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<Paper uid="P84-1016">
  <Title>QUASI-INDEXICAL REFERENCE IN PROPOSITIONAL SEMANTIC NETWORKS</Title>
  <Section position="1" start_page="0" end_page="0" type="metho">
    <SectionTitle>
QUASI-INDEXICAL REFERENCE IN PROPOSITIONAL SEMANTIC NETWORKS
</SectionTitle>
    <Paragraph position="0"/>
  </Section>
  <Section position="2" start_page="0" end_page="65" type="metho">
    <SectionTitle>
ABSTRACT
</SectionTitle>
    <Paragraph position="0"> We discuss how a deductive question-answering system can represent the beliefs or other cognitive states of users, of other (interacting) systems, and of itself. In particular, we examine the representation of first-person beliefs of others (e.g., the ~/v.~'~ representation of a user'A belief that he himself is rich). Such beliefs have as an essential component &amp;quot;'quasi-indexical pronouns&amp;quot; (e.g., 'he himself'), and, hence, require for their analysis a method of representing these pronominal constructions and performing valid inferences with them. The theoretical justification for the approach to be discussed is the representation of nested &amp;quot;'de ditto&amp;quot; beliefs (e.g., the system's belief that user-I believes that system-2 believes that user-2 is rich). We discuss a computer implementation of these representations using the Semantic Network Processing System (SNePS) and an ATN parser-generator with a question-answering capability.</Paragraph>
    <Paragraph position="1"> I- INTRODUCTION Consider a deductive knowledge-representation system whose data base contains information about various people (e.g., its users), other (perhaps interacting) systems, or even itself. In order for the system to learn more about these entities--to expand its &amp;quot;'knowledge&amp;quot; base--it should contain information about the beliefs (or desires, wants, or other cognitive states) of these entities, and it should be able to reason about them (cf. Moore 1977, Creary 1979, Wilks and Bien 1983, Barnden 1983, and Nilsson 1983: 9).</Paragraph>
    <Paragraph position="2"> Such a data base constitutes the &amp;quot;knowledge&amp;quot; (more accurately, the beliefs) of the system about these entities and about their beliefs.</Paragraph>
    <Paragraph position="3"> Among the interrelated issues in knowledge representation that can be raised in such a context are those of multiple reference and the proper treatment of pronouns. For instance, is the person named 'Lucy' whom John believes to be rich the same as the person named 'Lucy' who is believed by the system to be young? How can the system (a) represent the person named 'Lucy' who is an object of its own belief without (b) confusing her with the person named 'Lucy' who is an object..of. John'~ belief, yet (c) be. ..able to merge its representations of those two people if it is later determined that they are the same? A solution to this problem turns out to be a side effect of a solution to a subtler problem in pronominal reference, namely, the proper treatment of pronouns occurring within belief-contexts.</Paragraph>
    <Paragraph position="4"> i. OUASI-INDICATORS Following Casta~eda (1967: 85). an indic,tot is a personal or demonstrative pronoun or adverb used to make a strictly demonstrative reference.</Paragraph>
    <Paragraph position="5"> and a ouasi-indicator is an expression within a 'believes-that' context that represents a use of an indicator by another person. Consider the following statement by person A addressed to person at time ~ and ~lace ~: A says, &amp;quot;I am going to kill you here now. Person ~, who overheard this, calls the police and says. &amp;quot;A said .to ~ at ~ at A that he* was going to kill him* there* then*.&amp;quot; The starred words are quasi-indicators representing uses by A of the indicators 'I'. 'you'. 'here', and 'now'. There are two properties (among many others) of quasi-indicators that must be taken into account: (i) They occur only within intentional contexts, and (ii) they cannot be replaced salva veritate by any co-referential expressions.</Paragraph>
    <Paragraph position="6"> The general question is: &amp;quot;How can we attribute indexical references to others?&amp;quot; (Casta~eda 1980: 794). The specific cases that we are concerned with are exemplified in the following scenario. Suppose that John has just been appointed editor of Byte. but that John does not yet know this. Further. suppose that, because of the well-publicized salary accompanying the office of Byte'A editor, (1) John believes that the editor of Byte is rich.</Paragraph>
    <Paragraph position="7"> And suppose finally that. because of severe losses in the stock market.</Paragraph>
    <Paragraph position="8"> (2) John believes that he himself is not rich.</Paragraph>
    <Paragraph position="9"> Suppose that the system had information about each of the following: John's appointment as editor, Johnts (lack of) knowledge of this appointment.</Paragraph>
    <Paragraph position="10"> and John's belief about the wealth of the editor.</Paragraph>
    <Paragraph position="11"> We would not want the system to infer (3) John believes that he* is rich because (2) is consistent with the system's information. The 'he himself' in (2) is a quasiindicator, for (2) is the sentence that we use to express the belief that John would express as 'I am not rich'. Someone pointing to John. saying.</Paragraph>
    <Paragraph position="12">  (4) He \[i.e., that man there\] believes that he* is not rich could just as well have said (2). The first 'he' in (4) is not a quasi-indicator: It occurs outside the believes-that context, and it can be replaced by 'John' or by 'the editor of Byte', salva veritare. But the 'he*' in )4) and the 'he himself' in (2) could not be thus replaced by 'the editor of Byte' - given our scenario - even though John is the editor of Byte. And if poor John also suffered from amnesia, it could not be replaced by 'John' either.</Paragraph>
  </Section>
  <Section position="3" start_page="65" end_page="66" type="metho">
    <SectionTitle>
~. REPRESENTATIONS
</SectionTitle>
    <Paragraph position="0"> Entities such as the Lucy who is the object of John's belief are intentional (mental), hence intensional. (Of. Frege 1892; Meinong 1904; Casta~eda 1972; Rapaport 1978, 1981.) Moreover, the entities represented in the data base are the objects of the ~y.~'~ beliefs, and, so, are also intentional, hence intensional. We represent sentences by means of propositional semantic networks, using the Semantic Network Processing System (SNePS; Shapiro 1979), which treats nodes as representing intensional concepts (of. Woods 1975, Brachman 1977, Maida and Shapiro 1982).</Paragraph>
    <Paragraph position="1"> We claim that in the absence of prior knowledge of co-referentiality, the entities within belief-contexts should be represented separately from entities outside the context that might be co-referential with them. Suppose the system's beliefs include that a person named 'Lucy' is young and that John believes that a (possibly different) person named 'Lucy' is rich.</Paragraph>
    <Paragraph position="2"> We represent this with the network of Fig. I.</Paragraph>
    <Paragraph position="3"> Fig. I. Lucy is young (m3) and John believes that someone named 'Lucy' is rich (m12).</Paragraph>
    <Paragraph position="4"> The section of network dominated by nodes m7 and m9 is the system's de ditto representation of John's belief. That is, m9 is the system'~ representation of a belief that John might express by 'Lucy is rich', and it is represented as one of John's beliefs. Such nodes are considered as being in the system's representation of John's i&amp;quot;belief space&amp;quot;. Non-dominated nodes, such as ml4, m12, m15, mS, and m3, are the system's representation of its own belief space (i.e., they can be thought of as the object of an implicit 'I believe that' case-frame; cf. Casta~eda 1975: 121-22, Kant 1787: BI31).</Paragraph>
    <Paragraph position="5"> If it is later determined that the &amp;quot;two&amp;quot; Lucies are the same, then a node of co-referentiality would be added (m16, in Fig. 2).</Paragraph>
    <Paragraph position="6"> Fig. 2. Lucy is young (m3), John believes that someone named 'Lucy' is rich (mlS), and John's Lucy is the system's Lucy (m16).</Paragraph>
    <Paragraph position="7"> Now consider the case where the system has no information about the &amp;quot;content&amp;quot; of John's belief, but does have information that John's belief is about the ~.7_~/.f.~'E Lucy. Thus, whereas John might express his belief as, 'Linus's sister is rich', the system would express it as, '(Lucy system) is believed by John to be rich' (where '(Lucy system)' is the system's Lucy). This is a de re representation of John's belief, and would be represented by node ml2 of Figure 3.</Paragraph>
    <Paragraph position="8"> The strategy of separating entities in different belief spaces is needed in order to satisfy the two main properties of quasi-indicators.</Paragraph>
    <Paragraph position="9"> Consider the possible representations of sentence (3) in Figure 4 (adapted from Maida and Shapiro 1983: 316). This suffers from three major problems. First, it is ambiguous: It could be the representation of (3) or of (5) John believes that John is rich.</Paragraph>
    <Paragraph position="10"> But, as we have seen, (3) and (5) express quite different propositions; thus, they should be separate items in the data base.</Paragraph>
    <Paragraph position="11"> Second, Figure 4 cannot represent (5). For then we would have no easy or uniform way to represent (3) in the case where John does not know that he is named 'John': Figure 4 says that the person (m3) who is named 'John' and who believes m6, believes that that person is rich; and this would be false in the amnesia case.</Paragraph>
    <Paragraph position="12">  &amp;quot;John believes that he* is rich&amp;quot; Third, Figure 4 cannot represent (3) either, for it does not adequately represent the quasi-indexical nature of the 'he' in (3): Node m3 represents both 'John' and 'he', hence is both inside and outside the intentional context, contrary to both of the properties of quasiindicators. null Finally, because of these representational inadequacies, the system would invalidly &amp;quot;'infer&amp;quot;  (6iii) from (6i)-(6ii): (6) (i) John believes that he is rich.</Paragraph>
    <Paragraph position="13"> (ii) he = John (iii) John believes that John is rich.</Paragraph>
    <Paragraph position="14"> simply because premise (6i) would be represented by the same network as conclusion (6iii).</Paragraph>
    <Paragraph position="15">  Rather, the general pattern for representing such sentences is illustrated in Figure 5. The 'he*' in the English sentence is represented by node m2; its quasi-indexical nature is represented by means of node ml0.</Paragraph>
    <Paragraph position="16"> &amp;quot;I Fig. 5. John believes that he* is rich (m2 is the s~stem's representation of John's &amp;quot;'self-concept , expressed by John as 'I' and by the system as 'he*') That nodes m2 and m5 must be distinct follows from our separation principle. But, since m2 is the system's representation of Johnts representation of himself, it must be within the system's representation of John's belief space; this is accomplished via nodes ml0 and m9, representing John's belief that m2 is his &amp;quot;selfrepresentation&amp;quot;. Node m9, with its EGO arc to m2, represents, roughly, the proposition 'm2 is me'. Our representation of quasi-indexical de se sentences is thus a special case of the general schema for de ditto representations of belief sentences. When a de se sentence is interpreted de re, it does not contain quasi-indicators, and can be handled by the general schema for de re representations. Thus, (7) John is believed by himself to be rich would be represented by the network of Figure 4.</Paragraph>
  </Section>
  <Section position="4" start_page="66" end_page="67" type="metho">
    <SectionTitle>
~. INFERENCES
</SectionTitle>
    <Paragraph position="0"> Using an ATN parser-generator with a question-answering capability (based on Shapiro 1982), we are implementing a system that parses English sentences representing beliefs de re or de ditto into our semantic-network representations, and that generates appropriate sentences from such networks.</Paragraph>
    <Paragraph position="1"> It also &amp;quot;recognizes&amp;quot; the invalidity of arguments such as (5) since the premise and conclusion (when interpreted de din,o) are no longer represented by the same network. When given an appropriate inference rule, however, the system  will treat as valid such inferences as the follow-</Paragraph>
  </Section>
  <Section position="5" start_page="67" end_page="67" type="metho">
    <SectionTitle>
~. ITERATED BELIEF CONTEXTS
</SectionTitle>
    <Paragraph position="0"> Our system can also handle sentences involving iterated belief contexts. Consider (10) John believes that Mary believes that Lucy is rich.</Paragraph>
    <Paragraph position="1"> The interpretation of this that we are most interested in representing treats (I0) as the system's de ditto representation of John's de ditto representation of Mary's belief that Lucy is rich. On this interpretation, we need to represent the system'~ John--(John system)--the system's representation of John'~ Mary--(Mary John system)--and the system's representation of John's representation of Mary'~ Lucy--(Lucy Mary John system). This is done by the network of Figure 7. Such a network is built recursively as follows: The parser maintains a stack of &amp;quot;believers&amp;quot;. Each time a belief-sentence is parsed, it is made the object of a belief of the previous believer in the stack. Structure-sharing is used wherever possible. Thus, (II) John believes that Mary believes that Lucy is sweet Fig. 7. John believes that Mary believes that Lucy is rich.</Paragraph>
    <Paragraph position="2"> would modify the network of Figure 7 by adding new beliefs to (John system)'s belief space and tO (Mary John system)'s belief space, but would use the same nodes to represent John, Mary, and Lucy.</Paragraph>
  </Section>
  <Section position="6" start_page="67" end_page="68" type="metho">
    <SectionTitle>
~. NEW INFORMATION
</SectionTitle>
    <Paragraph position="0"> The system is also capable of handling sequences of new information. For instance, suppose that the system is given the following information at three successive times: tl: (121 The system's Lucy believes that Lucy's Lucy is sweet.</Paragraph>
    <Paragraph position="1"> t2: (13) The system's Lucy is sweet.</Paragraph>
    <Paragraph position="2"> t3: (14) The systemIs Lucy = LucyIs Lucy.</Paragraph>
    <Paragraph position="3"> Then it will build the networks of Figures 8-I0, successively. At tl (Fig. 8), node m3 represents the systemts Lucy and m7 represents Lucy's Lucy. At t2 (Fig. 9), m13 is built, representing the system's belief that the system's Lucy (who is not yet believed to be--and, indeed, might not be--Lucy's Lucy) is sweet.\[l\] At t3 (Fig. II), m14 is built, representing the system's new belief that there is really only one Lucy. This is a merging of the two &amp;quot;'Lucy&amp;quot;-nodes. From now on, all properties of &amp;quot;either&amp;quot; Lucy will be inherited by the &amp;quot;'other&amp;quot;, by means of an inference rule for the EQUIV case-frame (roughly, the indiscernibility of id___@enticals).</Paragraph>
    <Paragraph position="4"> It\]We are assumin B that tile system's concept of sweetness (node me) is also the system's concept of (Lucy system)'s concept of sweetness. This assumption seems warranted, since all nodes are in the system's belief space. If the system had reason to believe that its concept of sweetness differed from Lucy's, this could--and would have to-be represented.</Paragraph>
  </Section>
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