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<Paper uid="C94-2120">
  <Title>INCREMENTAb INTERPRETATION: APPLICATIONS, THEORY, AND RF, LATIONSHIP TO DYNAMIC SEMANTICS*</Title>
  <Section position="3" start_page="750" end_page="750" type="intro">
    <SectionTitle>
2. Logi(:al Forms to Smnantic Filt;ering
</SectionTitle>
    <Paragraph position="0"> In l)ro(:essing the sent(race A,larg introduced John to Susan, a, word-by-word ;~l)l)roach such as Milward (1992) provides the following logical fornls alTte, r the  li':mh input level rel)res(mtatiotl is apl)ropria.tc for the mealfing ol7 ~n incomplel, e senl;enee, I)eing either ~ propositi(m or a, function into a proposition.</Paragraph>
    <Paragraph position="1"> /n Cha.ter et al. (1990) it is argue(1 tlmt l, he inerementMly derived meanings are not .indged \[br plausibility directly, but instead ~re first tur~ ned into existentially (luantified propositio.s, l,br exa.mp\[e, instead of .ju(lghtg tim plausiiMity of )~x..~y.int:r(Inary, x,y), we judge the plausil~ility of _~(x,q',3(y,T,intr(mary, x,y))) s. This i~ just the proposition Mart introduced something to something using ~ generalized quantilier not~tion or the tbrm Quantitie.r (Variable,R(:stri('tor,Body).</Paragraph>
    <Paragraph position="2"> A|though the lambd:~ exl)ressions are built ul) monotonieMly, word by word, the, l)rOl)ositions \[brined 7Whe version of categorial grammar used is AP. (Sttcgorial C, rmnmar with Associativity.</Paragraph>
    <Paragraph position="3"> ~'\[hc prol)oSil;ion '.P is alw~Lys true. See Chatter et ~tl. (IDg,t) for discussion (ff whether it; is more al)prol)ri~tl:(: to use ~t lit-HItrivial rcsl, rictor.</Paragraph>
    <Paragraph position="4"> from them may need to be retraeted, a.long with all the resulting infi~relmeS. I,'or examl)le, Mart introduced something to something is ina.pl)ropriate if the thml sentence is Marg introduced noone to anybodg. A rough algorithm is as follows:  l. Parse a. new word, Word/ 2. l&amp;quot;orm ~ new lambda expression by eoml)ining the lambda~ exl&gt;ression formed after parsing Wordi_ 1 with the lexieal semantics h)r Word/ 3. Form a. proposition, Pi, by existentia.lly quantit):-. ing over the la.mbda a/)stracted va.riables.</Paragraph>
    <Paragraph position="5"> 4. Assert Pi. If Pi does not ent~dl Pi-1 retraet I)i_ ~md all conclusious made ft:om it s.</Paragraph>
    <Paragraph position="6"> 5. Judge the. phmsilfility of Pi. If iml)hmsible, block  this del:iwlLio,.</Paragraph>
    <Paragraph position="7"> It is worth uoting tht~t the need for retraction is not due to ~x failure to extract the eorrect qeast eolnDlitmenC' propositiotl from the semautic (:ontent of the fragment Mary introduced, 'l'hi~ is due to tim fm:t that it, is I)ossible to find pairs of l)ossible eontinuatious which m:e the negation el each other (e.g. M(rrg introd'ltccd noonc to anybody and Mary inl,'rodltced someone to somebody). The only propositiou comps&gt; tibk', with both a proposition, p, and its negation, ~1 ) is the trivial proposition, &amp;quot;P (see (.:hater et al. for further discussion).</Paragraph>
  </Section>
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