduction from five syntactic interpretations as a result of filtering out the possibility, (agt streams monkey).</Paragraph>
    <Paragraph position="17"> There is one arc in Figure 5, labeled near(51), that proved to be of considerable interest to us.</Paragraph>
    <Paragraph position="18"> 6In &amp;quot;infec'~ed drinking water&amp;quot;, (rood water drinking) is plausible but not in &amp;quot;drinking infected water&amp;quot;. If we attempt to generate a complete sentence using that arc, we discover that we can only produce, &amp;quot;The monkey lives in tropical jungles near rivers.&amp;quot; There is no way that that a generation with that arc can include &amp;quot;and streams&amp;quot; and no sentence with &amp;quot;and streams&amp;quot; can use that arc. The arc, near(51), shows a failure in our ability to rewrite the exclusion matrix correctly when we removed the interpretation &amp;quot;the monkey lives ... and streams.&amp;quot; There was a possibility of the sentence, &amp;quot;the monkey lives in jungles, (lives) near rivers, and (he) streams.&amp;quot; The redundant arc was not dependent on subj(16) (in Figure 3) and thus remains in the semantic graph. The immediate consequence is simply a redundant arc that will not do harm; the implication is that the exclusion matrix cannot filter certain arcs that are indirectly dependent on certain forbidden interpretations.</Paragraph>
  </Section>
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