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<Paper uid="C92-1052">
  <Title>Temporal Structure of Discourse*</Title>
  <Section position="4" start_page="0" end_page="0" type="metho">
    <SectionTitle>
3 Discourse Segments
</SectionTitle>
    <Paragraph position="0"> A discourse segment is a discourse object. It is represented by a discourse referent that can be used for later reference. In contrast to other discourse theories, segments ms dynamic structures that help to define context interpretations are considered as real discourse objects. Thus in our approach we use segments as objects with properties that will be defined later. A text is represented by a segment and a segment supplies context information for the semantic interpretation during discourse processing.</Paragraph>
    <Paragraph position="1"> Next segments will be defined as well as their construction and use in the semantic interpretation. null</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
3.1 Kind of segments
</SectionTitle>
      <Paragraph position="0"> We distinguish two kinds of segments: basic and non-basic ones.</Paragraph>
      <Paragraph position="1"> A basic segment represents an eventuality plus some features, typically syntactic ones like tense and aspect (tile leaves of fig. 1).</Paragraph>
      <Paragraph position="2"> A nonbasic segment has one or more subsegments (basic or not) obeying to a set of temporal constraints and a set of features. Every nonbasic segment has a sort depending on the temporal constraints it imposes on its subsegments.</Paragraph>
      <Paragraph position="3"> Segment features are necessary for discourse reasoning. Some of them may be dropped after a closing but others have to remain until the discourse is completely processed. The features we take into account in this paper are the following:  * tense - The feature tense is needed for temporal anaphora resolution.</Paragraph>
      <Paragraph position="4"> * eventuality - The semantic representation of an eventuality is important for temporal anaphora resolution, for causal reasoning and other kinds of reasoning that depend on the kind of the eventuality.</Paragraph>
      <Paragraph position="5"> * eventuality time - This is the main issue ill the definition of a segment as the abducted relation between eventuality times determines tile segment structure's behavior.</Paragraph>
      <Paragraph position="6"> * discourse referents - for solving discourse reference.</Paragraph>
      <Paragraph position="7"> * subsegments - an ordered list containing all its subsegments.</Paragraph>
    </Section>
    <Section position="2" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
3.2 Sorts of segments
</SectionTitle>
      <Paragraph position="0"> Depending on the abducted temporal relation between eventualities in a discourse, the eventualities are grouped into different sorts of segments. Using the above mentioned five temporal relations seven sorts of segments ~ can he de~  fined, e.g.</Paragraph>
      <Paragraph position="1"> 1. basic - the minimal segment.</Paragraph>
      <Paragraph position="2"> 2. none - this segment does not impose any restriction on tile temporal relation of its subsegments. The discourse of example VI will be represented by this sort of segment.</Paragraph>
      <Paragraph position="3"> 3. sequence -- the subsegments in the list of segments are temporally ordered, e.g. ex I (fig. l.a).</Paragraph>
      <Paragraph position="4"> 4. fb - contains only two subsegments with the first one temporally situated after the second one, e.g. ex H (fig. 1.b).</Paragraph>
      <Paragraph position="5"> 5. bk - has two subsegments with the first one temporally contained in tire second one, e.g.ex III.</Paragraph>
      <Paragraph position="6"> 6. elab - has two subsegments with the first one temporally containing the second one, e.g. ex IV.</Paragraph>
      <Paragraph position="7"> 7. over - every segment in the list of subseg- null ments must temporally intersect a nonempty time interval, e.g. ex V.</Paragraph>
      <Paragraph position="8"> For each sort of segment it must be defined how to compute its features representing properties from the features of its aubsegments.</Paragraph>
    </Section>
    <Section position="3" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
3.3 Properties of Segments
</SectionTitle>
      <Paragraph position="0"> Segments that can have a list of subsegments containing an unlimited number of segments are none, sequence sad over. These segments can be augmented during discourse processing. The features of these segments are the following: a none - The feature eventuality contains the set of all subsegments' eventualities, while the 2The nantes of these tmgments ar~ abbreviationt of some rhetorical relatlona that impose the marne temporal cormtralnts. There abreviations should not be read as if they meant the same M the rhetorical relations. They jute mean that their sub~egments obey a particular ternporal relation.</Paragraph>
      <Paragraph position="1">  feature time contains the set of all subsegments' times. The tense feature refers to the tense of the last subsegment.</Paragraph>
      <Paragraph position="2"> * sequence - the feature eventuality is the composition of all the segments' eventualities obtained by the seq operator. The time feature interval is the time interval \[t,,~, t,,s \], where t, h is the initial point of the first segment time interval and t,,s is the final point of the last segment time interval. The tense feature is the tense of the last segment (fig. 1.a). This segment can be augmented by adding a new segment to the list of segments. In this case the features of the sequence segment have to be evaluated again s.</Paragraph>
      <Paragraph position="3"> * over- the feature eventuality is unknown, the feature time is the time interval of the intersection of all time segments. The tense feature is the tense of its last subsegment.</Paragraph>
      <Paragraph position="4"> The segments that have two subsegments are fb, bk, and elab. These segments can only he augmented by the replacement of its second subsegment by a new one obeying the same set of constraints. The replaced segment is the first subsegment of the new one. These segments have the same features of the first subsegment (fig. 1.b for a segment of sort fb).</Paragraph>
    </Section>
    <Section position="4" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
3.4 Discourse Segmentation
</SectionTitle>
      <Paragraph position="0"> Discourse segmentation will be done incrementally. A sentence will be represented by a segment. The processed discourse will be represented by a segment.</Paragraph>
      <Paragraph position="1"> 3A notion similar to the sequence segntent is used in other theorlC/~ for discourse segmentation named in RST \[15\] u &amp;quot;narration&amp;quot;, in Hobba \[9\] also As &amp;quot;narration&amp;quot; and in planning \[10\] as U~quence'.</Paragraph>
      <Paragraph position="2"> The steps for the discourse segmentation are:  1. to obtain the first sentence segment. This segment will be the discourse segment.</Paragraph>
      <Paragraph position="3"> 2. to obtain the segment representing the next discourse sentence.</Paragraph>
      <Paragraph position="4"> 3. to insert the new segment in the discourse segment. This step will have the following substeps: null (a) To compute the set of visible segments (i.e. the right subsegments of the discourse segment) from the discourse segment. This set of segments can be ordered by some discourse preference rule, e.g. we may prefer to continue the current segment or prefer to continue the first opened segment and close the other ones 4 .</Paragraph>
      <Paragraph position="5"> (b) to choose one segment sl from the set of visible segments.</Paragraph>
      <Paragraph position="6"> (c) to add the new sentence segment s2 to segment s I by: * continuing the subsegment list of Sl if s2 can satisfy the constraints of sl.</Paragraph>
      <Paragraph position="7"> * substituting sj by a new one as. sz contains s I as first subsegment and s2 as second subsegment in its subsegnlent list. The sort of segment s3 is one of the 6 nonbasic ones.</Paragraph>
      <Paragraph position="8"> (d) if it is not possible to add the new segment then choose another segment from the set of the visible ones, call it sl and try again going back to step 3c.</Paragraph>
      <Paragraph position="9"> 4. go back to step 2 if there are more sentences to process in the discourse.</Paragraph>
    </Section>
    <Section position="5" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
3.5 Abduction of temporal relations
</SectionTitle>
      <Paragraph position="0"> The main process in discourse segmentation is to check for temporal relations between segments because this is the only criterion used for segmentation. null For deciding how to link segment s2 given seg- null ment sl, do: 1. find the referent for s2.</Paragraph>
      <Paragraph position="1"> * if sl is going to be continued by s2, then the referent will be the last subsegment in the subsegment list of segment Sl.</Paragraph>
      <Paragraph position="2"> * if sl is going to be substituted by a new segment sa then the referent will be Sl.  quenc~ on the discourse segmentation. In caAes where there are more then one possible segmentation preference will be given to the first one.</Paragraph>
      <Paragraph position="3">  ACTF.S DE COLING-92, NANTES, 23-28 ^OfYr 1992 3 3 4 PROC. OF COLING-92, NANTES. AUG. 23.28, 1992 2. After obtaining a referent, abduct the temporal relation between s2 and the referent. 3. After getting the relation between s2 and  the referent, do: * if sl is to be continued by s2 then cheek if s2 satisfies the set of constraints of st. If so, update the st features if needed and repeat the procedure (update features in the parent node and check constraints) until the root segment or a node segment whose features don't need to be updated is reached. If this process terminates successfully then s2 can continue st.</Paragraph>
      <Paragraph position="4"> * if s2 is to be replaced by a new segment sa then compute the features of segment sa and check if the set of temporal constraints of the old parent of segment sl is satisfied. If so, update the old parent st features if needed and repeat the procedure (update features in the parent node and check constraints) until the root or a node segment whose features don't need to be updated is reached. If this process ends sueceasfully then sa can replace st.</Paragraph>
      <Paragraph position="5"> Whenever a temporal entity in the form of a discourse referent is added to the discourse structure, the structure containing all temporal discourse referents as well as their temporal constraints should be updated (fig. 4 for ex. of see. 4). This way we can distinguish relations that are implied by the temporal system from those inferred using other knowledge sources, e.g. the constraints tl &lt; t2, ta &lt; t2 do not imply tl &lt; ta, but satisfy it.</Paragraph>
      <Paragraph position="6"> In order to check for temporal constraints we do not only deal with constraints over temporal intervals but use also world knowledge for abducting relations between eventualities that imply some temporal relation between them. In order to abduct a temporal relation it is not enough to block inconsistencies in the temporal system. There should also be some kind of justification, like: * temporal - if the temporal system implies relation t0,@t,~ there is a justification to abduct tot@t,~, with @ being a temporal relation.</Paragraph>
      <Paragraph position="7"> * causal - if et can cause e2 then there is a justification to abduct t~ &lt; t~.</Paragraph>
      <Paragraph position="8"> * contingent - Assuming an event ontology like that of Moens and Steedman \[17\] where eventualities have a tripartite structure with a preparatory phase, a culmination and a consequence state there are clauses stating what are the eventualities of the preparatory phase and those of the consequence state of an eventuality. - if el can be in the preparatory phase of e2 there is a justification to abduct t~ C re2.</Paragraph>
      <Paragraph position="9"> - if el can be in the consequence state of e2 there is a justification to abduct tet &gt; re2.</Paragraph>
      <Paragraph position="10"> * particular shared knowledge about eventualities - having a temporal knowledge base concerning eventualities, general rules for eventualtries can be stated, e.g. John usually drinks a cup of coffee before he catches the bus.</Paragraph>
      <Paragraph position="11"> - if e2 usually happens ~ et with ~ being a temporal relation, then there exists justification to assume te,t~tea.</Paragraph>
      <Paragraph position="12"> * Linguistic- verb tense and aspectual perspective (AP) are the linguistic features ~ that contribute to the temporal anchorage of eventualities. There are rules that justify a temporal relation taking into account these features and the order of the sentences. They should be used as default rules, i.e. if it can not be found anotber justification for a temporal anchoring then a linguistic justification should be used. The following rules are used in the detailed example. if tense of el and of e2 is simple past (SP) with perfective AP tben there is justification for assuming t~ &lt; re2.</Paragraph>
      <Paragraph position="13"> - if tense of el is SP with perfective AP and tense of e2 is SP with imperfeetive AP there exists justification to assume tea C it2.</Paragraph>
      <Paragraph position="14"> If a justification for the abduction of a particular temporal relation is not a logical consequence of the knowledge base then the justification sbould be added to the set of conditions. e.g. if we abduct in the discourse &amp;quot;John fell from the balcony. Mary pushed hzm.&amp;quot; that John fell because Mary had pushed him, we should add the clause &amp;quot;eause(et, e2)&amp;quot; in order to block the future inference tbat Mary was innocent in John's fall. In this example another interpretation, linguistically justified, could be t~l~t I &lt; t~pu,h s.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="0" end_page="0" type="metho">
    <SectionTitle>
4 Detailed Example
</SectionTitle>
    <Paragraph position="0"> Consider the following discourse represented by the segment in fig. 3.</Paragraph>
    <Paragraph position="1"> Last month I boughl a house (sl). It had an aquartum (s~). Mary offered me a red fish (sa). John gave me his frog (st). My fish died yesterday (ss). It stopped breathing (,~). It became blue (st). It went to the top of the aquarium (*s). SThese features may restrict the act of possible temporal relatiorta between two eventualities.</Paragraph>
    <Paragraph position="2"> 8When there are more then one poulhle temporal relation a system mult ch~e one, but it ehould be able  after processing sentence st. The only way to incorporate the sentence s2's segment is by replacing the current discourse structure by a new one (basic segments cannot be continued). Sl is the reference to anchor s2, the eventuality of s~ is a state, so the relation t~t C t,~ is abducted and the new segment is of sort bk (fig. 2.b).</Paragraph>
    <Paragraph position="3"> To insert Sa there are two visible segments: s2 and bk. Segment bk is the reference for sa because the eventuality of segment s2 is a state with an imperfective aspectnal perspective and there is no general knowledge about the eventualities of s2 and sa allowing us to abduct a temporal relation between them. The features of the bk segment are the same as those of sl, so the abducted relation between those segments is t,~ &lt; G~, so that the discourse structure is replaced by a new segment of sort sequence (fig.</Paragraph>
    <Paragraph position="4"> 2.c). To insert segment s4 there are two visible segments, namely s3 and sequence. Using sa as reference, no temporal relation can be abducted.</Paragraph>
    <Paragraph position="5"> Thus none is abducted using some general rule saying &amp;quot;eventualities to give and ~o offer are of to backtrack to that choice point.</Paragraph>
    <Paragraph position="6">  the same kind and if the subjects and objects are different and the recipient is the same it is not poesible to abduct a temporal relation between them&amp;quot;. So the segment s3 is replaced by a new segment of sort none (fig. 2.d) after the check to see if it is possible to abduct the relation t,b k &lt; t,, in order to satisfy the constraints of the sequence segment. The time of segment s5 is partially anchored in the time interval &amp;quot;yesterday&amp;quot; but it still must be anchored to a reference. Visible segments are s4, none and sequence. Considering that the abducted relation between s4 and s5 is t,4 &lt; ~,~ and between s3 and s~ is t,a &lt;: t, 8 it is not possible to use s4 as referent because the constraints of segment none were not satisfied. So the sequence segment is the only one left and it can be continued by s5 (fig. 2.e) because its constraints are satisfied, thus te~ &lt; tss,t,. &lt; t. s are abducted. In order to insert s6, the visible segments are ss and sequence. Using s5 as referent, the relation t,, C 6, is abducted because stop breathing is in the preparatory phase of dying. Segment s5 is replaced by a new segment of sort elab (fig.</Paragraph>
    <Paragraph position="7"> 2.f). In order to insert segment sT, segment s6 is replaced by a new sequence segment because the relation t,~ &lt; t, 7 is abducted (becoming blue is in the consequence state of stop breathing) and t, T C t,~ is abducted (becoming blue is in the preparatory ph~e of dying) (fig. 2.g). The insertion of ss leads to the final structure (fig. 3). ss cannot use s7 as reference because the relation t,. C t,~ cannot be abducted.</Paragraph>
    <Paragraph position="8"> After processing the discourse, the temporal discourse referents and their relations reflect the structure of fig. 4, containing all the temporal relations that can be inferred from the text without making unjustified abductions.</Paragraph>
  </Section>
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