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<Paper uid="P90-1012">
  <Title>NORMAL STATE IMPLICATURE</Title>
  <Section position="4" start_page="89" end_page="90" type="metho">
    <SectionTitle>
2 Scalar Implicature
</SectionTitle>
    <Paragraph position="0"> tIirschberg proposes the following set of six necessary and sufficient conditions for identifying conversational implicatures (p. 38). 3 A speaker S conversationally implicates Q to a hearer tI by saying U (where U is a realization of a proposition P) in a context C iff: 3.a .... a dead one b .... a live one A third problem is that in order to derive (lb) from (la) it is necessary to consider the beliefs of speaker (S) and hearer (H): e.g. S's and H's beliefs about why each said what they did, and about the appropriate state of the parrot.</Paragraph>
    <Paragraph position="1"> Grice \[Gri75\] described conversational implicature, a kind of non-truth-functional context-dependent inference based upon a speaker's and hearer's awareness of principles of cooperative conversation. In this paper, I claim that a speaker's use of (la) may conversationally implicate (lb).</Paragraph>
    <Paragraph position="2"> In order to formally describe this kind of conversational implicature, which I have termed 'normal state implicature', I adopt the methodology used by Hirschberg \[Hir85\] for the identification of another kind of conversational implicature, scalar implicature.</Paragraph>
    <Paragraph position="3"> In section 2, I present a brief description of scalar implicatures and Hirschberg's methodology for identifying them. In section 3, I present a convention for identifying normal state implicatures. Informally speaking, the convention is that if speaker S makes a request that hearer H perform an action A on an entity E, and if S and tt mutually believe that S has a plan whose success depends on the E being in a certain state N (which is the normal state for an E with respect to that plan) and that S's request is a step of that plan, then S is implicating a request for S to do A on an E in state N.</Paragraph>
    <Paragraph position="4"> In section 4, I clarify the notion of normal state with respect to a plan by distinguishing it from the notions of stereotype and plan-independent normal state. Next, in section 5, I show how states can be represented in the lexicon. In section 6, I compare scalar and normal state implicature; in section 7, survey related work; and, in section 8, present my conclusions.</Paragraph>
    <Paragraph position="5">  1. S intends to convey Q to H via U; and 2. S believes that S and H mutually believe that S is being cooperative; and</Paragraph>
    <Paragraph position="7"> S and H mutually believe that S's saying U in C, given S's cooperativity, licenses Q; and Q is cancelable; i.e., it is possible to deny Q without denying P; and Q is nondetachable; i.e., the choice of a realization U of P does not affect S's implicating Q (except in certain situations where Q is licensed via Grice's Maxim of Manner); and Q is reinforceable; i.e., it is possible to affirm Q without seeming redundant.</Paragraph>
    <Paragraph position="8"> Instead of using these conditions to identify particular scalar implicatures, Hirschberg argues that it is sufficient to provide a means of identifying instances of a class of conversational implicature, such as scalar implicatures. Then, she provides a convention for identifying instances of scalar implicat ure.</Paragraph>
    <Paragraph position="9"> Informally speaking, scalar implicature is based on the convention that (pp. 1 - 2)&amp;quot;cooperative speakers will say as much as they truthfully can that is relevant to a conversational exchange&amp;quot;; and distinguished from other conversational implicatures by &amp;quot;being dependent upon the identification of some salient relation that orders a concept referred to in an utterance with other concepts&amp;quot;; e.g. by saying (4a), B has scalar implicated (4b). 4  (4) A: How was the party last night? a. B: Some people left early.</Paragraph>
    <Paragraph position="10"> b. Not all people left early.</Paragraph>
    <Paragraph position="11">  The convention for identifying scalar implicature proposed by Hirschberg is of the form: if 3Her conditions are ~ revision of Grice's. Also, I have changed the names of her variables to be consistent with usage in the rest of my paper.</Paragraph>
    <Paragraph position="12"> 4 (4) is example (1) in \[Hir85\].</Paragraph>
    <Paragraph position="13"> there exists a partial order O such that S and H mutually believe that O is salient in context C, and utterance U realizes the proposition that S affirms/denies/is ignorant of some value in O, then by saying U to H in C, S licenses the scalar implicature that S has a particular belief regarding some other value of O.</Paragraph>
    <Paragraph position="14"> In the next section, I will apply Hirschberg's methodology to the problem of identifying normal state implicatures.</Paragraph>
  </Section>
  <Section position="5" start_page="90" end_page="91" type="metho">
    <SectionTitle>
3 Normal State Implicature
</SectionTitle>
    <Paragraph position="0"> In this section, I will argue that (lb) is a conversational implicature and propose a convention for identifying instances of that class of implicature, which I will call 'normal state implicature'. First, I claim that a speaker S conversationally implicates (lb) to a hearer H by saying (la) in the context described above; i.e. that (lb) is a conversational implicature according to the six conditions described in section 2. Condition 1 is met since S intends to cause H to believe (lb) by saying (la); condition 2 since S believes that it is a mutual belief of S and H that S is being cooperative; condition 3 will be satisfied by providing a convention for normal state implicature below. The previous discussion about (3a) and (3b) provides evidence for cancelability (condition 4) and reinforceability (condition 6), respectively; and, (lb) is nondetachable (condition 5) since alternate ways of saying (la), in the same context, would convey (lb).</Paragraph>
    <Paragraph position="1"> Next, in order &amp;quot;to motivate the general convention ((6) below) for identifying normal state implicatures, I'll present the instance of the convention that accounts for the implicature in (1). Let S, H, U, and C be constants denoting speaker, hearer, utterance, and context, respectively. Let b0, bl, and g be first order variables over parrots (PARROT), live parrots (the lambda expression), and plans (PLAN), respectively. 5 HAS-PLAN(Agent,Plan,Entity) is 5The model of plans used here is that of STRIPS \[FN71\] with minor extensions. A plan includes preconditions which must hold in order for the plan to succeed, and a sequence of actions to be carried out to achieve some goal. One extension to this model is to add a llst of entities playing a role in the plan either as instruments (e.g. a boat which is to be used to cross a river) or as the goal itself (e.g. a parrot to be acquired for a pet). The second extentrue if Agent has a plan in which Entity plays a role; PRECOND(Plan,Proposition) is true if Plan has Proposition as a precondition;  STEP(Plan,Action) is true if Action is a step of Plan. Also, BMB(A,B,Proposition) is true if A believes that A and B mutually believe that Proposition; REALIZE(Utterance, Proposition) is true if Utterance expresses Proposi null tion; REQUEST(S,H,Action) is true if S requests H to perform Action; and SAY(S,H,U,C) is true if S says U to H in C. 6 SHOW(A,B,C) is true if A shows C to B. IN-STATE(Entity,State) is true if Entity is in the given State; and NORMAL-STATE(State,Plan,Entity) is true if State is the normal state of Entity with respect to Plan. 7 Finally, NORMAL-STATE-IMP (Speaker, Hearer ,Utterance ,Prop osition ,Context ) is true if by use of Utterance in Context, Speaker conveys Proposition to Hearer.</Paragraph>
    <Paragraph position="2"> Now, to paraphrase (5) below, if S and H mutually believe that S has a plan in which a parrot plays a role and that a precondition of S's plan is that the parrot should be alive, which is its normal state with respect to the plan, and that S's saying U is a step of that plan; and, if U is a request to be shown a parrot, then S normal state implicates a request to be shown a live parrot.</Paragraph>
    <Paragraph position="4"> BMB(S, H, ~HAS-PLAN(S, g, b0) A PRECOND(g, IN-STATE(b0, LIVE)) A NORMAL-STATE(LIVE, g, b0) A STEP(g, SAY(S, H, U, C))) A REALIZE(U, REQUEST(S, H, SHOW(H, S, b0))) NORMAL-STATE-IMP(S, H, U, REQUEST(S, H, SHOW(H, S, bl)),C)  It is possible to generalize (5) as follows. Let K, N, and A be higher order variables over classifications (CLASSIF), states (STATE), and actions that may be performed as a step in a plan sloE, suggested in \[Car88\], is to distinguish preconditions which can be achieved as subgoais from those which are unreasonable for the agent to try to bring about (&amp;quot;applicability conditions&amp;quot; ). In (5) and (6), preconditions are meant in the sense of applicability conditions.</Paragraph>
    <Paragraph position="5"> eBMB, REALIZE, REQUEST, and SAY are from  (ACT), respectively. Then, (6) is the general convention for identifying normal state implicature.</Paragraph>
    <Paragraph position="7"> Unfortunately, if (6) is to be of maximum use, there are two problems to be solved. First, there is the problem of representing all preconditions of a plan, s and, second, is the problem of plan inference, i.e., how does H come to know what S's plan is (including the problem of recognizing that the saying of U is a step in S's plan)? 9 Both problems are outside the scope of this paper.</Paragraph>
  </Section>
  <Section position="6" start_page="91" end_page="92" type="metho">
    <SectionTitle>
4 States and Normal States
</SectionTitle>
    <Paragraph position="0"> First, what I mean by a state of an entity E is, adopted from \[Lan87\], a history of related events involving E. In Lansky's ontology, events may be causally or temporally related. Temporal precedence is transitive. Causality is not transitive and does not necessitate occurrence but does imply temporal precedence. A strong pre-requisite constraint (--,) can be defined such that &amp;quot;each event of type E~ can be caused by exactly one event of type El, and each event of type E1 can cause at most one event of type E2&amp;quot; (\[Lan87\],p. 142).</Paragraph>
    <Paragraph position="1"> Many classifications expressed as nouns denote a class of entity whose state varies over the period of existence during which it is aptly characterized by the classification. For example, Figure 1 and Figure 2 depict causal event chains ldeg of parrots and vases, respectively.</Paragraph>
    <Paragraph position="2"> (Nodes represent events and directed arcs represent causality.) The state of being dead or SE.g., see \[McC87\].</Paragraph>
    <Paragraph position="3"> 9E.g., see \[Car88\].</Paragraph>
    <Paragraph position="4">  phers have recently used it \[Sch77\], nor in the sense of \[SA77\], nor do I mean 'chain' in the mathematical sense of a total order.</Paragraph>
    <Paragraph position="5"> broken can be defined in terms of the occurrence of an event type of dying or breaking, respectively. Live is the state of an entity who has been born but has not yet died; ready-to-use is the state of an artifact between its creation or repair and its destruction. 11 Note that, paradoxically, language users would agree that a dead parrot or a vase with a crack in it is still aptly characterized as a parrot or vase, respectively. 12 Next, what I mean by a normal state of E is a state that E is expected to be in. For example, in the absence of information to the contrary, live or ready-to-use is expected by language users to be a state of parrots or vases, respectively. Note, however, that NORMAL-STATE in (6) represents a normal state of an entity with respect to some plan. That is, I am not claiming that, in the absence of information about S's plan, S's use of (la) conversationally implicates (lb).</Paragraph>
    <Paragraph position="6"> The reason for stipulating that NORMAL-STATE be relative to S's plan is that use of (la) in the context of a different plan could change what S and H consider to be normal. For example, in a taxidermist's plan, dead could be the normal state of a parrot. Also, consider 'coffee': a speaker's use of (7) in the context of a coffee farm could be used to request coffee beans; in a grocery store, ajar of instant; and in a restaurant, a hot beverage.</Paragraph>
    <Paragraph position="7">  7. I'd like some coffee.</Paragraph>
    <Paragraph position="8">  Note that more than one precondition of S's plan may be relevant to interpreting S's use of an expression. For example, a typical restaurant customer uttering (7) expects to be understood as not only requesting coffee in its hot-beverage state, but also in its safe-to-drink state. Also, more than one of S's plans may be relevant, Returning to the pet shop example, suppose that S and H mutually believe that S has plans to acquire a parrot as a pet and also to study its vocalizations; then it would be inappropriate for H to show S a parrot that H believed to be incapable of making vocalizations. Normal states differ from stereotypes. A stereotype is a generalization about prototypes of a category, 13 e.g. (8). 14  Qualifying an expression in a way which contradicts a stereotype may have a different effect on H than doing so in a way which specifies a non-normal state. For instance, if S says (9) after saying (la) in the above pet shop scenario, H may doubt S's sincerity or S's knowledge about parrots; while S's use of (3a) after saying (la) may cause tI to have doubts about S's sincerity or It's knowledge of S's plan, but not S's knowledge about parrots. null 9 .... a 100 pound one Another difference between stereotypes and normal states is that stereotypes are not affected by S's and H's mutual beliefs about S's plan, whereas I have just demonstrated that what is considered normal may change in the context of S's plan. Finally, another reason for making the distinction is that I am not claiming that, in the above pet shop scenario, S's use of (la) licenses (10); i.e., S does not intend to convey (10). 15 10. I \[the speaker\] would like to see a large, green, talking bird.</Paragraph>
  </Section>
  <Section position="7" start_page="92" end_page="93" type="metho">
    <SectionTitle>
5 The Role of Events in cer-
</SectionTitle>
    <Paragraph position="0"> tain Lexical Representations null Now I will show how the notion of state presented in the previous section can be represented in the lexicon via state predicates based on causal event chains. The purpose of this is to clarify what counts as a state and hence, what is prototype; e.g. contrast (8) with &amp;quot;Ripe bananas are yellow&amp;quot;. A statement of a stereotype in which the state of the prototypes is unspecified may describe prototypes in the plan-independent normal state for the category; e.g. consider &amp;quot;Bananas are yellow&amp;quot;. Also, note that stereotypical properties may be used to convey the state; e.g. consider &amp;quot;I want a green banana&amp;quot; used to convey &amp;quot;I want an unripe banana&amp;quot;.</Paragraph>
    <Paragraph position="1"> 15I recognize that it is possible for a speaker to exploit mutual beliefs about stereotypes or plan-independent norreal states to convey conversational implicatures. E.g., consider the conversation: A says, &amp;quot;Is your neighbor rich?&amp;quot; B replies, &amp;quot;He's a doctor.&amp;quot; However, this kind of implicature does not occur under the same conditions as those given for normal state implicature, and is outside of the scope of tiffs paper.</Paragraph>
    <Paragraph position="2">  to be identified by the convention for normal state implicature. This way of representing states has benefits in other areas. First, entaihnent relationships between states of an entity are thereby represented. Second, certain scalar implicatures may be based on the event ordering of a causal event chain.</Paragraph>
    <Paragraph position="3"> For example, Figure 3 contains pictorial and formal representations of a causal event chain for the ripening of fruit. Definitions of states are given as state predicates; e.g. the expression 'unripe' is used to denote a state such that no event of ripening (R) has occurred (yet). Note that, as (11) shows, 'ripe' may be used to scalar implicate but not to entail 'not overripe'; the event ordering of the causal event chain serves as the salient order for the scalar implicature. The expected entailments follow from the constraints represented in Figure 3.</Paragraph>
    <Paragraph position="4"> ll.a. It's ripe. In fact, it's just right for eating. b. It's ripe. In fact, it's overripe/too ripe.</Paragraph>
    <Section position="1" start_page="93" end_page="93" type="sub_section">
      <SectionTitle>
6 Comparison of Scalar and
Normal State Implicature
</SectionTitle>
      <Paragraph position="0"> These two classes of conversational implicature have some interesting similarities and differences. null First, licensing a scalar implicature requires the mention of some specific value in an ordering, while licensing a normal state implicature requires the absence of the mention of any state. For example, consider a situation where S is a restaurant customer; H is a waiter; S and H have mutual belief of the salience of an ordering such that warm precedes boiling hot; and, S and H have mutual belief of S's plan to make tea by steeping a tea bag in boiling hot water.</Paragraph>
      <Paragraph position="1"> 14.a. I'd like a pot of water.</Paragraph>
      <Paragraph position="2"> b. I'd like a pot of warm water.</Paragraph>
      <Paragraph position="3"> c. I'd like a pot of boiling hot water.</Paragraph>
      <Paragraph position="4"> d. I'd like a pot of warm but not boiling hot water.</Paragraph>
      <Paragraph position="5"> In this situation, use of (14a) would license the normal state implicature (14c) but no scalar implicature. IIowever, use of (14b) would license the scalar implicature (14d) but not the normal state implicature (14c). (In fact, use of 'warm' in (14b) would cancel (14c), as well as be confusing to H due to its inconsistency with H's belief about S's intention to make tea.) Thus, at least in this example, scalar and normal state implicature are mutually exclusive.</Paragraph>
      <Paragraph position="6"> Second, saliency and order relations play a role in both. Scalar implicature is based on the salience of a partially ordered set (from any domain). Normal state implicature is based on the salience of a plan; one of a plan's preconditions may involve a normal state, which can be defined in terms of a causal event chain.</Paragraph>
      <Paragraph position="7"> normal state implicature, while the presence of a qualification (the marked case), blocks it (thereby allowing the scalar implicature to be conveyed). Finally, Herskovits \[Her87\] addresses the problem that the meaning of a locative expression varies with the context of its use. Her approach is to specify &amp;quot;a set of characteristic constraints constraints that must hold for the expression to be used truly and appropriately under normal conditions. &amp;quot; (p. 20) Her constraints appear to include stereotypes and plan-independent normal states; normal is distinguished from prototypical; and the constraints may include speaker purpose.</Paragraph>
    </Section>
  </Section>
  <Section position="8" start_page="93" end_page="93" type="metho">
    <SectionTitle>
7 Related Work
</SectionTitle>
    <Paragraph position="0"> This work is related to work in several different areas.</Paragraph>
    <Paragraph position="1"> First, one of the goals of research on non-monotonic reasoning 16 has been the use of default information. The classic example, that if something is a bird then it can fly, appears to involve all three notions that I have distinguished here; namely, stereotype, plan-independent normal state, and normal state with respect to a plan. (It is a stereotype that birds are genetically suited for flight; a plan-independent normal state that a bird is alive or uninjured; and a normal state with respect to a plan to send a message via carrier pigeon that the bird be able to fly.) Also, I have shown that the calculation of normal state implicature is based only on the third notion, i:e., that certain &amp;quot;defaults&amp;quot; are context-dependent.</Paragraph>
    <Paragraph position="2"> In another area, work has been done on using knowledge of a speaker's plans to fill in missing information to interpret incomplete utterances, e.g. sentence fragments \[AP80\] and ellipsis \[car89\].</Paragraph>
    <Paragraph position="3"> As for related work on conversational implicature, both \[iior84\] and \[ALS1\] describe pragmatic inferences where what is conveyed by an utterance is more precise than its literal meaning. They claim that such inferences are based on a principle of speaker economy and exploit the speaker's and hearer's shared beliefs about stereotypes. Also, Horn points out that an unmarked expression tends to be associated with the stereotype of an extension and its marked counterpart with the non-stereotype. Roughly, this corresponds to my observation regarding (14), that the absence of a qualification (the unmarked case) licenses a lOFor a survey, see \[GinS7\]. 94</Paragraph>
  </Section>
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