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<Paper uid="W91-0220">
  <Title>Presuppositions and Default Reasoning: A Study in Lexical Pragmatics</Title>
  <Section position="4" start_page="233" end_page="235" type="metho">
    <SectionTitle>
4 What Remains
</SectionTitle>
    <Paragraph position="0"> How to apply this method in a practical implementation still needs to be investigated.</Paragraph>
    <Paragraph position="1"> Some of the remaining problems are in the domain of research in Default Logic. Default Logic is not even semi-decidable in the first order case. In the propositional case it is intractable even for syntactically very restricted forms of theories. One issue which has recently become a focus of attention in the default reasoning area is the notion of scope,  that is, when deciding whether the default succeeds, what part of the theory should he investigated for the potentially defeating information. \[Etherington et al., to appear\] The interest in scope is twofold: to make default reasoning more tractable, and the commonly held belief that defaults in general are somewhat localized in their influence. For our purposes here, the sentence presents a very natural scope. It is probably not coincidental that most of the examples given above deal with intrasentential competition among presuppositional triggers and entailments.</Paragraph>
    <Paragraph position="2"> Although this view of scoping can be used to overcome a variety of problems, some of the very (in)famous examples of presupposition deal with noun phrases. Here, we come in contact with referring phrases, which again force us into potentially considering every object in our domain as a possible argument to defeat the default assumption. However, we believe that a proper reading of Grice and an application of Gazdar's epistemic view of communication can provide the needed relief from this problem (although the details have yet to he worked out). In particular, if the speaker uses a particular referring expression in the utterance, then the speaker is suggesting that it is under this description that the information is stored. Thus the speaker is also communicating that he knows the information being communicated is related to this descriptor rather than some other descriptor. Our task of deciding what the speaker is communicating is therefore limited to this descriptor. (This of course requires an epistemic operator that is not omniscient.) This limitation assumes that there is no commonly known synonym for the referring expression (which the speaker would not need to include in the utterance). If common synonyms exist, then we regard this as a problem of knowledge representation, that is, how do we deal with these localized equalities without recourse to a promiscuous equality relation.</Paragraph>
    <Paragraph position="3"> Earlier we suggested that we have been interested in formalizing the notion of presupposition. Inherent in this task is the use of a formal apparatus, in this case, Default Logic. The application of these ideas to the practical situation of lexicon design and use will require some more effort. For example, the lexical presuppositions that have been discussed are attached to particular lexical items. So, for instance, the presuppositions of 'not a bachelor' do not hold for the logically equivalent expression 'not an unmarried adult male' nor does 'female' which logically entails 'not a bachelor' allow the default assumption of 'adult' to hold. In order to prevent these unwanted inferences, we have used guards on the default rules (the LF predicate) to limit them to appropriate contexts.</Paragraph>
    <Paragraph position="4"> Another method would be to allow defaults to enter the inferencing process for limited periods of time rather than being constantly available. How this method compares with the standard view of default rules in a Default Logic remains to be investigated. Once these questions are answered, the attachment of the defaults to lexical items in the lexicon and their proper use in computing the meaning of an utterance can be achieved.</Paragraph>
    <Paragraph position="5"> Lastly, it is of some importance to see what questions can be asked given this view of lexical features. Figure 1 represents a small portion of an ISA hierarchy of some hearer, H. The arcs have been labelled with features and the nodes have been labelled by the term which is associated with the set of features defined by the path from the root node. The deciding criterion for a negated lexeme's meaning is associated with the last feature which labels the last arcs in the paths from the root node to the negated and unnegated lexical nodes. In this instance the non-presuppositional feature is MARRIED -- &amp;quot;-,MARRIED. The emboldened path in Figure 1 represents the preferred interpretation of 'not a bachelor', that is, 'a married adult male'. Given this simplistic taxonomic structure two questions arise. Can the lexicon be organized in such a way that the  presuppositional and non-presuppositional features are given implicitly by the structure rather than having to be explicitly represented? Negation would normally modify only the last arc. Given that this type of representation can be achieved are there any interesting answers that arise from the structure, that is, are presuppositions given by the way we structure our linguistic (world) knowledge?</Paragraph>
  </Section>
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