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<Paper uid="E87-1041">
  <Title>SITUATIONS AND PREPOSITIONAL PHRASES</Title>
  <Section position="3" start_page="259" end_page="260" type="intro">
    <SectionTitle>
COND \[REL car
ARG1 IND
LFOL
LSPEC THE
</SectionTitle>
    <Paragraph position="0"> This schema tells us that IND1 has to be anchored to an individual a that must be a car. The SPEC feature can either be used to pick out the unique car in the described situation or to make a generalized quantifier out of ARG2. The situation schemata are hence open to several interpretations.</Paragraph>
    <Paragraph position="1"> The LOC feature in this schema has the structure: l IND IND2 \] COND {---} The location is tied to a location indeterminate IND2. The COND feature is a set (notice the set brackets) of constraints on IND2. The first one expresses that ND2 must be anchored to a location I that temporally precedes the location that 10 gets anchored to. By convention 10 is always anchored to the discourse location I d. This constraint accounts for the past tense of ran. In the second constraint the semantics of to tells us that 1 must be a curve in space-time that ends at the location of a. The headrelation run in SIT.~ 1 asserts that the individual named Peter is in the state of running along the trajectory 1. An interesting project would be to furnish the domain L of locations with a set of &amp;quot;primitive&amp;quot; relations which could be used to spell out the meaning of the different prepositions. For the moment the only primitive relation on L that has been accounted for in the axiomatizatlon of the structure &lt;S,L,R,D&gt; is &amp;quot;&lt;&amp;quot;, the relation &amp;quot;temporally precedes.&amp;quot; A more precise interpretation of S1T.O 1 is: The relation d,c \[S1T.O1 \] s holds if and only if there exists an anchor g on S1T.~ I'I'PSX~, i.e.</Paragraph>
    <Paragraph position="2"> ~0): ld g(IND2) &lt; g(1 O) andanextensienf ofg that anchorsIND1 such thatf(IND1) is the unique individual such that in s: c(car),f(IND1); 1 such that in s: c(to), gtlND2),f(IND1); I ins: at g(IND2 ): c(run), c(Peter); I Note that relations between locations can easily be extended to include individuals among their arguments. This is done by introducing a function /oc~f from D to L mapping individuals on their locations. A relation r between locations is extended to a relation r' where some of the arguments are individuals by letting: r', .... al, ...; pol ~f r ..... loc.ofla i), ...; pol.  The PP gets here two readings; one as an adjunct and one as an oblique object, but we have omitted the adjunct reading since it isn't natural. The relation lie takes two arguments: ARG1 end ARG3. The indeterminate IND2 must be anchored to a location that temporally precedes the discourse location. IND1 must be anchored to an individual al which is the unique book in the discourse situation, and ~ must be anchored to an indivildual a2 which is the unique table in the discourse situation. SIT.~2.ARG3.COND forces IND5 to be anchored to an individual a3 such that the relation on holds between a3 and a2. The relation lie will hold between al and a3 if al is lying and the locations of al and a3 are the same.</Paragraph>
    <Paragraph position="3"> A precise interpretation is: The relation d,c \[SIT.02\] s holds if and only if there exists an anchor g on SIT.~b2.L(X~, i.e.</Paragraph>
    <Paragraph position="4"> g:lo)-- td g(IND2) &lt; g(l O) and an extension fof g that anchors IND1, IND4 and IND5 such thatf(IND1) is the unique individual such that/n s: c(book),fllND1); 1 andfllND4) is the unique individual such that/n s: c(table),fllND4); 1 such that in s: c(on),/(IND5)j?IND4); 1 in s: at g(IND2): c(lie),f(IND1),f(INDS); I</Paragraph>
  </Section>
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