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<Paper uid="C86-1119">
  <Title>apos;TOWARDS DISCOURSE-0RIENTED NONMONOTONIC SYSTEM</Title>
  <Section position="4" start_page="0" end_page="504" type="metho">
    <SectionTitle>
NONMONOTONICITY
IN DISCOURSE UNDERSTANDING
</SectionTitle>
    <Paragraph position="0"> q~o show the universality of nonmonotonicity in a natural language 5 we shall present a number of examples concerning various linguistic phenomena commonly occurring in a discourse.</Paragraph>
    <Paragraph position="1"> One should be aware that analogous treatment of such different concepts as, for instance, anaphora and presupposition is inappropriate.</Paragraph>
    <Paragraph position="2"> Anaphora, as well as quantification or negation are purely surface phenomena. One must resolve ~them while processing a discourse, but their solutions lead to conclusions describing the discourse rather, than the external world under consideration. For this reason we shall refer PSo those conclusions as surface conclusions.</Paragraph>
    <Paragraph position="3"> Presupposition, on the other hand, as well aS time line COnStruction, conditionals or various conversational rules, concerns conclusions describing directly the world being represented by a discourse. Vge shall refer to those conclusions as .~eneral conclusions.</Paragraph>
    <Paragraph position="4"> Our purpose is not to review all the linguistic phenomena dealing with nonmonotonicity, but to demonstrate that  (i) both kinds of conclusions are subject to invalidation, (ii) canceliable conclusions of both types can  be supported either by semantic or pragmatic sources.</Paragraph>
    <Paragraph position="5"> This leads to an important observation that nonmonotonicity exists on various levels of discourse understanding, viewing both processing method and data to be processed.</Paragraph>
    <Paragraph position="6"> Surface conclusions The following examples of pronoun anaphora and quantification show that semantic-based as well as progmatic-based surface conclusions can be invalidated.</Paragraph>
    <Paragraph position="7"> Example i (pronoun anaphora) (i) The Vice-President entered the President's office. He was nervous and clutching his briefcase.</Paragraph>
    <Paragraph position="8">  &amp;quot;l~his example is from (Ascher, 1984). There are semantic reasons supporting the conclusion that the Vice-President is the one who is nervous given the information that he has a meeting with  the President. &amp;quot;I'his conclusion can be, however, overturned by adding (2) After all, he couldn't fire the Vice-President without making trouble for himself with the chairman of the board.</Paragraph>
    <Paragraph position="9"> Example 2 (pronoun anaphora) (3) Peter' WaS sitting in a room. When John entered the room he seemed nervous.</Paragraph>
    <Paragraph position="10"> Although there are two possible referents of &amp;quot;he&amp;quot; in (3), it is pragmatically well motivated that &amp;quot;he&amp;quot; refers to &amp;quot;Peter&amp;quot;, This follows from Gricels Cooperative Principle. Assuming that the speaker is obeying it, he should replace (5) by the unmistakable (4) Peter was sitting in a room. Entering the  room, John seemed nervous.</Paragraph>
    <Paragraph position="11"> if it were the case that John had been nervous. lqeverthelesm, this preferred coreference is invalidated if (4) is extended to  (5) Peter was sitting in a room. When John entered the room he seemed nervous. He was afraid of Peter.</Paragraph>
    <Paragraph position="12"> (quantification) (6) There are three men in a room. Every man loves a woman, ~here are clearly two possible paraphrases of (6): (?) &amp;quot;Phere are three men in a room. q?here is a woman such that she is loved by each of them, (8) There are three men in a room. For each  man there is a woman such that he loves her.</Paragraph>
    <Paragraph position="13"> Applying his &amp;quot;ordering principles&amp;quot;, based on the observation that humans are used to handle information from left to right, IIintikka in (Ilintikka, 1977) convincingly suggests that (8) is pragmatically preferred reading for (6). Nevertheless, this conclusion may be overturned, lPor instance, it (6) is extended to  (9) &amp;quot;l~here are three men in a room. Every man loves a woman. Her name is Melinda.</Paragraph>
    <Paragraph position="14"> Example 4: (quantification) (10) A rifle has been given to all soldiers,  From among two possible readings of (10), the one asserting that different rifles have been given to different sotdiers should be semantically preferreddeg But this interpretation is immediately inv~lidated when (10) is replaced by  (11) A rifle has been given to all soldiers. It has turned out to be broken.</Paragraph>
    <Paragraph position="15"> General conclusions 'l~he following examples of presupposition illustrate that semantic-based as well as pragmatic-based general conclusions are subject to cancellation.</Paragraph>
    <Paragraph position="16"> (presupposition) (3.2) John regrets that he didn't win the prize. (12) presupposes that John did not winthe prize. Nevertheless, this general conclusion is immediately invalidated when (12) is extended to ed to (3.3) John regrets that he didn't win the prize. In fact, he doesn't know that he did.</Paragraph>
    <Paragraph position="17"> Example 6_ (presupposition) (24) &amp;quot;If I had money I would buy a rifle to defend yeu from the Wolf&amp;quot;, Red Riding Hood maid to her Grrandmother.</Paragraph>
    <Paragraph position="18"> (14) presupposes that RRH had no money.</Paragraph>
    <Paragraph position="19"> This follows from the pragmatic rules of interpretation of counterfactuals in English. &amp;quot;\]2he cancel~ ability of this conclusion is easily seen, if (14) is extended to (15) &amp;quot;If I had money I would buy a rifle to defend you from the W'olf&amp;quot;, RRH said to her CTrandmother. In fact, RRH WaS cheating her. 5he had money, but she wanted to buy  herself a new dress.</Paragraph>
    <Paragraph position="20"> According to the presented examples, nonmonotonicity is not a local phenomenon. It exists on various levels of discourse analysis. It seems, therefore, that no high quality discourse understanding system can i~nore this fact.</Paragraph>
  </Section>
  <Section position="5" start_page="504" end_page="505" type="metho">
    <SectionTitle>
q?OWARDS A DI~SCOURSE-ORIEN'J?ED
NONMONOG)ONIC FORMALISM
</SectionTitle>
    <Paragraph position="0"> Although a great number of various nonmonotonic (nm, for short) formalisms can be found in AI literature, none of them seems to be fully appropriate for the purpose of discourse understanding. In our opinion, only default logic pare tially captures the expressive power of natural language. \]Deriving from Minsky's frame concept, this formalism has turned out to be useful for various natural language applications (see (Dunin-K~plicz, 1984), (Mercer, Reiter, 1984).</Paragraph>
    <Paragraph position="1"> Default logic has been introduced by Relier in (P.eiter, 1980) to model default reasonin_q, i.e., the drawing of plausible conclusions from incomplete information in the absence of evidence to the contrary, f typical example of default reasoning is the inference rule &amp;quot;&lt;Pypically birds fly&amp;quot;. If &amp;quot;l~weety is e bird, then in the absence of evidence to the contrary, we normally assume that q~weefy flies. But we are prepared to reject this conclusion, if we learn theft (Dweety is a pinguiru In default logic the rule about birds is represen\[ed by the following default:</Paragraph>
    <Paragraph position="3"> with the intended interpretation: &amp;quot;for each individual x, if x is a bird and i{ is consistent to assume that x flies, then it may be assumed that x flies&amp;quot;.</Paragraph>
    <Paragraph position="4"> In default logic lhe world under consideration is represented as a default the~, i.e. a pair consisting of a set of first-order formulae, the axioms of the theory, and a set of defaults. Defaults extend the information contained in axioms by sanctioning plausible, but not necessarily true, conclusions.</Paragraph>
    <Paragraph position="5"> A set of formulae derivable from a given default theory is; called an extension of the theory and is interpreted as a set of beliefs about the world being *h~delled. (see (Relier, 3_980) fop details).  Specifying a nm discourse-oriented formalism is a difficult problem. &amp;quot;\])he first step is to determine all its relevant properties. In this section we shall try to accomplish this point and to discuss some weaknesses of default logic in this respect.</Paragraph>
    <Paragraph position="6"> The first problem is to choose an appropriate standard logic as a basis of the constructed system. Although the majority of existing nm formalisms are based on classical first-order logic, it is well recognized that to capture the structure of natural languages, at least intensional logic, preferable with tense operettors, is required. It should be, however, stressed that for computational reasons some compromise between adequacy and simplicity is necessary.</Paragraph>
    <Paragraph position="7"> The next step is to add a nonmonotonic deductive structure to the chosen monotonic logic. This amounts to the following task. Given a theerr A, i.e., a set of formulae describing relevant information about a world, determine a set E(A) of conclusions nonmonotonically derivable from A. The general idea is to identify this set with the set of conclusions monotonically derivable from some extension of A. For this reasonlD(A) is called an extension of A, and is interpreted as the set of plausible conclusions about the world under consideration.</Paragraph>
    <Paragraph position="8"> Defining a language and nm deductive structure, determines a nm system. But to make the system applicable for discourse processing, a number of additional factors should be taken into consideration.</Paragraph>
    <Paragraph position="9"> ~irst, a semantics mus\[ be specified. In particular, a model regarded as a nm description of a real world under consideration should be defined.</Paragraph>
    <Paragraph position="10"> Second, a method of determining whether a conclusion can be inferred from a given set of premises should be specified. Because nm derivability depends not only on what can be proved, but also on what cannot be proved, there are technical problems involved here. In particular, even if the system is based on semi-decidable first-order logic, its proof theory is generally undecidable. &amp;quot;\])his means that some kind of heuristics is necessary, and the system will sometimes arrive at mistaken conclusions.</Paragraph>
    <Paragraph position="11"> Nevertheless, it is often sufficient to consider only models with finite domains limited to the individuals explicitely occurring in the discourse. In such a case, the logic we are dealing with is, in fact, the propositional one. &amp;quot;I~he nm formalism based on propositional logic is, of course, decidable.</Paragraph>
    <Paragraph position="12"> &amp;quot;l~hird, belief___.~s \[evision~ that is a method of reorganizing world model when new information leads to inconsistency should be specified. (\['his very difficult problem has been marginally treated in the most of existing nm systems, On the other hand, since each discourse utterance modifies the actual world model, beliefs revision seems one of the central problems of discourse analysis.</Paragraph>
    <Paragraph position="13"> Fourth, the existence of extensions should be guaranteed. Although this demand seems obvious, it iS not satisfied in many existing nm formalisms, in particular~ in Reite~s default logic, An example of a discourse, whose representation in lqeiter's system lacks an extension, can be found in (Lukaszewicz, 1984). &amp;quot;l~his paper pre~sents also an alternative formalization of default logic which satisfies the above postulated property. null Fifth, the system should ~ model common sense reasoning. In terms of extension, this means that such an extension should contain those discourse-connected conclusions which would be drawn by humans. In our opinion, none of existing nm formalisms fully captures this requirement. The detailed discussion of this hypothesis can be found in (Lukaszewicz, 1986).</Paragraph>
    <Paragraph position="14"> In the majority of nm systems the notion of an extension is defined in a way admitting the existfence of many different extensions for a given theory, q~his poses the question of how to define the set of conclusions derivable from such a theory. 'l~here are two possibilities. First, to view each extension as an alternative set of beliefs one can hold about a world under consideration.</Paragraph>
    <Paragraph position="15"> In fact, this solution has been adopted in default logic. Second, to identify the set of conclusions with the intersection of all extensions. Both solutions are reasonable but have different interpretations, q~he first represents what an agent beliefs about a world, the second, wh~t an outside observer would know about the agent~ beliefs, given the set of the agent's premises about the world.</Paragraph>
    <Paragraph position="16"> In our opinion, the second solution is better motivated in discourse processing, q~his follows from the fact that both the speaker' and the hearer try to achieve a common representation of a discourse. &amp;quot;l~his would be impossible, if each of them accepted a different extension.</Paragraph>
  </Section>
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