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<Paper uid="C96-2196">
  <Title>Parsing Plans Situation-Dependently in Dialogues</Title>
  <Section position="4" start_page="0" end_page="1094" type="metho">
    <SectionTitle>
2 Requirements for Treating
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
Effects and Preconditions
</SectionTitle>
      <Paragraph position="0"> Let us examine typical situations where the effects and preconditions of actions must be treated.</Paragraph>
    </Section>
    <Section position="2" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
2.1 Effect-Based Action Descriptions
</SectionTitle>
      <Paragraph position="0"> In describing plan recipes, it is convenient to specify an action in terms of its effects ms follows: Recipe 1 Action: informref(S, H, Term, Prop) Decomposition: achieve(bel(H, P)) Effects: belref(H, Term, Prop) Constraints: parameter(Term, Prop) A description of the form 'achieve(P)' specifies the action for achieving the state where the proposition P holds. This recipe thus says that an informref action can be performed by an action that has 'bel(H, P)' as its effect. There may be many such actions. Furthermore, the action specified by 'achieve(P)' depends on the situation where P is about to be achieved. In the extreme case, ifP already holds, the agent need not do anything. For example, a speaker may not perform any action to make a hearer believe a proposition if the speaker believes the hearer already believes it. If we are not permitted to use this form, we must enumerate all the actions that achieve P together with the conditions under which they do. Treating this form requires calculating the effects of actions.</Paragraph>
    </Section>
    <Section position="3" start_page="0" end_page="1094" type="sub_section">
      <SectionTitle>
2.2 Action-Enabling
</SectionTitle>
      <Paragraph position="0"> Given a goal, a planning procedure searches for an action to achieve the goal (a main action). If the procedure identifies such an action with preconditions, it calls itself recursively to search for actions  that satisfy them (enabling actions of tile main action), and then provides the action sequence consisting of the main action preceded by its enabling actions. Given an action sequence of this form, a plan recognition procedure must thus regard it as I)erforming a main action to achieve its ettb.ct(s).</Paragraph>
      <Paragraph position="1"> There are many kinds of dialogue phenomena that can be captured by such action-enabling relationships. Understanding snch dialogue phenomena reqnires handling effects and preconditions.</Paragraph>
    </Section>
    <Section position="4" start_page="1094" end_page="1094" type="sub_section">
      <SectionTitle>
2.3 State-Dependent Interi)retation
</SectionTitle>
      <Paragraph position="0"> There are cases where state-dependent interpretation is iml)ossible unless the effects and preconditions of actions are treated. Consider, for example, the folh)wing dialogue fragment: A: Please tell Ine how to go to the Laboratories.</Paragraph>
      <Paragraph position="1"> B: Take the bus to Tokyo.</Paragraph>
      <Paragraph position="2"> Whereas an imperative sentence (with surface speech act type surface_request) is generally interpreted as a request, the second utterance actually describes a step in tile plan to go to the Laboratories because the first utterance convinces B that A wants to have that plan. This latter interpretation can be captured by using the heuristic rule for seh;cting an interpretation with fewer unsatisfied preconditions and the following recipe: Recipe 2 Action: describe_step(S, H, Action, Plan) Preconditions: bel(S, want(H, Plan)) Decomposition: surface_request(S, It, Action) Constraints: stei)(Aetion , Plan) This interpretation would be possible instead by using a recipe whose decomposition Mso contains the action of making B believe A's want. However, such a recipe can handle only cases where the belief has been established by the action just before surface_request.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="1094" end_page="1095" type="metho">
    <SectionTitle>
3 Effects and Preconditions
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="1094" end_page="1094" type="sub_section">
      <SectionTitle>
3.1 Effects of Actions
</SectionTitle>
      <Paragraph position="0"> The efl&gt;cts of a linguistic action in a dialogue mainly I)roducc unobservable mental state changes of the diMogne participants. For a computer to participate in a dialogue like people do, it must simulate such mental state changes.</Paragraph>
      <Paragraph position="1"> The clthcts of an action are the propositions tlmt hold after the action's successfltl execution.</Paragraph>
      <Paragraph position="2"> The effects are taken to be cah:nlated recursively</Paragraph>
      <Paragraph position="4"> fl'om tile action's recipe and component actions if any: the effects are essentially those specified by the action's recipe, plus those of component actions. Since an action is modeled to have a certain tenq)oral extent, an action's effect is inodeled to hohl at the point in time where the action has just finished and to continue, to persist infinitely or until the first instance that a contradictory fact holds. An effect of an a(:tion's component action also holds in the same way. Therefore, an action ~ with (71,-..,%) as its component actions has component action 7{'s effect ~oi as its own ef-R'~ct if there is no component action 3'3 after 3'/ with an e\[fect 99j contradictory to ~oi written as contradicts(~,i, ~j)- and does not if such &amp;quot;~i exists as in Figure 1.</Paragraph>
    </Section>
    <Section position="2" start_page="1094" end_page="1095" type="sub_section">
      <SectionTitle>
a.2 Preconditions of Actions
</SectionTitle>
      <Paragraph position="0"> Tile preconditions of an action are tile proi)osi(ions that must hold before the action's successful execution. Recognizing an action thus requires that its preconditions can be ~msured or at letust hypothesized to be believed by the agent.</Paragraph>
      <Paragraph position="1"> The preconditions of an action are essentiMly taken to consists of those specified by the ac~ tion's recipe and those of its component actions if atty. A component action's precondition, however, can be satisfied by another component action's effect. Consider action a with its component actions (%,...,%~), as shown in Fignre 2. Let us focus on precondition '~b/~ of action %. When the.re is an action 7j before % such that its ef~ fect q0j is identical to '~bk as in Case (a) in the figure, &amp;quot;~b k is satisfied by ~oj, so *Pk need not hoht at (~'s starting time. That is, ~ does not have ~/J/~ as its precondition. On the contrary, when there is an action ~i before % such that its effect q0i contradicts ~/;k, ~bk's hohting at a's starting time cannot contribute to the satisfaction of %'s pre- null condition */;k- If there exists an action 7j between 7i and % with its effect qoj identical to ~bk, ~/Jk can be satistied \[Case (b)\]. Otherwise, *Pk emmot be satisfied \[Case (c)\], so a cannot be successflflly ex-ecuted and shonht not be recognized. This kind of  interference is hereafter called 'effect-precondition  (E-P) conflict.' There is another kind of interference called 'precondition-precondition (P-P) conflict:' if a precondition specified by ~'s recipe, or a precondition C/i of any other component action 7i contradicts Ck, they cannot hold simultaneously at c~'s starting time \[Case (d)\]. In such a case, should not be recognized.</Paragraph>
    </Section>
  </Section>
  <Section position="6" start_page="1095" end_page="1096" type="metho">
    <SectionTitle>
4 Active Chart Plan Parsing
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="1095" end_page="1095" type="sub_section">
      <SectionTitle>
4.1 Decomposition Grammar
</SectionTitle>
      <Paragraph position="0"> The relationship between an action and its decomposition specified by a recipe can be viewed as a phrase structure rule. The decomposition relationship specified by Recipe 2, for example, can be view as describeostep(S, H, Action, Plan) surface_request(S, H, Action).</Paragraph>
      <Paragraph position="1"> This interpretation of the decomposition relationships specified by recipes in a plan library gives us a decomt)osition grammar and allows us to apply syntactic parsing techniques to plan recognition. Based on this idea, we constructed a plan parsing method that handles the effects and precondi= tions of actions. Hereafter, we focus on bottom-up active chart parsing, although the core of the discussion below can be applied to other parsing methods.</Paragraph>
    </Section>
    <Section position="2" start_page="1095" end_page="1095" type="sub_section">
      <SectionTitle>
4.2 Calculating Effects and Preconditions
Time Map Management
</SectionTitle>
      <Paragraph position="0"> Time map management is used to capture the temporal state changes caused by the effects of actions. A time map consists of a set of (potential) fact tokens) A fact token is a triple (tl,t2,~o), where tl and t2 are time points and ~ is a timeless fact description (a term), that represents the proposition that ~ holds at tl and continues to persist through t2 or until a contradictory fact holds. As a time point, we use a vertex in a chart, which is an integer. As a special case, time point T is used to represent unbounded persistence. An effect ~ of action finishing at t is represented by a fact token (t, T, ~o}.</Paragraph>
      <Paragraph position="1"> A time map with a set ~&amp;quot; of fact tokens supports queries about whether it guarantees that a fact ~ holds over an interval \[t~, t2\] (written as tm_holds((h,t2, ~),~-)). i fact ~ is guaranteed to hold over an interval \[tl, t2\] exactly if there is an intervalrt' gl such that (t~ &lt;tl &lt;t2 &lt;t~)A L1, 21 -- -- -(t~,t~,qo) e ~&amp;quot; an d if there is no (ta,t4, v') 6 ~&amp;quot; such that contradicts(~0,~0') A (t~ &lt; ta _&lt; t2).</Paragraph>
      <Paragraph position="2"> A precondition C/ of an action can be represented by a triple similar to a fact token. Since it must be satisfied at the action's starting time t, it is represented by (t, t, C/).</Paragraph>
    </Section>
    <Section position="3" start_page="1095" end_page="1095" type="sub_section">
      <SectionTitle>
Data Structures
</SectionTitle>
      <Paragraph position="0"> In our chart parsing, an action is represented by an edge. Since information on the effects and pre-conditions of the action represented by an edge must be kept locally, we use the edge structure shown in Figure 3. An edge's start and end values are vertices that are the respective integers representing the starting and ending time points of (the part of) the action represented by the edge. The action and rsubactions (remaining subaetions) values are respectively an action description and a sequence of descriptions of actions to find in order to recognize the action. An edge is called active if its rsubaetions vahm is a non-empty sequence and is inactive otherwise. The constraints value is a set of constraints on variable instantiation.</Paragraph>
      <Paragraph position="1"> The effects and preconditions values respectively are sets of triples representing the action's effects and preconditions. The aend (action end) value is a variable used as the placeholder of the action's ending time point. The ending time of the action represented by an active edge is not determined yet, and neither is the starting point of the effects specified by the action's recipe. To keep information on those effects in the edge, fact tokens with the aend value as their starting time points are used. An unbound time point variable is taken to be greater than any integer and to be less than T.</Paragraph>
      <Paragraph position="2"> An edge's aend value is bound to its end value if it is inactive. Given an edge e and its field field, field(e) denotes the value of field in e.</Paragraph>
    </Section>
    <Section position="4" start_page="1095" end_page="1096" type="sub_section">
      <SectionTitle>
Chart Procedures
</SectionTitle>
      <Paragraph position="0"> Given an observed action, chart parsing applies the following procedure: Procedure 1 Let ~j be the description of the j-th observed action. For each recipe with action ~r, and for each most general unifier 0 of ~j and C~r satisfying the constraints Cr specified by the recipe, create an inactive edge from j - 1 to j such that its action, constraints, effects, and preconditions values respectively are a j0, CrO, {(j, T, ~T0)I~T e E~}, and {(j-1,j-1, C/~0} IC/,&amp;quot; E Pr}, where Er and Pr are the effects and preconditions specified by the recipe.</Paragraph>
      <Paragraph position="1"> Chart parsing proceeds using the following two procedures.</Paragraph>
      <Paragraph position="2">  l'rocedure 2 Let ei be an inactive edge. For each recipe with its a.ction a,., decomposition (71,.-.,%), effects Er, and preconditions P,, and for each most general unifier 0, satisfying constraints(ei) and recipe's constrains C,., of action@i) and 71 such that</Paragraph>
      <Paragraph position="4"> ~tm_holds((t, t, C/), g)} U{(start(ei), start(ed,GO) l G c/',.}, without E-P or P-I' contlict, where v is a new variable, create an edge from start(ci) to cnd(ci) such that its action, rsubactions, constraints, effects, prceonditions, and aend values respectively are &lt;Y,.O, (%,... ,7,~)0, (C,. O eonstraints(ci))O, g, 7), and V.</Paragraph>
      <Paragraph position="5"> Procedure 3 Let c~ and ei be adjacent active and inactive edges such that rsubactions(e~) is (71,.-., 7~). For each most generM unifier 0, satisfying C = constraints(e~) O constraints(ci), of 71 and action(el) such that</Paragraph>
      <Paragraph position="7"> t.,_holds ((t, t, C/), C) }, without F,-P or P-P conflict, create an edge fr&lt;)m start(e&lt;,) to end(el) such that its action, rsubaetions, constraints, effects, preconditions, and acnd values respectively are (action(e,))O, (Tu,-.. ,7~)0, CO, g, ~P, and acnd(c,~).</Paragraph>
      <Paragraph position="8"> Now that we have the basic means to eah:ulate the effects and preconditions of the action represented by an edge, we can augment plan parsing to handle the situations described in Section 2.</Paragraph>
      <Paragraph position="9"> Effect-based action descriptions The fact that the description of the form achieve(P) can specify an action with P as its effect is captured by augmenting Procedures 2 and 3. The set of effects of the action represented by an inactive edge ei that hold at the. action's ending time is /?7/ = {qo I tm_holds({qo, end(ei), cnd(ei)), effects@i))}. The fact is thus captured in these procedures by checking that Ei contains P, instead of unifying 71 with action(ei), if 71 is of that form.</Paragraph>
      <Paragraph position="10"> The fact that achieve(P) can specify the null action if P already holds is captured by a new procedure that, given an active edge e~ with as its rsubactions value (achieve(P), 72,.-., %}, creates a new edge whose rsubactions value is (%,..., %} and whose preconditions value is preconditions (e,~) if e~, has P aa its effect and preconditions(ca) plus {end(e.), end(c~), P} otherwise.</Paragraph>
      <Paragraph position="11"> Action-enabling An action-enabling relationship can be captured by a new procedure that, given two adjacent inactive edges el and e2 such that el's effects satisfy some of eu's preconditions, treaties a new inactive edge with action(c2) ,as its action value. .+ State-dependent interpretation A dialogue state is determined by the initial state and the effects of the I)receding actions. The initial state is treated by using a special 'initialize' inactive edge from 0 to 0 with the effects value representing it. The influence of the qnitialize' edge is propagated by the procedure for treating action-enabling relationships and preference rules referring to precon(litions, a</Paragraph>
    </Section>
  </Section>
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