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<Paper uid="E95-1035">
  <Title>Algorithms for Analysing the Temporal Structure of Discourse*t</Title>
  <Section position="4" start_page="0" end_page="256" type="metho">
    <SectionTitle>
2 Constraints on narrative
</SectionTitle>
    <Paragraph position="0"> continuations Probably the best known algorithm for tracking narrative progression is that developed by Kamp (1979), Hinrichs (1981), and Partee (1984), which formalises the observation that an event will occur just after a preceding event, while a state will overlap with a preceding event. This algorithm gives the correct results in examples such as the following:  (1) John entered the room. Mary stood up.</Paragraph>
    <Paragraph position="1"> (2) John entered the room. Mary was  seated behind the desk.</Paragraph>
    <Paragraph position="2"> In (1) the event of Mary's standing is understood to occur just after John enters the room, while in (2) the state in which Mary is seated is understood to overlap with the event of John's entering the room.</Paragraph>
    <Paragraph position="3"> However, if there is a rhetorical relationship between two eventualities such as causation, elaboration or enablement, the temporal defaults can be overridden, as in the following examples:  (3) a. John fell. Mary pushed him.</Paragraph>
    <Paragraph position="4"> b. Local builders constructed the Ford  St. Bridge. They used 3 tons of bricks.</Paragraph>
    <Paragraph position="5"> In (3a) there is a causal relationship between Mary's pushing John and his falling, and the second event is understood to precede the first. In (3b), the second sentence is an elaboration of the first, and they therefore refer to aspects of the same event rather than to two sequential events.</Paragraph>
    <Paragraph position="6"> It has been suggested that only world knowledge allows one to detect that the default is being overridden here. For example, Lascarides Asher (1991) suggest that general knowledge postulates (in the case of (3a): that a pushing can cause a falling) can be invoked to generate the backward movement reading.</Paragraph>
    <Paragraph position="7"> The problem for practical systems is twofold: we could assume that in the case of narrative the Kamp/Hinrichs/Partee algorithm is the default, but each time the default is applied we would need to check all our available world knowledge to see whether there isn't a world knowledge postulate which might be overriding this assumption. Clearly this would make the processing of text a very expensive operation. An alternative is to assume that the temporal ordering between events in two consecutive sentences can be any of the four possibilities (just_after, precede, same-event and overlap). But then the resulting temporal structures will be highly ambiguous even in small discourses. And sometimes this ambiguity is unwarranted. Consider: (4) Mary stared at John. He gave her back her slice of pizza.</Paragraph>
    <Paragraph position="8"> Here, it would appear, only one reading is possible, i.e. the one where John gave Mary her slice of pizza just after she stared or started to stare at him. It would be undesirable for the temporal processing mechanism to postulate an ambiguity in this case.</Paragraph>
    <Paragraph position="9"> Of course, sometimes it is possible to take advantage of certain cue words which either indicate or constrain the rhetorical relation. For example, in (5) the order of the events is understood to be the reverse of that in (1) due to the cue word because which signals a causal relationship between the events: (5) John entered the room because Mary stood up.</Paragraph>
    <Paragraph position="10"> As Kehler (1994) points out, if forward movement of time is considered a default with consecutive event sentences, then the use of &amp;quot;because&amp;quot; in (5) should cause a temporal clash-whereas it is perfectly felicitous. Temporal expressions such as at noon and the previous Thursday can have a similar effect: they too can override the default temporal relations and place constraints on tense. In (6), for example, the default interpretation would be that John's being in Detroit overlaps with his being in Boston, but the phrase the previous Thursday overrides this, giving the interpretation that John's being in Detroit precedes his being in Boston: (6) John was in Boston. The previous Thursday he was in Detroit.</Paragraph>
    <Paragraph position="11"> This suggests that the temporal information given by tense acts as a weaker constraint on temporal structure than the information given by temporal adverbials.</Paragraph>
    <Paragraph position="12"> The possibilities for rhetorical relations (e.g., whether something is narration, or elaboration, or a causal relation) can be further constrained by aspect. For example, a state can elaborate another state or an event: (7) a. Mary was tired. She was exhausted.</Paragraph>
    <Paragraph position="13"> b. Mary built a dog house. It was a labour of love.</Paragraph>
    <Paragraph position="14"> But an event can only elaborate another event, as in (8):</Paragraph>
    <Section position="1" start_page="254" end_page="256" type="sub_section">
      <SectionTitle>
Sl Relation Example
</SectionTitle>
      <Paragraph position="0"> just-after $1 Mary pushed John. He fell.</Paragraph>
      <Paragraph position="1"> past event precede Sx John fell. Mary pushed him.  overlap $1 NO same-event $1 I assembled the desk myself. The drawers only took me ten minutes.</Paragraph>
      <Paragraph position="2"> just-after S1 Mary stared at John. He gave her back her slice of pizza. past activity precede $1 NO overlap $1 NO same-event S~ NO past state past perf event past perf activity past perf state</Paragraph>
      <Paragraph position="4"> ?John fell. He was in pain. Mary pushed him.</Paragraph>
      <Paragraph position="5"> Mary was angry. She pushed John.</Paragraph>
      <Paragraph position="7"> I assembled the desk myself. It was beautiful. The drawers only took me ten minutes.</Paragraph>
      <Paragraph position="8"> Sam had arrived at the house. He rang the bell.</Paragraph>
      <Paragraph position="9"> Sam arrived at the house. He had lost the key. He rang the bell. NO I had assembled the desk myself. The drawers only took me ten minutes.</Paragraph>
      <Paragraph position="10"> Mary had stared at John. He gave her back her sfice of pizza.</Paragraph>
      <Paragraph position="12"> Martha discovered the broken lock. Someone had been in the garage. They rearranged the, tools.</Paragraph>
      <Paragraph position="14"> Martha discovered the broken lock. Someone had been in the garage. They rearranged the tools,</Paragraph>
      <Paragraph position="16"> Mary built the desk herself. She had been happy taking it on.</Paragraph>
      <Paragraph position="17"> The drawers only todk her ten minutes.</Paragraph>
      <Paragraph position="18">  (8) a. Mary built a dog house. She used two tons of bricks.</Paragraph>
      <Paragraph position="19"> b. Mary was tired/working hard. ?She  built a dog house.</Paragraph>
      <Paragraph position="20"> For the eventive second sentence of (8b) to be an elaboration of the first sentence, it must occur in a stative form--for example as a progressive (i.e., She was building a dog house). Because of considerations like these, our aim in the implementation work was to treat tense, aspect, cue words and rhetorical relations as mutually constraining, with more specific information such as explicit cue words having higher priority than less specific information such as tense. The main advantage of this approach is that it reduces temporal structure ambiguity without having to rely on detailed world knowledge postulates.</Paragraph>
      <Paragraph position="21"> Table 1 lists the possible temporal relations between the eventualities described by two consecutive sentences without temporal expressions or cue words, where the first sentence (S1) may have any tense and aspect and the second sentence (S~) expresses a simple past event. We constrain $2 in this way because of lack of space; additional constraints are given in (Hitzeman et al., 1994). For example, if a simple past eventive sentence follows a simple past eventive sentence the second event can be understood to occur just after the first, to precede the first or to refer to the same event as the first (an elaboration relation), but the two events cannot overlap; these constraints  are weaker, however, than explicit clues such as cue words to rhetorical relations and temporal expressions. When $1 expresses a state, it is possible for the temporal relation to hold between the event described by $2 and the event or activity most closely preceding $1, i.e., the temporal focus of $1, here referred to as TF1.1 However, we haven't solved the problem completely at this point: although tense can provide a further constraint on the temporal structure of such discourses, it can also add a further ambiguity. Consider (9): (9) Sam rang the bell. He had lost the key.</Paragraph>
      <Paragraph position="22"> Clearly, the event described by the past perfect sentence must precede the event described by the first, simple past sentence. However, if a third sentence is added, an ambiguity results. Consider the following possible continuations  of (9): (10) a .... Hannah opened the door.</Paragraph>
      <Paragraph position="23"> b .... It fell through a hole in his pocket.</Paragraph>
      <Paragraph position="24">  The temporal relation between these continuations and the portion of earlier text they attach to is constrained along the lines sketched before. The problem here is determining which thread in (9) they continue; (10a) continues the thread in which Sam rings the bell, but (10b) continues the thread in which Sam loses the key.</Paragraph>
      <Paragraph position="25"> A further ambiguity is that when the third sentence is past perfect, it may be a continuation of a preceding thread or the start of a new  thread itself. Consider: (11) a. Sam rang the bell. He had lost the key. It had fallen through a hole in his pocket.</Paragraph>
      <Paragraph position="26"> b. John got to work late. He had left the house at 8. He had eaten a big breakfast.</Paragraph>
      <Paragraph position="27"> In (a) the third sentence continues the thread about losing the key; in (b) the third starts a 1 In this chart it appears that whether the tense is simple past or past perfect makes no difference,  and that only aspect affects the possible temporal relations between $1 and $2. However, it is important not to ignore tense because other combinations of tense and aspect do show that tense affects which relations are possible, e.g., a simple past stative $2 cannot have a precede relation with any $1, while a past perfect stative $2 can. new thread. 2 For the problem with multi-sentence discourses, and the &amp;quot;threads&amp;quot; that sentences continue, we use an implementation of temporM centering (Kameyama et al., 1993; Poesio, 1994). This is a technique similar to the type of centering used for nominal anaphora (Sidner, 1983; Grosz et al., 1983). Centering assumes that discourse understanding requires some notion of &amp;quot;aboutness.&amp;quot; While nominal centering assumes there is one object that the current discourse is &amp;quot;about,&amp;quot; temporal centering assumes that there is one thread that the discourse is currently following, and that, in addition to tense and aspect constraints, there is a preference for a new utterance to continue a thread which has a parallel tense or which is semantically related to it and a preference to continue the current thread rather than switching to another thread. Kameyama et al. (1993) confirmed these preferences when testing their ideas on the Brown corpus.</Paragraph>
      <Paragraph position="28"> As an example of how the temporal centering preference techniques can reduce ambiguity, recall example (9) and the possible continuations shown in (10). The difficulty in these examples is determining whether the third sentence continues the thread begun by the first or second sentence. For example, in (10a) the preference technique which allows us to choose the first thread over the second is one which assigns a higher rating to a thread whose tense is parallel to that of the new sentence; in this case both Sam rang the bell and Hannah opened the door are in the simple past tense. In example (10b) the fact that the key is mentioned only in the second sentence of (9) links (10b) with the second thread. To handle an example like (12), we employ a preference for relating a sentence to a thread that has content words that are rated as semantically &amp;quot;close&amp;quot; to that of the sentence: (12) Sam rang the bell. He had lost the key.</Paragraph>
      <Paragraph position="29"> His keyring b~okeJ We store semantic patterns between words as a cheap and quick form of world knowledge; these 2We will not discuss the additional problem that if the final sentence in (llb) is the end of the text, the text is probably ill-formed. This is because a well-formed text should not leave threads &amp;quot;dangling&amp;quot; or unfinished. This is probably also the reason for the awkwardness of the well-known example Max poured a cup of coffee. He had entered the roo~'l.</Paragraph>
      <Paragraph position="30">  patterns are easier to provide than are the detailed world knowledge postulates required in some other approaches, and result in similar and sometimes more precise temporal structures with less processing overhead. Using the semantic patterns we know that key and keyring are semantically close, and through that semantic link between the second and third sentences we prefer to connect the third sentence to the thread begun by the second. 3 The approach to representing semantic relationships we take is one used by Morris &amp;: Hirst (1991) wherein the words in the lexicon are associated with each other in a thesaurus-like fashion and given a rating according to how semantically &amp;quot;close&amp;quot; they are. We thus avoid relying on high-level inferences and very specific world knowledge postulates, our goal being to determine the temporal structure as much as possible prior to the application of higher-level inferences.</Paragraph>
      <Paragraph position="31"> those in previous threads, in order to rate the semantic &amp;quot;closeness&amp;quot; of the DCU to each thread.</Paragraph>
      <Paragraph position="32"> SEM_ASPECT: Contains the semantic aspect (event, state, activity). We have extended the Penn &amp; Carpenter implementation of the HPSG grammar so that semantic aspect is calculated compositionally (and stored here).</Paragraph>
      <Paragraph position="33"> RHET_RELN: The relation between this DCU and a previous one. Lexical items and phrases such as cue words (stored in CUE_WORD) affect the value of this slot.</Paragraph>
      <Paragraph position="34"> TEMP_CENTER: Used for temporal centering; Keeps track of the thread currently being followed (since there is a preference for continuing the current thread) and all the threads that have been constructed so far in the discourse.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="256" end_page="257" type="metho">
    <SectionTitle>
3 An HPSG implementation of a
</SectionTitle>
    <Paragraph position="0"> discourse grammar Following Scha ~ Polanyi (1988) and Priist et al (1994), our model of discourse consists of units called Discourse Constituent Units (ecus) which are related by various temporal and rhetorical relations. A basic DCU represents a sentence (or clause), and complex DCUs are built up from basic and complex DCUs.</Paragraph>
    <Paragraph position="1"> In our ALE implementation, a DCU contains the following slots for temporal information: FWD_CENTER: Existing threads BKWD_CENTER: The thread currently being followed CLOSED_THREADS: Threads no longer available for continuation TEMP..EXPR_RELNS: Stores the semantic interpretation of temporal expressions associated with this DCU.</Paragraph>
    <Paragraph position="2"> TEMP-RELNS: Stores the temporal relations between the eventualities in the discourse. CUE_WORD: Cues to rhetorical structure, e.g., &amp;quot;because.&amp;quot; V_AND_NP_LIST: Contains content words found in this DcU, and is used to compare the content words of the current DCU with 3Semantic closeness ratings won't help in examples (9) - (10) because there is as strong~a relationship between door and bell as there is between door and key.</Paragraph>
    <Paragraph position="3"> TEMPFOC: The most recent event in the current thread which a subsequent eventuality may elaborate upon (same-event), overlap, come just_after or precede.</Paragraph>
    <Paragraph position="4"> TENASP: Keeps track of the tense and syntactic aspect of the DCU (if the DCU is simple).</Paragraph>
    <Paragraph position="5"> TENSE: past, pres, fut ASPECT: simple, perf, prog, perf_prog  To allow the above-mentioned types of information to mutually constrain each other, we employ a hierarchy of rhetorical and temporal relations (illustrated in Figure 1), using the ALE system in such a way that clues such as tense and cue words work together to reduce the number of possible temporal structures. This approach improves upon earlier work on discourse structure such as (Lascarides and Asher, 1991) and (Kehler, 1994) in reducing the number of possible ambiguities; it is also more precise than the Kamp/Hinrichs/Partee approach in that it takes into account ways in which the apparent defaults can be overridden and differentiates between events and activities, which behave differently in narrative progression.</Paragraph>
    <Paragraph position="6"> Tense, aspect, rhetorical relations and temporal expressions affect the value of the RHET..RELN type that expresses the relationship between two I)CVs: cue words are lexicMly marked according to what rhetorical relation they specify, and this rel.ation is passed on to the DCU. Explicit relation markers such as cue words and temporal relations must be consistent and take priority over indicators such as tense and aspect. For example, sentence (13) will be ruled out because the cue phrase as a result conflicts with the temporal expression ten minutes earlier: (13) #Mary pushed John and as a result ten minutes earlier he fell.</Paragraph>
    <Paragraph position="7"> On the other hand, if temporal expressions indicate an overlap relation and cue words indicate a background relation as in (14), these contributions are consistent and the KHET_R.ELN type will contain a background value (the more specific value of the two): (14) Superman stopped the train just in time. Meanwhile, Jimmy Olsen was in trouble.</Paragraph>
  </Section>
  <Section position="6" start_page="257" end_page="258" type="metho">
    <SectionTitle>
4 The algorithm
</SectionTitle>
    <Paragraph position="0"> For reasons of space it is difficult to give examples of the sign-based output of the grammar, or of the ALE rules, so we will restrict ourselves here to a summary of the algorithm and to a very limited rendition of the system output. The Mgorithm used for calculating the temporal structure of a discourse can be summarised as follows. It consists of two parts, the  constraint-based portion and the preference-based portion: 1. The possible temporal/rhetorical relations are constrained.</Paragraph>
    <Paragraph position="1"> (a) If there is a temporal expression, it determines the temporal relationship of the new DCU to the previous ones, and defaults are ignored.</Paragraph>
    <Paragraph position="2"> (b) Lexical items such as cue words influence the value of the RHET~ELN type (See Figure 1).</Paragraph>
    <Paragraph position="3"> (c)-If steps (a) and (b) attempt to place conflicting vMues in the I~HET_RELN slot, the parse will fail.</Paragraph>
    <Paragraph position="4"> (d) If there is no temporal expression or cue phrase, tense and semantic aspect also influence the vMue of the I~HET..RELN type (See Table 1), so that rhetorical relations, tense and aspect constrain each other.</Paragraph>
    <Paragraph position="5"> 2. If more than one possibility exists, semantic preferences are used to choose between the possibilities.</Paragraph>
    <Paragraph position="6"> (a) A &amp;quot;semantic distance&amp;quot; rating between the new DCU and each previous thread is determined. (If there are no existing threads a new thread is started.) (b) Other preferences, such as a prefer- null ence for relating the new DCU to a thread with parallel tense, are employed (See (Kameyama et al., 1993; Poesio, 1994) for details), and the resulting ratings are factored into the rating for each thread.</Paragraph>
    <Paragraph position="7"> (c) If the thread currently being followed is among the highest rated threads, this thread is continued. (This corresponds to temporal centering's preference to continue the current thread.) (d) If not, the DCU may continue any of the highest rated threads, and each of these solutions is generated.</Paragraph>
    <Paragraph position="8"> Charts such as Table 1 provide the observations we use to fill in the vMue of I~HET_RELN. Those observations are summarised below. In what follows, the event variable associated with DCOi is e~ and the TEMPFOC of el is the most recent event/activity processed, possibly el itself: null  * e2 can overlap with el if -- DCU 2 describes a state, or - DCU1 describes a state and DCU2 describes an activity.</Paragraph>
    <Paragraph position="9"> * e2 can occur just-after the TEMPFOC of el if -- DCU2 describes a simple tense event, or - DCU1 describes a complex tense clause and DCU2 describes a complex tense event, or - DCU1 describes an event and DCU2 describes an atelic or a simple tense state, or - DCU1 describes a state and DCU2 describes a simple tense activity.</Paragraph>
    <Paragraph position="10">  either DCU2 describes a simple tense state or DCU1 describes a complex tense state.</Paragraph>
    <Paragraph position="11"> Using this algorithm, we can precisely identify the rhetorical and temporal relations when cue words to rhetorical structure are present, as in (15): (15) John fell (el) because Mary pushed him TEMP-RELNS: e 2 precedes el We can also narrow the possibilities when no cue word is present by using constraints based on observations of tense and aspect interactions such as those shown in Table 1. For example, if DCU1 represents a simple past eventive sentence and DCU2 a past perfect eventive sentence, then in spite of the lack of rhetorical cues we know that e2 precedes el, as in (16): (16) Sam rang the doorbell (el). He had lost the key (e2).</Paragraph>
    <Paragraph position="12"> TEMP-RELNS: e2 precedes el Also, when several structures are possible we can narrow the possibilities by using preferences, as in the examples below: (17) Sam arrived at the house at eight (el). He had lost the key (e~).</Paragraph>
    <Paragraph position="13"> a .... He rang the bell (e3).</Paragraph>
    <Paragraph position="14"> TEMP-RELNS: e2 precedes el, e3 just-after el b .... It fell through a hole in his pocket (e~,).</Paragraph>
    <Paragraph position="15"> TEMP_RELNS: e 2 precedes el, e3, just-after e2 If we allow any of the four possible temporal relations between events, both continuations of sentence (17) would have 17 readings (4 x 4 + 1 reading in which the third sentence begins a new thread). Using constraints, we reduce the number of readings to 4. Using preferences, we reduce that to 2 readings for each continuation. The correct temporal relations are shown in (17). 4</Paragraph>
  </Section>
  <Section position="7" start_page="258" end_page="258" type="metho">
    <SectionTitle>
5 An underspecified
</SectionTitle>
    <Paragraph position="0"> representation By using constraints and preferences, we can considerably reduce the amount of ambiguity in the temporal/rhetorical structure of a discourse. However, explicit cues to rhetorical and temporal relations are not always available, and these cases result in more ambiguity than is desirable when processing large discourses.</Paragraph>
    <Paragraph position="1"> Consider, however, that instead of generating all the possible temporM/rhetorical structures, we could use the information available to fill in the most restrictive type possible in the type hierarchy of temporal/rhetorical relations shown in Figure 1. We can then avoid generating the structures until higher-level information can be applied to complete the disambiguation process.</Paragraph>
  </Section>
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