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<Paper uid="W94-0302">
  <Title>DPOCL: A Principled Approach to Discourse Planning</Title>
  <Section position="4" start_page="13" end_page="14" type="metho">
    <SectionTitle>
3 Desiderata for Planning Algorithms
</SectionTitle>
    <Paragraph position="0"> A formal characterization of the capabilities of discourse planning algorithms is essential to understanding their \]imitations and is necessary before one can make claims about the kinds of discourse plans those planners can produce.</Paragraph>
    <Section position="1" start_page="13" end_page="13" type="sub_section">
      <SectionTitle>
3.1 Completeness
</SectionTitle>
      <Paragraph position="0"> The planning process of a generative planner is typically viewed as s search through the space of possible plans to locate a solution for a given planning problem. For some planning problems, no solutions exist. For others, many solutions can be constructed. A general-purpose discourse planner cannot anticipate the structure of the solutions to every problem. In order for these planners to be useful, they must be able to construct all solutions.</Paragraph>
      <Paragraph position="1"> Planners that are guaranteed to find all solutions to s planning problem are complete.</Paragraph>
      <Paragraph position="2"> Suppose there is a class of solutions to a planning problem that a discourse planning algorithm cannot find.</Paragraph>
      <Paragraph position="3"> It may be the case that the most appropriate solutions to the problem fall entirely into this class. If this happens, the planner will only be able to construct the lessdesirable plans. It may also be the case that the oni~ solutions to a planning problem fall into this class. If this happens, the planner will unnecessarily report failure.</Paragraph>
      <Paragraph position="4"> Consider those discourses in which individual utterances play several roles. Maier \[12\] describes the need for a system to generate this type of discourse and Hobbs \[7\] provides an example of one such discourse. We provide another example here: Lucentio has asked for Bianca's hand. He always considered her Senior Baptista's fairest daughter.</Paragraph>
      <Paragraph position="5"> That is also why Lucentio always chose her to model for his paintings.</Paragraph>
      <Paragraph position="6"> Here the second sentence provides support for the hearer's acceptance of both surrounding sentences.</Paragraph>
      <Paragraph position="7"> In a discourse planning model, these multi-role utterances correspond to actions that axe part of subplans for two different parent actions. That is, the plans that represent these actions are structured as directed acyclic graphs (DAGS) rather than trees. Planning algorithms that are incomplete because they can only produce tree-structured plans are not able to generate plans for this class of discourse. For the example above, these types of planners would produce less appropriate plans where the second sentence appeared twice as support in two distinct subtrees.</Paragraph>
    </Section>
    <Section position="2" start_page="13" end_page="14" type="sub_section">
      <SectionTitle>
3.2 Soundness
</SectionTitle>
      <Paragraph position="0"> Any system that plans before it acts assumes that its model of action is a useful one. Given that a system is using such a model, the plans that it produces should at least be internally consistent. That is, these plans should not have steps that interfere with one another.</Paragraph>
      <Paragraph position="1"> Furthermore, the planner should continue to add steps to a plan until the model indicates that all the plan's goals have been accounted for. Planning algorithms that have these properties are called 8outed.</Paragraph>
      <Paragraph position="2"> Given a model of planning where actions are related both causally and decompositionally, a sound planning algorithm must consider two factors when constructing</Paragraph>
    </Section>
    <Section position="3" start_page="14" end_page="14" type="sub_section">
      <SectionTitle>
7th International Generation Workshop * Kennebunkport, Maine * June 21-24, 1994
</SectionTitle>
      <Paragraph position="0"> plans. First, for every step in a plan, the planner must ensure that each precondition of that step will be true just prior to its execution \[3\]. Second, the planner must consider the manner in which the steps of a subplan achieve the goals of the parent \[23, 25\]. While a parent step specifies the effects it has on the mental state of the hearer, it is the responsibility of the executable steps at the leaves of the subplan rooted at the parent step to ensure that those conditions are indeed established.</Paragraph>
      <Paragraph position="1"> Note that the soundness of a planning algorithm does not guarantee the success of the plans it produces. However, the information about causal and decompositional relationships recorded in sound plans is crucial for determining where the planning model is in error and how to replan when an execution failure occurs.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="14" end_page="14" type="metho">
    <SectionTitle>
4 Previous Discourse Planning Systems
</SectionTitle>
    <Paragraph position="0"> Most current discourse planners (e.g., \[1, 2, 9, 13, 15\]) are based on the original NOAH model of hierarchical planning. They rely on customized planning algorithms with pr0cedurai semantics for the purposes of solving specific text-planning problems, and thus their representations and algorithms suffer from being unprincipled and difficult to analyze. Although these systems have resulted in successful text generation for specific domains and text types, careful analysis of these programs shows that there is nothing in their semantics to prevent them from generating incorrect plans, generating plans with redundant steps, or failing to find plans in situations where they exist.</Paragraph>
    <Paragraph position="1"> As Hovy et ai. \[8\] point out, these problems stem from an approach to discourse planning that does not clearly distinguish between the representation of communicative action and the design of a planning algorithm that manipulates that representation. In most previous work, there has been no clear separation between the knowledge about the preconditions and effects of communicative acts and the knowledge about planning used to construct discourse plans. To the extent that these planners have been able to avoid generating incorrect or redundant plans, they have done so by severely limiting the expressive power of action descriptions and/or requiring the designer of action descriptions to handcraft each description to fit correctly into the ad/~oc semantics of the specific plan for which the action is intended. As Hovy et al. describe, when the number of operators for such systems increases, it becomes impractical for their designers to maintain their consistency.</Paragraph>
    <Section position="1" start_page="14" end_page="14" type="sub_section">
      <SectionTitle>
4.1 Representation of Discourse Plans
</SectionTitle>
      <Paragraph position="0"> Plans produced by most previous discourse planners have not adequately represented both the causal and decompositional relations between actions in a discourse plan. As a result, their plans do not represent the manner in which preconditions are established, and, in cases where they represent action decomposition, the plans do not capture the relationship between the effects of actions in a subplan and the effects of their parent action.</Paragraph>
      <Paragraph position="1"> Furthermore, they do not represent intentional and in-</Paragraph>
      <Paragraph position="3"/>
    </Section>
  </Section>
  <Section position="6" start_page="14" end_page="15" type="metho">
    <SectionTitle>
ent/Subplan Effects
</SectionTitle>
    <Paragraph position="0"> formational structure in a way that clearly distinguishes the two. As a result, the intentional and informational structures in their plans are di~cult to analyze. Furthermore, the discourse operators for these systems lack the generality that would come from separating the two structures.</Paragraph>
    <Paragraph position="1"> Intention To illustrate these problems, consider the discourse plan shown schematicaily in Figure 1. 1 This plan has a structure that is typical of those produced by most previous discourse planning systems \[2, 9, 13, 15\]. In this plan there is no explicit connection between the effects established by the parent action (c4 and c5) and those established by its subplan (c6, c7, c9, el0, el2 and c13). Previous approaches only represent the relationship between actioas at different levels; they fail to capture the relationship between the effects of those actions. In Figure 1, the top-level goal is cdAc5. Suppose that c6 unifies with c4, and that c9, el0, and c12 together have a consequence that unifies with c5. In this case, c7 and c13 are side effects of choosing the decomposition of the PARENT-ACTION into ACTION1, ACTION2 and ACTION3. This fact, however, is not captured in the discourse plan of Figure 1. A system relying on this plan could not distinguish intended effects from side effects, and so would be unable to determine that a different response is warranted when c6 fails than when c7 falls.</Paragraph>
    <Paragraph position="2"> In addition, there is no explicit representation of the relationship between two steps when one establishes a precondition for another. In Figure 1, ACTION3 has ell as a precondition. Suppose that both el0 and c7 unify with ell. If el0 falls it is possible that c7 will serve to establish the condition needed by ell. Without a representation of the causal roles that these effects play, a system cannot determine whether an additional response is required.</Paragraph>
    <Paragraph position="3"> Informat|onal Structure in Prev|ous Systems Most previous planning systems do not provide an explicit representation for either intentional or informational structure. As noted in Hovy, et al \[8\], to the extent that informational constraints were represented, each set of constraints was duplicated for many similar discourse tin this plan, the dashed arcs indicate the decomposition of PARENT-ACTION into the actions in its subplan. The ci's represent conditions in the world - those to the left of an action are the action's preconditions and those to the right of an action are its effects.</Paragraph>
    <Section position="1" start_page="15" end_page="15" type="sub_section">
      <SectionTitle>
7th International Generation Workshop * Kennebunkport, Maine * June 21-24, 1994
</SectionTitle>
      <Paragraph position="0"> operators. Many of these operators differed only in their intentional structure. As described in \[16\], combiningintentional and informational representations in this way can result in a proliferation of operators. Every intentional structure must be paired with every informational one, possibly requiring as many as n x m operators for domains with n intentional and m informational structures. null</Paragraph>
    </Section>
    <Section position="2" start_page="15" end_page="15" type="sub_section">
      <SectionTitle>
4.2 Computational Properties
</SectionTitle>
      <Paragraph position="0"> While previous discourse planners have been successful at generating appropriately structured plans for specific domains, these systems have ignored the analysis of the formal properties of the planning algorithms that produce them. As has been noted in \[20, 3\], NOAH, and consequently those discourse planners based on it, use ad hoc procedures for the construction of plans. As a result, the formal properties of these planning algorithms are difficult to characterize. While a complete analysis of the planning algorithms used by previous systems \[2, 9, 13, 15\] is beyond the scope of this paper, several properties of these algorithms are straightforward to describe. null First, these planners do not guarantee that a step's preconditions hold prior to the step's execution and thus they are not sound. Furthermore, there is no relationship in any oftbese planners between the effects of parent actions and their subplans - planning to achieve an effect at one level of abstraction does not guarantee that the effect is realized by any combination of executable actions.</Paragraph>
      <Paragraph position="1"> Second, these planners are not complete. While there may be many classes of plans that these systems cannot generate, their incompleteness can easily be seen when considering two factors. First, all of these systems use tree-structured plan representations. As a result, they cannot produce discourse plans where individual components play a role in more than one subplan. Second, most current discourse planning systems restrict steps in subplans to be totally ordered with respect to one another. For total-order planners to be complete they must be able to construct every possible step ordering.</Paragraph>
      <Paragraph position="2"> While the sacrifice of formal properties may be necessary for constructing an efficient implementation, it is important to characterize the conditions under which a planning system falls short of soundness or completeness.</Paragraph>
      <Paragraph position="3"> By characterizing the soundness of a planner two things become apparent. First, the conditions under which a planner will introduce flaws into a plan are completely characterized. Second, the nature of the flaws that might be introduced under those conditions are specified. Similarly, characterizing the completeness of a planner specifies the classes of plans that can and cannot be produced by a planner. Without an understanding of these properties for a given algorithm, it is impossible fully to evaluate its usefulness for a particular application.</Paragraph>
    </Section>
  </Section>
  <Section position="7" start_page="15" end_page="17" type="metho">
    <SectionTitle>
5 The DPOCL Discourse Planner
</SectionTitle>
    <Paragraph position="0"> The DPOCL discourse planner is an extension to recent partial-order causal link planners \[14, 17\]. In POCL planners, a plan is represented as a set of partially-ordered steps connected by causal links. Two steps in a plan are connected by a causal link when the effect of the first step is used to establish the precondition of the second step. Steps and corresponding links are added to the plan to establish unsatisfied preconditions, and additional constraints are placed on the plan only when needed to maintain consistency. Previous POCL planners have been non-hierarchical; DPOCL provides an extension that introduces action decomposition into the POCL framework. For a complete definition of DPOCL see \[25\].</Paragraph>
    <Paragraph position="1"> In the following discussion we will refer to the sample discourse from Section 3.1. Figure 2 shows an example of a DPOCL plan structure for this discourse. Consider * the subplan for Support~modeled(L,B)), rooted at the step marked as step ~1. ~ A decomposition link (shown using dashed arcs) connects Support(modeled(L,B)) to the begin and end-subplan steps bounding its subplan. 3 This subplan is made up of the two Cause-to-Believe steps and the Combine-Belief step shown in between the begin-subplan and end-subplan. A causal link (shown using a solid arc and labeled with the effect that it contributes) connects Cause-to-Believe(falrest(L,B)) to the End-Subplan step.</Paragraph>
    <Paragraph position="2"> The manner in which a hearer combines the information in an utterance with his prior beliefs is critical to the generation of the utterance. Most previous work has made use of highly simple models of this process: for instance, it has assumed that the effect of asserting a proposition p is that the hearer believes p. In fact, a speaker may go to great lengths to convince the hearer of the truth of a proposition. She may first assert it, then support it, and then provide support for the intermediate statement. In such a case, the speaker presumably believes that the combination of utterances is what leads the hearer to accept the main proposition.</Paragraph>
    <Paragraph position="3"> This phenomenon is represented by the Combine-Belief(z'~ action, where ~ is a vector of relevant beliefs. This Combine-Belief action provides an abstract model for an action taken by the hearer rather than by the speaker. A complete model of the manner in which a user combines belief from several utterances is beyond the scope of this paper. Further formal work in this area, such as that in \[I0\] is essential for accurately representing the structure of discourse plans. DPOCL provides a 2 Subplans in this figure are g~ouped inside rounded boxes for ease of reference.</Paragraph>
    <Paragraph position="4"> 3DPOCL uses the standard POCL technique of encoding the initial conditions and the goals of a planning problem as the effects of a null initial action and the preconditions of a null final action, respectively. Simi|arly, every subplan is bounded by a null stsxt-subplan and a null end-subplan.</Paragraph>
    <Paragraph position="5"> Each staxt-subplan has as its dfects the preconditions of its parent action, and each end-subplan has as its preconditions the dfects of its parent action.</Paragraph>
    <Paragraph position="7"> LucentIo has asked for ~.Bel(propolled(Lji))) Bianca's hand in marriage. Combine-Be.lid(x)</Paragraph>
    <Paragraph position="9"> He considers her the fairest J  framework for incorporating these approaches.</Paragraph>
    <Section position="1" start_page="16" end_page="17" type="sub_section">
      <SectionTitle>
5.1 Representation in DPOCL
</SectionTitle>
      <Paragraph position="0"> The representation of each action in DPOCL is separated into two parts corresponding to the causal and decompositional roles the action plays: the action operator, and a set of decomposition operators. The action operator captures the action's preconditions and effects, sets of first-order unquantified sentences similar to the typical precondition and addldelete lists of STRIPS \[5\]. Each decomposition operator represents a slngle-layer expansion of a composite step, essentially providing a partial specification for the subplan that achieves the parent step's effects given its preconditions. In addition to specifying the steps in the subplan, the decomposition operator specifies any variable binding and temporal ordering constraints between the steps, and the causal links between steps of the subplan that enable them to establish the parent step's effects.</Paragraph>
      <Paragraph position="1"> Figure 3 shows the action operator and one decomposition operator for the Support act. 4 As we see in the action operator in this figure, Support(?prop) has the effect of increasing the belief in proposition ?prop for the hearer. The decomposition operator in Figure 3 was responsible for expanding the Support labeled #I in 'The operators in this t~gure are shown wlth some detail omitted for clarity.</Paragraph>
      <Paragraph position="2">  has three steps in its body: two Cause-to-Believe actions and a combination of belief by the hearer to strengthen her belief in ?prop. The constraints placed on this decomposition restrict the propositions used in the Cause-to-Believe steps to be ones that cause the proposition being supported. Dec0mpositional constraints are discussed further in Section 6.1 This decomposition operator is only a partial specification of the subplan for the Support step. In DPOCL, when a subplan is only partially specified, the planner is free to complete the subplan by using steps already appearing in the plan. In this way, DPOCL can avoid generating plans with redundant communicative actions.</Paragraph>
    </Section>
    <Section position="2" start_page="17" end_page="17" type="sub_section">
      <SectionTitle>
5.2 Overview of the DPOCL Algorithm
</SectionTitle>
      <Paragraph position="0"> In DPOCL, the process of cresting a completed plan involves iterating through a loop that chooses between refining the current plan decompositionaUy or refining the plan cansaily and then modifying the plan to ensure that the refinement has not introduced any errors. Figure 4 summarizes the DPOCL planning algorithm. For a complete definition, see \[25\].</Paragraph>
      <Paragraph position="1"> Causal refinement in DPOCL is essentially identical to causal refinement in previous POCL planners. An unsatisfied precondition of some step in the plan is selected and a causal link is added to establish the needed condition. Decompositional refinement essentially creates a subplan for some composite action and adds the subplan to the plan. First, a decomposition operator for the chosen step is selected and the steps indicated in the operator are added to the plan. These steps are created in one of two ways. In the first case, a step is created by selecting an action operator of the correct ~ction type and instantiating s new step just as is done when a new step is added during causal refinement. In the second case, a step is added to the subplan by finding a step of the correct action type that already exists in the plan and using that step in the appropriate place in the new subplan.</Paragraph>
      <Paragraph position="2"> The DPOCL algorithm ensures that a subplan's actions establish the effects of the parent action in a straightforward manner. The preconditions of a sub-Termination: If the plan is inconsistent, then backtrack. Otherwise,  remove unused step and return the plan.</Paragraph>
      <Paragraph position="3"> Plan Refinement; Non-detenninlstlcally do one of the following: I. Causal Planning: (a) Goal Selection: Nondeterminlstlcally select a goal. (b) Operator Selection: Add a step to the plan that adds an effect that can be unified with the goal (either by instantiating the step from the operator library or by finding a step already in the plan). H no such step exists, bac.ktrack. Otherwise, add the binding constraints required for the conditions to unify, an ordering constraint that orders the new step before the goal step and add the causal llnk between the two.</Paragraph>
      <Paragraph position="4"> 2. Decompositional Planning: (a) Action Selection: Nondeterministlcally select some unexpunded composite step in the plan.</Paragraph>
      <Paragraph position="5"> (b) Decomposition Selection: Nondetermlnlstic2dly chose an ap null propriate decomposition schema for this action whose constraints axe satisfied. Add the steps and subplaa components of the decomposition schema to the plan and update the llst of decomposition links to indicate the new subplan.</Paragraph>
      <Paragraph position="6"> Threat Resolution: Find any step that might threaten to undo any causal link. For every such step, nondetermlaisticai\]y do one of the following: .</Paragraph>
      <Paragraph position="7">  s Promotion: If possible, move the threatened steps to occur before the threat in the plan.</Paragraph>
      <Paragraph position="8"> s Demotion: If possible, move the threatened steps to occur ufter the threat in the plan.</Paragraph>
      <Paragraph position="9"> s Separation: If possible, add binding constraints on the steps involved so that no conflict can srlse.</Paragraph>
      <Paragraph position="10"> Recursive Invocation: Call the planner recursively with the new plan structure.</Paragraph>
      <Paragraph position="11">  plan's final step are an copy of the effects of the subplan's parent step. The DPOCL planner will attempt to achieve them through causal refinement just as it achieves all other unsatisfied preconditions. In this way we guarantee that the effects of every composite action are achieved by the steps in its subplan. Furthermore, the exact relationship between the actions in a subplan and the establishment of those effects is made explicit in the causal links establishing those conditions in the subplan.</Paragraph>
      <Paragraph position="12"> As a result of adding steps to a plan, newly created steps may introduce threats to existing causal links. A step, $6, threatens a causal link between two steps Sb and Sc when 56 might occur between Sb and Sc and one of S~'s effects might undo the condition established in the causal link. To ensure that no causal links are undone by plan refinement, each threat in s plan is eliminated before planning proceeds. This is done either by ordering the steps so that the threatening step cannot occur between the two causally-linked steps or by restricting the variable bindings of the steps to eliminate harmful interactions.</Paragraph>
    </Section>
  </Section>
  <Section position="8" start_page="17" end_page="18" type="metho">
    <SectionTitle>
6 DPOCL's Properties
</SectionTitle>
    <Paragraph position="0"> Plan structures in DPOCL represent three critical components. First, every causal connection between some  plan and e, be an effect of s. Effect e, is intended precisely ~uhen at least one of the follozuing conditions holds: * There is some causal link from * to the final step of the plan such that e, establishes one of the goals of the plan. * There is some causal link from s to some step s! where s! is the final step of a subplan for a parent action sp such that - e, establishes one of the goals of the subplan (that is, a precondition of s ! ) and - the corresponding effect e,~ of sp is intended.</Paragraph>
    <Paragraph position="1"> * There is some causal link from s to another step s' such that - e, establishes one of the preconditiorts of s' and - some effect e,, of s' is intended.</Paragraph>
    <Paragraph position="2">  step's effect and another step's precondition that relies upon it is marked by a causal link. Second, the connection between the effects of every abstract action and the substeps that achieve those effects are marked by a combination of causal and decompositional links. Finally, the constraints restricting the applicability of decomposition operators are noted for every abstract step expansion. By providing an explicit representation for each of these components an adequate characterization of the intentional and informational structure of the discourse can be made.</Paragraph>
    <Section position="1" start_page="18" end_page="18" type="sub_section">
      <SectionTitle>
6.1 DPOCL's Representational Properties
</SectionTitle>
      <Paragraph position="0"> A Principled Representation of Intention The forrnalrepresentation of causal and decompositional connections between steps in the DPOCL plan makes the definition of intention in terms of these concepts straightforward. Informally, an effect is intended if it plays a causal role in the plan. That is, if it is used in a causal link and the step that asserts that effect is connected by that causal link through subsequent causal and decompositional links ultimately to the final step of the plan. The formal definition of an intended effect is shown in Figure 5.</Paragraph>
      <Paragraph position="1"> Although the plan shown in Figure 2 does not explicitly illustrate how our representation addresses cases where action descriptions have multiple effects and so distinguishes between intended and side-effects in the same action, our model handles these cases appropriately. Our solution rests on the fact that our model makes a clear distinction between effects of discourse actions that play a role in achieving the top-level goals of the discourse plan and effects that are not causally linked in a way that contributes to the agent's ultimate goals.</Paragraph>
      <Paragraph position="2"> An Explicit Representation of Informational Structure Decomposition operators in DPOCL enable us to represent the knowledge speakers have about how to use domain information to achieve communicative intentions. For example, one way for a speaker to increase a bearer's belief in a proposition (i.e., to support a proposition) is to describe a plausible cause of that proposition. In DPOCL, we represent this &amp;quot;rule of language&amp;quot; using a decomposition operator as illustrated by the decomposition operator in Figure 3. This operator says that one way to support a proposition ?prop1 is to find another proposition, ?peop2, such that causes(?prop2, ?propl) is true in the domain. If such a ?prop2 can be found, then the speaker can support ?propl by making the hearer believe ?prop2 and the relation causes(?prop2, ?prop1) In this way, information in the domain acts to constrain what language rules are appropriate and, given any particular rule, what objects can be referred to when it is used.</Paragraph>
      <Paragraph position="3"> The representation of the informational structure in a DPOCL plan is straightforward. Each decomposition operator in DPOCL lists the informational constraints that must hold in order for an abstract action to be achieved by the subplan dsfined in that operator. During plan generation, informational constraints are checked for consistency whenever a modification is made to the plan and backtracking occurs when a constraint is violated. In addition, these constraints are explicitly recorded in the plan data structure. The informational structure is made available to the realization component that is responsible for transforming the discourse plan into a series of natural language utterances.</Paragraph>
    </Section>
    <Section position="2" start_page="18" end_page="18" type="sub_section">
      <SectionTitle>
6.2 DPOCL's Computational Properties
</SectionTitle>
      <Paragraph position="0"> Because DPOCL is built upon well-understood POCL planning algorithms, DPOCL inherits many of these algorithms' formal properties. Specifically, DPOCL is both sound and, for certain classes of plans, complete.</Paragraph>
      <Paragraph position="1"> Proofs of soundness and completeness can be found in \[25\]. With respect to the class of plans that DPOCL can generate, DPOCL is primitive complete. That is, it can generate sl1 possible sequences of executable actions, but not necessarily all hierarchical structures that could account for those executable actions. In particular, DPOCL cannot generate plans where two abstract steps are ordered one before the other in order to avoid a harmful interaction but some interleaving of the steps in their subplans exists that avoids this interaction. For a more complete description of this restriction on DPOCL's completeness, see \[25\].</Paragraph>
    </Section>
  </Section>
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