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<Paper uid="C86-1041">
  <Title>SITUAT\]Or~JA L</Title>
  <Section position="4" start_page="174" end_page="174" type="metho">
    <SectionTitle>
3. Formal Theory of Presupposition
</SectionTitle>
    <Paragraph position="0"> We are concerned in this section with formalizing the notion of presupposition within the framework of SS.</Paragraph>
    <Paragraph position="1"> Our theory is a little different than the version presented In Barwise and P(~rrv (1983) or Barwise (1985), for we Introduce some modifications in the theory so that we can accomodate presupposition in natural language, More specifically, our formalism assumes a non-monotonic relation between events called plausibility orderin9, as opposed to the monotonic 'persistence' relation assumed in Barwise and Perry (198\]). As a consequence, our theory is not only capable of treating presupposition In an elegant way, but is able to deal with default and autoepistemic reasonings as well.</Paragraph>
  </Section>
  <Section position="5" start_page="174" end_page="175" type="metho">
    <SectionTitle>
3,1 Outline of Situation Semantics
</SectionTitle>
    <Paragraph position="0"> |n this section we review briefly some basic points of SS.</Paragraph>
    <Paragraph position="1"> Here we mainly follow the formalism recently introduced in Barwise (1984, 1985) rather than the original one in Barwise and Perry (1983) since it is simpler and more comprehensive.</Paragraph>
    <Paragraph position="2"> The most attractive idea of SS is the shift of attention from 'truth conditions to 'information conditions'. $5 can be said to be an attempt at explicating the nature of language focussing on the following two aspects:  (1) under what conditions a sentence can be used to convey information.</Paragraph>
    <Paragraph position="3"> (2) what information the sentence conveys under those conditions.</Paragraph>
    <Paragraph position="4">  A situation S can contain information in virtue of some constraint the holds between types of situations. We denote types of situa.tions as S, S' .... We write s:S If situation s is S, A type of situation S is realized if there is a real situation s such that, s:S, There are three categories of objects across situations: namely, individua.~ denoted as: a, b .... ; relations: r, s .... : and Iocat~ L 1 .... Corresponding to each category, there are purely abstract, sort or dummy. entities called indeterminates that stand proxy for genuine objects. We represent indeterminates by So, $b .... ; $r. $r' .... ; $\], $1' .... Anehorin 9 is a function that assigns individuals, relations, and locations to the indeterminates.</Paragraph>
    <Paragraph position="5"> For example, the following is a type of situation where a is in relation R to be b: &amp;quot; S - ($s\]ln $s: at $1: R. a, b: 1\] where R, a, and b denote some respectively specific relation and individual, and $s and $1 are indeteminates.</Paragraph>
    <Paragraph position="6"> Given an anchor that assign 1' to $1, the following can be a real situation where a and b are in the same relation R: in s: at \]' : R, a, b; 1.</Paragraph>
    <Paragraph position="7"> A Constraint is a relation holding between types of situation, S -&gt; ~r, we read it as S involves S'. Intuitively this means that if S is realized, that is, there is a real situation s:S, then there is a real situation s' such that s':S'.</Paragraph>
    <Paragraph position="8"> Given any constraint and any anchor f for some or all of the parameters in S, the result of replacing the parameters by appropriate values will give rise te an actual constraint. To wit, if</Paragraph>
    <Paragraph position="10"> is actual, then so is S(f) * S'(f).</Paragraph>
    <Paragraph position="11"> We call the latter an instance of the former, t4ere we can extend the involves relation to a three-place relation as</Paragraph>
    <Paragraph position="13"> whhere B is the backcjround conditions on the situations in which constrain(between S and S' holds.</Paragraph>
    <Paragraph position="14"> Let R be n*l-place relation taking n+l objects al ..... an*l. Suppose parameter-free type S - \[$slin $s: R, al ..... an, Sam1; i\] (l - 0 or 1) is realized. \]f $an*l Js an environment constant, that is, it Is fixed in some way, then it only takes n objects and a truth value to determine the same proposition.</Paragraph>
    <Paragraph position="15"> In the above mentioned remark of involves relation, B corresponds to an environment constant. Parametric Information is relative to some assignment to parameters in a type of situation.</Paragraph>
    <Paragraph position="16"> Barwise (19B~) uses the two distinct terms for 'meaning', namely, situation meaning and situation-type meanin 9, The former is used for talking about the meaning of particular situation, while tile latter Is for the meaning of a certain tvPe of situation. We can identlfv situation meaning with information, so a particular state of affairs has a situation meaning. And understanding 4he situation meaning of particular mental state requires an understanding of the situation-type meaning of that type of state, as it normally functions in the external life of the agent, Here If we take into account a congnitive state of the agent we need two parallel sets of constraints, one on some activity A and the other on cognitive activity about A. '~, More formally, let #S, #S' .... be types of situation of the mental state for a fixed agent. Also tile agent is able to construct #0: #S ~ #S', Usually we assume the following diagram of constraints between mental situations and situations,  Here we assume there exists a homomorphJsm F from a collection of types of situation to a collection of corresponding types of situation of mental states, namely there is an F such that F(s) - flS, This generates that an agent can interpret real situations in various ways. Thus involve relation relation between real situations and mental si%uations can be regarded as an inverse of F, namelv F-'(#S) - S. According to the above mentioned definitions we can eostruct some types of situation of mental state in the effective way, If there is no agent, as is the case in a knowledge system, #S is considered as self-referential statement on fie. We think its foundations are more or less cotroversial, \]n SS an inference is an activity that attempts to use facts about the world to extract additional information, information implicit in the facts, A sound inference then is the appropriate chain of information.</Paragraph>
    <Paragraph position="17"> 3,2. Formalism of Modified SS There are two main features to be taken into account when providing an appropriate definition for presupposition in natural language, One thing is to accommodate a lack of complete information. The other thing is to accommodate the agent's belief context, fhe former is called 'default' and the latter autoepistemic' respectively. Although they appear to be independent of each other in their involvement in presupposition, our formalism is capable of dealing with both of them. Our modification of SS is mainly concerned with revising the involves relation between situations. As we said at the outset of this chapter, instead of the partial ordering of information, namely, ~.nccA~e assumed in the original version of Barwise and Perry (1983), we shah introduce the plausibility ordering, -(, satisfying the following conditions:  (1) A -{ B implies Ac_B (=_ is an ordinary monotonic relation), (Z) A ~ A (reflexivity), (3) A -( B and B -( C impllies A -C C (transitivitv),  Although the exact nature of' the plausibility ordering is rather vague, its intuitive meaning is that any information, whether correct or incorrect in the actual, is of use in the model for SS.</Paragraph>
    <Paragraph position="18"> For instance, we presuppose b y__defau\]t in a certain cognitive state towards the world. Presuppositions are appropriate interpretations of information depending on the agent even if it includes both information and misinformation, We now revise the theory of constraints on the basis of the plausible chain of information introduced above.</Paragraph>
    <Paragraph position="19"> We assume the following conditions on the modified involves relation:  (1) If B is fixed, then if $1 $ S2/B and 62 ~ SS/B then $1 ~ SS/B, (2) If S * S'/B and B'&amp;quot;( B, where B' is co_ompatible with S, then S .~ S'/B'.</Paragraph>
    <Paragraph position="20"> (\]) If S ~) S'/B and B'-( B, where B' is not compatible with S, then S e -S'/B'.</Paragraph>
    <Paragraph position="21"> (4) If S ~ S'/B then S is c.ompatible with B, that is, SUB is coherent.</Paragraph>
    <Paragraph position="22"> (5) If S * S-~/B and f is a coherent anchor for some of the parameters of B. then S(f) ~ S'(f)/B(f).</Paragraph>
    <Paragraph position="23"> (6) If S ~ S'/B where B has no parameters, and if B is realized by some real situation, then S ~ S' is actual, (1) If S e S'/B and B-( 8', then S ~ S'/B' or S ~  It is to be noticed that condition (7) means that certain parametric constraints can affect a truth condition as information increases. In the original approach Jn SS it is nontrivial to represent any nonmonotonicitv in the effective way.</Paragraph>
    <Paragraph position="24"> We now define presupposition in the framework of SS as  A 4 -B/C if #A~#B = where A, B denote type of situation of the world and IIA, t/B, types of situation of the agent's mental states relative r.g A, B.</Paragraph>
    <Paragraph position="25"> In the definil;ion we of course assume the involve relation satisfies'the above mentioned seven conditions. And if there is no agent in the krlowledge sVstem, #A is part of' A since any knowledge base is itself coherent structure in the I~ruth eondition. In such a case presuppositions correspond to the default as loog as we adopt ordinary inference system.</Paragraph>
    <Paragraph position="26"> We can formalize va|-ious t~pes ill presuppositions bv making use el' this definition. For example, this definition predicts we can do valid inference from rnJsinformation arid do invalid inference from correct information. The inferences carried out by human being have manv demonstrai:ive characters related to tbe cognitive processes of information of the world. Here we shall regard any information to be used bvtbe agent as a presupposition in a certain context, I~. Conclusion I~eehanizing presuppositions in natural language is Lr~e mosl. importanl:, task Fur pragmatics. Fur the sake of partiality or inf'eL'matiun presented in a senLeoce, SS is more suitable than a rllodel-Lheol'etJc selrlaatigs. In eLIr ~,l'eatmeat every information is considered useful tbo~J w(9 dispense with such ae ideal principle as persistence of information.</Paragraph>
  </Section>
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