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<Paper uid="J91-2003">
  <Title>Semantics of Paragraphs Wlodek Zadrozny *</Title>
  <Section position="6" start_page="204" end_page="206" type="concl">
    <SectionTitle>
7. Conclusions
</SectionTitle>
    <Paragraph position="0"> We hope that the reader has found this paper coherent, and its topic--the correspondence between paragraphs and models--interesting. Our strategy was to divide the  Computational Linguistics Volume 17, Number 2 subject into three subtopics: a theory of anaphora, which corresponds to the logical theory of equality in p-models; a theory of background knowledge, expressed as the logical theory of reference in the three-level semantics; and principles of communication encoded in metarules. These principles include Gricean maxims and the semantics of cohesion, and specify a model theory for the three-level semantics. The framework resulting from putting these theories together is computational, empirical, and verifiable (even if incomplete); furthermore, it has strong links to already existing natural language processing systems. In particular, the new logical level--the referential level--is exemplified by on-line dictionaries and other reference works, from which we extract background information about defaults and plausibility rankings.</Paragraph>
    <Paragraph position="1"> We also hope that the reader would be inclined to share our belief that natural language text can be properly and usefully analyzed by means of a three-level semantics that includes an object level, a metalevel, and a referential level. We believe that the coherence of an essay, a paper, or a book can be described by an extension of our theory. The work of van Dijk and Kintch (1983) on &amp;quot;macrostructures&amp;quot; could probably form the basis for such an expansion. Similarly, much of the abovementioned work by Hobbs, Webber, Grosz, and Sidner can be incorporated into this framework.</Paragraph>
    <Paragraph position="2"> Our main intention was to demonstrate that formal notions of background knowledge can be used to * define coherence, make it semantically distinct from mere consistency, and link it formally with the notion of a topic; * define a class of p-models--logical models of paragraphs; * provide a semantics for &amp;quot;but&amp;quot; (which exemplifies our understanding of grammatical cohesion); * express the Gricean maxims formally, and use them in a computational model of communication (which seems to contradict Allen 1988, p. 464).</Paragraph>
    <Paragraph position="3"> Moreover, we tried to convince the reader that paragraph is an important linguistic unit, not only because of its pragmatic importance exemplified by coherence and links to background knowledge, but also because of its role in assignment of syntactic structures (viz. ellipsis) and in semantics (viz. its possible role in evaluating semantic representations).</Paragraph>
    <Paragraph position="4"> A great many issues have been omitted from our analysis. Thus, although we are aware that anaphora resolution and consistency depend on previously processed text, the problem of connecting a paragraph to such text has been conveniently ignored. Notice that this doesn't make our thesis about paragraphs being units of semantic processing any weaker, we have not claimed that paragraphs are independent. The questions of how to translate from natural language to a logical notation needs a lot of attention; we have merely assumed that this can be done. Continuing this list, we have accepted a very classical theory of meaning, given by Tarski: the truth is what is satisfied in a model. This theory should be refined, for instance by formalizing Lakoff's (1987) concept of radial categories, and proposing mechanisms for exploiting it. By the same token, the concept of reference has to be broadened to include iconic (e.g., visual and tactile) information. And certainly it would be .nice to have a more detailed theory describing the role of the metalevel. In particular, we can imagine that the simple structure of a collection of set theoretic formulas can be replaced by something more interesting. We leave this as another open problem.</Paragraph>
    <Paragraph position="5"> We have shown that it is possible to develop a formal system with an explicit relationship between background knowledge and text, showing mechanisms that take  Zadrozny and Jensen Semantics of Paragraphs advantage of preference, coherence, and contradiction (the reality of these phenomena has never been disputed, but their semantic functions had not been investigated). We should also mention that we have also begun some work on actually checking the empirical validity of this model (cf. e.g. Braden-Harder and Zadrozny 1990), using on-line dictionaries (LDOCE and Webster's) as the referential level. We know, of course, that existing dictionaries are very imperfect, but (1) they can be accessed and used by computer programs; (2) they are getting better, as they are very systematically created with help of computers (see Sinclair 1987 for an account of how COBUILD was constructed); (3) obviously, we can imagine useful new ones, like a Dictionary of Pragmatics; (4) we believe that we can explore the new inference mechanisms even in such unrefined environments.</Paragraph>
    <Paragraph position="6"> Although the scheme we have proposed certainly needs further refinement, we believe that it is correct in two of its most important aspects: first, in the separation of current paragraph analysis (the object theory) from background information (the referential level); and second, in asserting that the function of a paragraph is to allow the building of a model of the situation described in the paragraph. This model can be stored, maybe modified, and subsequently used as a reference for processing following paragraphs.</Paragraph>
    <Paragraph position="7"> Finally, the paper can be viewed as an argument that the meaning of a sentence cannot be defined outside of a context, just as the truth value of a formula cannot be computed in a vacuum. A paragraph is the smallest example of such a context--it is &amp;quot;a unit of thought.&amp;quot;</Paragraph>
  </Section>
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