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<Paper uid="P95-1020">
  <Title>A Uniform Treatment of Pragmatic Inferences in Simple and Complex Utterances and Sequences of Utterances</Title>
  <Section position="3" start_page="144" end_page="145" type="metho">
    <SectionTitle>
2 Stratified logic
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="144" end_page="145" type="sub_section">
      <SectionTitle>
2.1 Theoretical foundations
</SectionTitle>
      <Paragraph position="0"> We can offer here only a brief overview of stratified logic. The reader is referred to Marcu (1994) for a comprehensive study. Stratified logic supports one type of indefeasible information and two types of defeasible information, namely, infelicitously defeasible and felicitously defeasible. The notion of infelicitously defeasible information is meant to capture inferences that are anomalous to cancel, as in: (1) * John regrets that Mary came to the party but she did not come.</Paragraph>
      <Paragraph position="1"> The notion of felicitously defeasible information is meant to capture the inferences that can be cancelled without any abnormality, as in:  (2) John does not regret that Mary came to the party because she did not come.</Paragraph>
      <Paragraph position="2"> The lattice in figure 1 underlies the semantics of stratified logic. The lattice depicts the three levels of strength that seem to account for the inferences that pertain to natural language semantics and pragmatics: indefeasible information belongs to the u layer, infelicitously defeasible information belongs to the i layer, and felicitously defeasible information belongs to the d layer. Each layer is partitioned according to its polarity in truth, T ~, T i, T a, and falsity, .L =, .l J, .1_ d. The lattice shows a partial order that is defined over the different levels of truth. For example, something that is indefeasibly false, .l_ u, is stronger (in a sense to be defined below) than something that is infelicitously defeasibly true, T i, or felicitously defeasibly false, .L a. Formally, we say that the u level is stronger than the i level, which is stronger than the d level: u&lt;i&lt;d. At the syntactic level, we allow atomic formulas to be labelled according to the same underlying lattice. Compound formulas are obtained in the usual way. This will give us formulas such as regrets u ( John, come(Mary, party)) ---,  cornel(Mary, party)), or (Vx)('-,bachelorU(x) --~ (malea( ) ^ The satisfaction relation is split according to the three levels of truth into u-satisfaction, i-satisfaction, and d-satisfaction: Definition 2.1 Assume ~r is an St. valuation such that t~ = di E and assume that St. maps n-ary  predicates p to relations R C 7~ x ... x 79. For any atomic formula p=(tl, t2,... ,t,), and any stratified valuation a, where z E {u, i, d} and ti are terms, the z-satisfiability relations are defined as follows:</Paragraph>
      <Paragraph position="4"> * o&amp;quot; ~d pd(tl,...,tn ) iff (di,...,dr,) C= R d Definition 2.1 extends in a natural way to negated  and compound formulas. Having a satisfaction definition associated with each level of strength provides a high degree of flexibility. The same theory can be interpreted from a perspective that allows more freedom (u-satisfaction), or from a perspective that is tighter and that signals when some defeasible information has been cancelled (i- and d-satisfaction). Possible interpretations of a given set of utterances with respect to a knowledge base are computed using an extension of the semantic tableau method.</Paragraph>
      <Paragraph position="5"> This extension has been proved to be both sound and complete (Marcu, 1994). A partial ordering, &lt;, determines the set of optimistic interpretations for a theory. An interpretation m0 is preferred to, or is more optimistic than, an interpretation ml (m0 &lt; ml) if it contains more information and that information can be more easily updated in the future. That means that if an interpretation m0 makes an utterance true by assigning to a relation R a defensible status, while another interpretation ml makes the same utterance true by assigning the same relation R a stronger status, m0 will be the preferred or optimistic one, because it is as informative as mi and it allows more options in the future (R can be defeated).</Paragraph>
      <Paragraph position="6"> Pragmatic inferences are triggered by utterances.</Paragraph>
      <Paragraph position="7"> To differentiate between them and semantic inferences, we introduce a new quantifier, V vt, whose semantics is defined such that a pragmatic inference of the form (VVtg)(al(,7) --* a2(g)) is instantiated only for those objects t' from the universe of discourse that pertain to an utterance having the form al(~- Hence, only if the antecedent of a pragmatic rule has been uttered can that rule be applied. A recta-logical construct uttered applies to the logical translation of utterances. This theory yields the following definition: Definition 2.2 Let ~b be a theory described in terms of stratified first-order logic that appropriately formalizes the semantics of lezical items and the necessary conditions that trigger pragmatic inferences. The semantics of lezical terms is formalized using the quantifier V, while the necessary conditions that pertain to pragmatic inferences are captured using V trt. Let uttered(u) be the logical translation of a given utterance or set of utterances. We say that utterance u pragmatically implicates p if and only if p d or p i is derived using pragmatic inferences in at least one optimistic model of the theory ~ U uttered(u), and if p is not cancelled by any stronger information ('.p~,-.pi _.pd) in any optimistic model schema of the theory. Symmetrically, one can define what a negative pragmatic inference is. In both cases, W uttered(u) is u-consistent.</Paragraph>
    </Section>
    <Section position="2" start_page="145" end_page="145" type="sub_section">
      <SectionTitle>
2.2 The algorithm
</SectionTitle>
      <Paragraph position="0"> Our algorithm, described in detail by Marcu (1994), takes as input a set of first-order stratified formulas * that represents an adequate knowledge base that expresses semantic knowledge and the necessary conditions for triggering pragmatic inferences, and the translation of an utterance or set of utterances uttered(u). The Mgorithm builds the set of all possible interpretations for a given utterance, using a generalization of the semantic tableau technique. The model-ordering relation filters the optimistic interpretations. Among them, the defeasible inferences that have been triggered on pragmatic grounds are checked to see whether or not they are cancelled in any optimistic interpretation. Those that are not cancelled are labelled as pragmatic inferences for the given utterance or set of utterances.</Paragraph>
    </Section>
  </Section>
  <Section position="4" start_page="145" end_page="148" type="metho">
    <SectionTitle>
3 A set of examples
</SectionTitle>
    <Paragraph position="0"> We present a set of examples that covers a representative group of pragmatic inferences. In contrast with most other approaches, we provide a consistent methodology for computing these inferences and for determining whether they are cancelled or not for all possible configurations: simple and complex utterances and sequences of utterances.</Paragraph>
    <Section position="1" start_page="145" end_page="147" type="sub_section">
      <SectionTitle>
3.1 Simple pragmatic inferences
</SectionTitle>
      <Paragraph position="0"> A factive such as the verb regret presupposes its complement, but as we have seen, in positive environments, the presupposition is stronger: it is acceptable to defeat a presupposition triggered in a negative environment (2), but is infelicitous to defeat one that belongs to a positive environment (1). Therefore, an appropriate formalization of utterance (3) and the req~fisite pragmatic knowledge will be as shown in (4).</Paragraph>
      <Paragraph position="1">  co e i (y, z) ) (Vu'=, y, z)( regret,&amp;quot; (=, come(y, z)) -* corned(y, z) ) The stratified semantic tableau that corresponds to theory (4) is given in figure 2. The tableau yields two model schemata (see figure 3); in both of them, it is defeasibly inferred that Mary came to the party. The model-ordering relation &lt; establishes m0 as the optimistic model for the theory because it contains as much information as ml and is easier to defeat.</Paragraph>
      <Paragraph position="2"> Model m0 explains why Mary came to the party is a presupposition for utterance (3).</Paragraph>
      <Paragraph position="3">  &amp;quot;~regrets(john, come(mary, party)) (Vx, y, z)(-~regrets(x, come(y, z) ) ---* corned(y, z) ) (Vx, y, z)(regrets(x, come(y, z)) --* comei(y, z)) I -.regrets(john, come(mary, party)) -- corned(mary, party) regrets(john, come(mary,party)) --* comei(mary, party) regrets(john, come(mary, party)) corned(mary, party) u-closed -.regrets(john, come(mary, party)) come i(mary, party)</Paragraph>
      <Paragraph position="5"> Consider utterance (5), and its implicatures (6).</Paragraph>
      <Paragraph position="6"> (5) John says that some of the boys went to the theatre.</Paragraph>
      <Paragraph position="7"> (6) Not {many/most/all} of the boys went to the  theatre.</Paragraph>
      <Paragraph position="8"> An appropriate formalization is given in (7), where the second formula captures the defeasible scalar implicatures and the third formula reflects the relevant semantic information for all.</Paragraph>
      <Paragraph position="10"> The theory provides one optimistic model schema (figure 4) that reflects the expected pragmatic inferences, i.e., (Not most/Not many/Not all) of the boys went to the theatre.</Paragraph>
      <Paragraph position="11">  Assume now, that after a moment of thought, the same person utters: (8) John says that some of the boys went to the theatre. In fact all of them went to the theatre. null By adding the extra utterance to the initial theory (7), uttered(went(ail(boys),theatre)), one would obtain one optimistic model schema in which the conventional implicatures have been cancelled (see figure 5).</Paragraph>
    </Section>
    <Section position="2" start_page="147" end_page="147" type="sub_section">
      <SectionTitle>
3.2 Complex utterances
</SectionTitle>
      <Paragraph position="0"> The Achilles heel for most theories of presupposition has been their vulnerability to the projection problem. Our solution for the projection problem does not differ from a solution for individual utterances.</Paragraph>
      <Paragraph position="1"> Consider the following utterances and some of their associated presuppositions (11) (the symbol t&gt; precedes an inference drawn on pragmatic grounds):  (9) Either Chris is not a bachelor or he regrets that Mary came to the party.</Paragraph>
      <Paragraph position="2"> (10) Chris is a bachelor or a spinster.</Paragraph>
      <Paragraph position="3"> (11) 1&gt; Chris is a (male) adult.</Paragraph>
      <Paragraph position="4">  Chris is not a bachelor presupposes that Chris is a male adult; Chris regrets that Mary came to the party presupposes that Mary came to the party. There is no contradiction between these two presuppositions, so one would expect a conversant to infer both of them if she hears an utterance such as (9). However, when one examines utterance (10), one observes immediately that there is a contradiction between the presuppositions carried by the individual components. Being a bachelor presupposes that Chris is a male, while being a spinster presupposes that Chris is a female. Normally, we would expect a conversant to notice this contradiction and to drop each of these elementary presuppositions when she interprets (10).</Paragraph>
      <Paragraph position="5"> We now study how stratified logic and the model-ordering relation capture one's intuitions.  An appropriate formalization for utterance (9) and the necessary semantic and pragmatic knowledge is given in (12).</Paragraph>
      <Paragraph position="7"> come i (y, z ) ) Besides the translation of the utterance, the initial theory contains a formalization of the defeasible implicature that natural disjunction is used as an exclusive or, the knowledge that Mary is not a name for males, the lexical semantics for the word bachelor, and the lexical pragmatics for bachelor and regret.</Paragraph>
      <Paragraph position="8"> The stratified semantic tableau generates 12 model schemata. Only four of them are kept as optimistic models for the utterance. The models yield Mary came to the party; Chris is a male; and Chris is an adult as pragmatic inferences of utterance (9).</Paragraph>
      <Paragraph position="9">  Consider now utterance (10). The stratified semantic tableau that corresponds to its logical theory yields 16 models, but only Chris is an adult satisfies definition 2.2 and is projected as presupposition for the utterance.</Paragraph>
    </Section>
    <Section position="3" start_page="147" end_page="148" type="sub_section">
      <SectionTitle>
3.3 Pragmatic inferences in sequences of
utterances
</SectionTitle>
      <Paragraph position="0"> We have already mentioned that speech repairs constitute a good benchmark for studying the genera- null tion and cancellation of pragmatic inferences along sequences of utterances (McRoy and Hirst, 1993). Suppose, for example, that Jane has two friends --John Smith and John Pevler -- and that her roommate Mary has met only John Smith, a married fellow. Assume now that Jane has a conversation with Mary in which Jane mentions only the name John because she is not aware that Mary does not know about the other John, who is a five-year-old boy. In this context, it is natural for Mary to become confused and to come to wrong conclusions. For example, Mary may reply that John is not a bachelor. Although this is true for both Johns, it is more appropriate for the married fellow than for the five-year-old boy. Mary knows that John Smith is a married male, so the utterance makes sense for her. At this point Jane realizes that Mary misunderstands her: all the time Jane was talking about John Pevler, the five-year-old boy. The utterances in (13) constitute a possible answer that Jane may give to Mary in order to clarify the problem.</Paragraph>
      <Paragraph position="1"> (13) a. No, John is not a bachelor.</Paragraph>
      <Paragraph position="2"> b. I regret that you have misunderstood me.</Paragraph>
      <Paragraph position="3"> c. He is only five years old.</Paragraph>
      <Paragraph position="4"> The first utterance in the sequence presupposes (14).</Paragraph>
      <Paragraph position="5"> (14) I&gt; John is a male adult.</Paragraph>
      <Paragraph position="6"> Utterance (13)b warns Mary that is very likely she misunderstood a previous utterance (15). The warning is conveyed by implicature.</Paragraph>
      <Paragraph position="7"> (15) !&gt; The hearer misunderstood the speaker.</Paragraph>
      <Paragraph position="8"> At this point, the hearer, Mary, starts to believe that one of her previous utterances has been elaborated on a false assumption, but she does not know which one. The third utterance (13)c comes to clarify the issue. It explicitly expresses that John is not an adult. Therefore, it cancels the early presupposition (14): (16) ~ John is an adult.</Paragraph>
      <Paragraph position="9"> Note that there is a gap of one statement between the generation and the cancellation of this presupposition. The behavior described is mirrored both by our theory and our program.</Paragraph>
    </Section>
    <Section position="4" start_page="148" end_page="148" type="sub_section">
      <SectionTitle>
3.4 Conversational implicatures in indirect
</SectionTitle>
      <Paragraph position="0"> replies The same methodology can be applied to modeling conversational impIicatures in indirect replies (Green, 1992). Green's algorithm makes use of discourse expectations, discourse plans, and discourse relations. The following dialog is considered (Green, 1992, p. 68): (17) Q: Did you go shopping? A: a. My car's not running.</Paragraph>
      <Paragraph position="1"> b. The timing belt broke.</Paragraph>
      <Paragraph position="2"> c. (So) I had to take the bus.</Paragraph>
      <Paragraph position="3"> Answer (17) conveys a &amp;quot;yes&amp;quot;, but a reply consisting only of (17)a would implicate a &amp;quot;no&amp;quot;. As Green notices, in previous models of implicatures (Gazdar, 1979; Hirschberg, 1985), processing (17)a will block the implicature generated by (17)c. Green solves the problem by extending the boundaries of the analysis to discourse units. Our approach does not exhibit these constraints. As in the previous example, the one dealing with a sequence of utterances, we obtain a different interpretation after each step. When the question is asked, there is no conversational implicature. Answer (17)a makes the necessary conditions for implicating &amp;quot;no&amp;quot; true, and the implication is computed. Answer (17)b reinforces a previous condition. Answer (17)c makes the preconditions for implicating a &amp;quot;no&amp;quot; false, and the preconditions for implicating a &amp;quot;yes&amp;quot; true. Therefore, the implicature at the end of the dialogue is that the conversant who answered went shopping.</Paragraph>
    </Section>
  </Section>
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