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<Paper uid="C86-1082">
  <Title>Quantification in Ordinary English', In: Hintikka, J.,</Title>
  <Section position="2" start_page="0" end_page="347" type="metho">
    <SectionTitle>
2. Case-based Treatments
</SectionTitle>
    <Paragraph position="0"> Among natural language processing systems which attempt to incorporate spatial information, the following strategy seems to prevail. Directional or locative modifiers are treated either as corresponding to slots in case &amp;quot;/rames in the canonical lexical representations of verbs (cf. Celce 1972, Hendrix, Thompson and Slocum 1973), or as corresponding to conceptual cases in the (meta-linguistic) conceptualization of actions (Schank 1975).</Paragraph>
    <Paragraph position="1"> Case based approaches to the semantics of directional modifiers can be characterized as weakly compositional in the following sense: In a verb phrase such as fly to Chicago the prepositional phrase contributes semantically the meaning of the NP Chicago ' as the directional or locative goal of the action associated with ~.he verb phrase. However, the directional preposition to itself does not make a semantic contribution at all to the meaning of the verb phrase as a whole. Instead, to merely serves as a syntactic marker for a semantic entity, namely a locative or directional case whose meaning cannot be separated from, but rather is an integral part of a given verb frame or conceptual structure. By contrast, the semantics of directional modifiers that I will be advocating in this paper is strongly csmpositional in the sense that directional prepositions serve as autonomous syntactic and semantic units. Consequently, each word in a phrase such as fly to Chicago contributes its own, independent meaning to the meaning of the phrase as a whole.</Paragraph>
    <Paragraph position="2"> This strongly compositional analysis of directional modifiers has a number of crucial computational advantages over case-based approaches. Consider how inferences between sentences such as  (1) and (2) can be handled by the two types of approaches.</Paragraph>
    <Paragraph position="3"> (I) John went to New York.</Paragraph>
    <Paragraph position="4"> (2) John was in New York.</Paragraph>
    <Paragraph position="5"> In Schank (1975, p.53) sentence (I) corresponds to the conceptual structure in (3).</Paragraph>
    <Paragraph position="6"> (3) \[~New York John ~-%-~ PIRAte ~ John e-~-~ L .X (3) be should read as: &amp;quot;John is at some time in the past (p) engaged in an act of physical transfer (PTRANS) whose object (o) is John and whose direction (D) is from some location X to New York.&amp;quot; The fact that (1) implies (2) is expressed by attaching to the bi-directional arrow in (3).the structure in (4). (of. Schank 1975, p. 54) (4) John~ LOC(N.Y.) Schank calls the r-lin/c (v for result) between structures (3) and (4) an inference. However, the term inference is really a misnomer because the association between structures such as (3) and (4) is merely a matter of stipulation but does not follow from any general principles or axioms that would constrain the language of conceptual structures. For that matter, there is nothing in Schank's system that prevents a link between (3) end  a structure which expresses that John does not reach the location New York. In the analysis we will develop below, on the other hand, the inference between (1) and (2) follows logically from the semantics of motion verbs such as go in conjunction with the semantics of directional modifiers, Consider next the issue of how easy or difficult it is to upscale natural language systems whose treatment of directional modifiers is case-based. Assume a case-based system in which only those verbal frames or conceptual structures are implemented that relate locative or directional case to verbs of motion. Now imagine that we! want to extend coverage to verbs such as wave which, as illustrated in (5), allow directional modifiers such as to, (5) The President waved to the reporters.</Paragraph>
    <Paragraph position="7"> Since wave, unlike verbs of motion, does not entail a change of location for the agent involved, a new verbal frame or conceptual structure would have to be introduced into a system which only covers motion verbs. Moreover, locative or directional case would have to be reintroduced into the system as well because in a case-based system the specific effect of a given semantic case has to be determined for each mdividual frame or conceptual structure. This is a direct consequence of the weakly compositional semantics of suctl systems and in turn leads to an highly redundant method of upscaling. Since my analysis of directional modifiers is, by contrast, strongly compositional, upscaling becomes much easier. In the case of extending coverage to a verb like wave, all that needs to be added is the lexical semantics for the w.~rb itself, while the semantics of directional modifiers can remain untouched.</Paragraph>
    <Paragraph position="8"> Finally, consider how a case-based approach to directional modifiers fares with respect to phrases such as the ones given m (6).</Paragraph>
    <Paragraph position="9">  (6) From Russia with Love  To New York and then to Atlanta Since in case-based systems locative or directional case is a relational notion and is crucially dependent on a verbal frarae or conceptual structure, it becomes impossible to assign an interpretation to verbless phrases as in (6). One strategy for extending case-based systems to such verbless phrases would consist in supplementing the relational notion of directional or locative case by a non-relational counterpart which does not depend on some verbal frame or conceptual structure. But the resulting account of locative or directional case would once again be highly redundant since essentially all of the cases in the system wouhi have to be split into a relational and a non-relational version.</Paragraph>
    <Paragraph position="10"> 2, Motion Verbs as Location Predicates In their literal sense, locative use to and toZvavd typically modify motion verbs such as wal~, ru~, drive, slither, move etc. An adequate treatment of the directional modifiers themselves is, therefore, closely connected to a semantic account of such motion verbs. In Hinrichs (1985) I argue that motion verbs should be treated as stage level predicates in the sense of Carlson (1977), namely as predicates whose arguments refer to stages of individuals. Stages are connected to individuals in Carlson's ontology by a realization relation R, which associates a given individual with all of the (spoils-temporal) stages at which that individual is present.</Paragraph>
    <Paragraph position="11"> Motion verbs such as move can be understood as prototypical examples of stage-level predicates, since such verbs predicate something about the spatio-.-temporal location of one or more objects. Following Hiurichs (1985), I interpret a motion verb like move in terms of a three-place stage level predicate move + , whose first two argument positions range over individual stages realizing th~ referents of the object and subject NPs, respectively. Fallo~ing Davidson (1977), the rightmcst argument position r ~n~,es over events, or more specifically over evenl  stages which realize the event that the referents of the subject and object NPs are engaged in. Thus, move+(xs)(ys)(e s) should be read as: &amp;quot;the referents of x s and ys are engaged in an event stage e s realizing an event of moving.&amp;quot; As is customary in Montague Grammar, I express constraints on lexical meaning in terms of meaning postulates that constrain the set of possible models of semantic interpretation? The meaning postulate in (7) states that an event stage e s which realizes a moving event spatio-temporally includes (symbolized as K) at least the location of the referent denoted by the object argument, i.e. yS K e s. This does not exclude the possibility that the location of the referent of the subject NP can be contained in the event stage as well, but this is not required for move, as (8) shows.</Paragraph>
    <Paragraph position="12">  (7) V xS,yS,e&amp;quot; \[ move+(xS)(yS)(e s) ---&gt; yS ~ es\] (8) John moved the troops.</Paragraph>
    <Paragraph position="13">  Of course, different motion verbs will have different properties with respect to how the locations of the event stages relate to the stages that realize the individuals involved in these event stages. Consider verbs like slither, walk, and run which in my framework are analyzed as two-place stage level predicates. For these predicates the location of the event stage is equal to the location of the agent, i.e. the referent of the subject NP. This can be enforced by a meaning postulate as in (9).</Paragraph>
    <Paragraph position="14"> (9) V xS,e s \[8+(xS)(e s) --&gt; xS=e s \], where ~ translates slither, walk, run, etc..</Paragraph>
    <Paragraph position="15"> The lexical entailment associated with the verb move to the effect that the location of the referent of the object NP changes can be captured by the meaning postulate in (10). (The symbols &lt; and #~ used in (10) stand for temporal precedence and spatial</Paragraph>
    <Paragraph position="17"/>
  </Section>
  <Section position="3" start_page="347" end_page="347" type="metho">
    <SectionTitle>
3, The Semantics of to and toward
</SectionTitle>
    <Paragraph position="0"> Now I let a t0-phrase, as a modifier of untensed verb phrases (IV*), operate semantically on the event stages in the denotation of the unmodified verb phrase in such way that the event stages in the denotation of the resulting IV* phrase constitute a spatio-temporal path (in the sense of Cresswell 1978) between some specified point of origin to the location of the term combining with to. The translation of to is given in (11).</Paragraph>
    <Paragraph position="1">  (11) to translates as XPXPXllXXiP \[kyIS12\[R(12,Yi ) &amp;</Paragraph>
    <Paragraph position="3"> The formula following the lambda abstractions in (11) introduces an individual stage /2 realizing an individual object yi which is the one bound by the noun phrase (NP) combining with to to form the IV* modifier. The second conjunct in the formula asserts that the denotation of the event stage located at l 1, which is to be bound by the translation of the IV* phrase that the to-phrase combines with, qualifies as a spatio-temporal path (a notion formally defined in Hinrichs 1985) between some point of origin I r and the spatio-temporal location of the point of destination. Finally, the third conjunct asserts the truth of the unmodified IV* phrase that the to-phrase combines with. It is this last conjunct that automatically guarantees the inference from sentences such as (12) to sentences such as (13).</Paragraph>
    <Paragraph position="4">  (12) Fangs slithered to the rock.</Paragraph>
    <Paragraph position="5"> (13) Fangs slithered.</Paragraph>
    <Paragraph position="6">  some individual event of Fangs' slithering such that that event stage lies in the past and the spatio-temporal location of the event stage constitutes a path between some implicit point of reference l r and the location of some unique rock object. The point of reference l r occurs as a free variable in the formula in (14); l r is to be understood as an indexical parameter similar to the notion of a reference point proposed by Reichenbach (1947) for the interpretation of tenses in English.</Paragraph>
    <Paragraph position="7"> Notice that the notion of a path in the translation of to in (11) and hence also in the translation for (12) given in (14) is defined to hold of the process making up a particular event. Moreover, due to the postulate in (9), the referent of the subject NP, when it combines with a motion verb such as slither to the rock, is realized by a stage spatio-temporally co-extensive to the path denoted by the to phrase. This fact guarantees the inference between sentences such as (12) and (15).</Paragraph>
    <Paragraph position="8"> (15) Fangs was at the rock.</Paragraph>
    <Paragraph position="9"> For other classes of verbs the same type of inference, namely identifying the path with the position(s) of the referent of the subject NP, cannot be drawn. For sentences such as (16) we do not want to claim that the stages realizing John make up a path to Boston. Rather it is the object NP, in this case an event term, that constitutes the path. The same is true of (17); it is the ball whose locations constitute a path to the location specified in the to-phrase.</Paragraph>
    <Paragraph position="10">  (16) John made a phone call to Boston.</Paragraph>
    <Paragraph position="11"> (17) Carol set the ball to Lucy.</Paragraph>
    <Paragraph position="12"> Let us now turn to the treatment of the preposition toward whose lexical translation rule is given in (18).</Paragraph>
    <Paragraph position="13"> (18) toward translates as kPkPkeakxlP(ky I 31 \[R(l,y i) &amp; 31' \[PATH(I',lr,\])) &amp; e s _&lt;, 1' &amp; I r &lt; e s &amp; P(xi)(eS)\]\]) The translation for toward constrains the value of the event stage variable s s in such a way that e s has to be spatio-temporally contained in some initial segment of a path l' from some implicit point of origin I r to the location I of the referent . of the NP with which toward. The requirement that the value of e s has to be an initial segment of such a path follows from the  condition that the implicit point of origin I r has to be properly contained in e s. Proper containment is necessary in order to avoid that the value of e s could be equal to the point of origin, in which case an object could count as moving toward another object if the spatial location of the first object remains unchanged.</Paragraph>
    <Paragraph position="14"> Using (18), sentence (19) is translated as in (20).</Paragraph>
    <Paragraph position="15"> (19) Fangs slithered toward the rock.</Paragraph>
    <Paragraph position="16"> (20) 3eS,e i \[R(ee,e i) &amp; PAST(e s) &amp; 3x ~ \[R(xa,f) &amp; ~xdeg\[Vz deg \[rock'(z deg) &lt;--&gt; xO=z o\] &amp; 3z a \[R(ze,z deg) &amp; slither'(xS,e s) &amp; 31 \[PATH(1,1r,Z s) &amp; e s _~ 1 &amp; 1 r &lt; eS\]\]\]\]\] The translation in (E0) says that there is an event stage realizing some individual event of Fangs' slithering such that that event stage lies in the past and the spatio-temporal location of the event stage constitutes the initial part of a path between some implicit point of reference I r and the location of some unique rock object. Since es in (20) is an initial part of a complete path to the rock, the truth of a sentence such as (12) entails the truth of (19), but not vice versa. Moreover, (12), but not (19), entails (15).</Paragraph>
  </Section>
  <Section position="4" start_page="347" end_page="348" type="metho">
    <SectionTitle>
4. The AspeetualEffect of to and toward
</SectionTitle>
    <Paragraph position="0"> Apart from supporting the relevant inference patterns between sentences such as (12), (15) and (19), an adequate analysis of to and toward should also account for a systematic difference in  the aspectual behavior of these two directional modifiers. Sentences such as (21a) which involve the preposition to describe atelis events or, in the terminology of Vendler (1967), activities. Sentences such as (21b), on the other hand, refer to telic events or to accomplishments in Vendler's classification, (21) a. John walked to the library.</Paragraph>
    <Paragraph position="1"> b. John walked toward the library.</Paragraph>
    <Paragraph position="2"> These aspeetual properties can be demonstrated by examining the cooccurrenee restrictions of the sentences in (21) with temporal modifiers such as in an hour as in (22) and with for an hour as in (23).</Paragraph>
    <Paragraph position="3">  (22) a. John walked to tile library in an hour.</Paragraph>
    <Paragraph position="4"> b. * John walked toward the library in an hour.</Paragraph>
    <Paragraph position="5"> (23) a. Johu walked to the library for an hour.</Paragraph>
    <Paragraph position="6"> b. Johu walked toward the library for an hour.</Paragraph>
    <Paragraph position="7">  As first pointed out by Vendler, only relic events or accomplishments can occur with temporal modifiers such as in an hour. Modifiers such as for an hour can occur with both activities and accomplishments. However, when modified by temporal for, only activities as in (23a) can be interpreted as describing a single event. If temporal for occurs with sentences that describe accomplishments as in (23b), such sentences have to be interpreted in some special fashion to make them semantically acceptable, (23b), for example, can best be understood as referring to an iterative event, namely of John's repeatedly walking to the library during the period of one hour, Since doing something for x amount of time means doing something during most if not all subintervals of the interval x, sentences such as (24), which refer to atelic events or activities, can be characterized as being temporally homogeneous.</Paragraph>
    <Paragraph position="8"> (24) Fangs slithered toward the rock.</Paragraph>
    <Paragraph position="9"> To do something in x amount of time, on the other hand, means to do something at some unique interval within x. Since relic events or accomplishments can be modified by temporal in, they, in contrast to activities or atelic events, can be described as being temporally heterogeneous: telic events such as (25) come about over tile course of some unique time interval I', i,e. not at some subinterval of I' or at some interval properly containing I'. (25) Fangs slithered to the rock.</Paragraph>
    <Paragraph position="10"> If my analysis of directional toward and to is an adequate one, it should predict that verb phrases formed with directional toward refer to temporally homogeneous events, while verb phrases formed with to refer to temporally hcterogenous events, Due to the way in which I have defined toward as an initial subpart of a path to the projected point of destination, the reference property of temporal homogeneity associated with toward can, in fact, be reconstructed in the following way. Let us assume that there is a location I t which qualifies as an initial segment of a path from a putative point of origin r t to a destination d. Moreover, let us assume that r 2, the temporally final bound of l/, is in turn the temporally initial bound for a location 12 which forms the intial part of a path from r 2 to d. Then it follows that lf+l 2, the spatio-temporal sum of l t and l 2, is also an initial segment of a path from r I to d. This is precisely what is required to stake the semantics of toward homogeneous.</Paragraph>
    <Paragraph position="11"> Since my account of motion verbs and directional toward does predict that sentences such as (26) correspond to atelic and semantically homogeneous events, my analysis can support inferences from sentences such as (26) to sentences such as (27).</Paragraph>
    <Paragraph position="12"> (26) United Flight 342 has moved toward Logan Airport for the last fifteen minutes.</Paragraph>
    <Paragraph position="13"> (27) United Flight 342 moved toward Logan Airport ten minutes ago.</Paragraph>
    <Paragraph position="14"> Inference patterns between sentences such as (26) and (27) are, in fact, highly relevant for data base interface systems that process spatial information. Imagine that sentence (26) is presented to a database that monitors plane movements. If the system does not have the capability to infer that the event described in (26) is true at any subinterval of the fifteen minutes mentioned in (26), the United flight in question would erroneously not be counted when the answer to a subsequent query such as (28) is computed.</Paragraph>
    <Paragraph position="15"> (28) How many planes moved toward Logan Airport ten minutes ago? If we compare the semantics of toward with the semantics of to as defined in (11), it turns out that to is heterogeneous in its reference in the same way as accomplishments. Recall that the semantics of to is defined in terms of a complete path between a point of origin and a point of destination, Since for any given path there do not exist any sublocations within that path that themselves would qualify as a path between the same two locations, the heterogeneons reference property of to follows automatically.</Paragraph>
  </Section>
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