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<?xml version="1.0" standalone="yes"?> <Paper uid="E93-1048"> <Title>DELIMITEDNESS AND TRAJECTORY-OF-MOTION EVENTS *</Title> <Section position="4" start_page="412" end_page="413" type="metho"> <SectionTitle> 2 The Accidental Referential </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="412" end_page="413" type="sub_section"> <SectionTitle> Homogeneity Problem </SectionTitle> <Paragraph position="0"> REFERENTIAL HOMOGENEITY is the conjunction of the properties of REFERENTIAL DIVISIVENESS and REFERENTIAL CUMULATIVITY. An expression refers divisively if whenever it applies to a given entity, it also applies to all subentities of that entity, down to a certain limit in size. For example, if there is a material entity to which beer applies, then beer also applies to all its (macroscopic) subparts; the same is clearly not true of a pint of beer. Cumulativity works in the other direction: an expression refers cumulatively if whenever it applies to two entities, it also 'applies to their collection. Here again, if we collect two entities to which beer applies then we get something to which beer also applies; in contrast, if we collect two entities to which a pint of beer applies, we get an entity to which two pints of beer applies instead. Similarly, we may observe that the atelic expression John drink beer refers homogeneously to situational entities (eventualities), unlike the telic expression John drink a pint of beer.</Paragraph> <Paragraph position="1"> With these properties in mind, THE ACCIDENTAL REFERENTIAL HOMOGENEITY PROBLEM may be stated as follows: some expressions which on intuitive and syntactic grounds should be in the heterogeneous class &quot;happen&quot; to refer homogeneously (cf. Schubert and Pelletier 1989). This problem has been noted in passing by Mittwoch (1982), Moens (1987), and Krifka (1989), but to my knowledge has not been systematically addressed by those focusing on the semantics of aspect. The easiest examples to construct involve lexical or quantificational vagueness, though more insidious examples exist involving self-similar objects. For instance, consider Mittwoch's example below: (2) John wrote something in ten minutes which it took me half an hour to translate.</Paragraph> <Paragraph position="2"> The problem here is that the expression John write something refers homogeneously, but nevertheless combines with an in-adverbial -- if there is an event of John writing something, then all the subevents of that event (down to a certain limit in size) will also be events of John writing something (Mbeit not the same thing), and thus the expression refers divisively; similar considerations show that it refers cumulatively as well. To take another example, consider the following sentence: (3) John typed a sequence of characters in thirty seconds (which it took me two minutes to write by hand).</Paragraph> <Paragraph position="3"> In (3) the problem is that subsequences of characters are also sequences of characters (albeit different ones), and thus the expression John type a sequence of characters happens to refer homogeneously too.</Paragraph> <Paragraph position="4"> Since the indicated expressions in (2) and (3) turn out referentially homogeneous rather than heterogeneous, their compatibility with in-adverbials (and not for-adverbials) is problematic for the theories of Dowty, Hinrichs and Krifka. 1 Now, as an alternative to the present approach, one might want to consider basing an account of this problem on differing scope possibilities for the expressions which &quot;accidentally&quot; and &quot;truly&quot; refer homogeneously -- that is, to somehow allow for different subquantities of beer but not different subsequences of characters. A serious problem for any such approach, however, is the existence of readings where the temporal adverbial has wide scope, as in (4): (4) Amazingly, John replied to every new email message in under two hours.</Paragraph> <Paragraph position="5"> The availability of such wide scope readings does not seem compatible with the idea of requiring the quantified phrase to outscope the temporal adverbial, which would seem to be necessary in order to (always) correctly predict the appropriate temporal adverbial by means of a referential homogeneity test.</Paragraph> <Paragraph position="6"> Beyond the empirical problems engendered by referential homogeneity tests, there appear to be significant computational ones as well. From the generation standpoint, it seems quite unreasonable to test whether any or all subevents of an event to be described happen to meet the same description before choosing a temporal adverbial to convey duration. Likewise, from the standpoint of interpretation, if one is to make use of aspectual information in processing successive sentences in discourse (as in the theories of Hinrichs, 1986, Moens and Steedman, 1988, and Lascarides and Asher, 1991, for example), there is equally little time for performing such tests. 2</Paragraph> </Section> </Section> <Section position="5" start_page="413" end_page="416" type="metho"> <SectionTitle> 3 Theory </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="413" end_page="413" type="sub_section"> <SectionTitle> 3.1 Ontology </SectionTitle> <Paragraph position="0"> Various authors (including Link, 1983, Bach, 1986, Krifka, 1989, Eberle, 1990) have proposed model-theoretic treatments in which a parallel ontological distinction is made between substances and things, processes and events, etc. A similarly parallel distinction is employed here, but in a rather different way: unlike the above treatments, the present account models substances, processes, and other such entities as abstract kinds whose realizations vary in amount. As such, the approach developed here may be seen as building upon the work of Carlson (1977) and his successors; it also represents one way to further formalize the intuitions found in Moens and Steedman (1988) and Jackendoff (1991).</Paragraph> <Paragraph position="1"> Following Schubert and Pelletier (1987), the present account distinguishes individuals from kinds, but not from stages or quantities. Extending their ontology, the same distinction is assumed to hold not only in the domain of materials but also in the domain of eventualities, and derivatively in the domains of space and time as well. This extension sets the stage for taking a sortal approach to the semantics of aspect, in contrast to previous model-theoretic accounts.</Paragraph> </Section> <Section position="2" start_page="413" end_page="414" type="sub_section"> <SectionTitle> 3.2 Semantics </SectionTitle> <Paragraph position="0"> Let us assume a many-sorted higher-order logic with model structures consisting of the following elements, 2A similar point was suggested by Manfred Krifka (p.c.). Entity * Material - Substance - Thing * Eventuality - Process - Event * Space - Trajectory * Time * Amount - Quantity - Distance - Duration * Number Figure 1: The (Abbreviated) Sort Hierarchy plus an interpretation function: * a set of entities: E * sorts: Material, Eventuality, Kind, ... * binary relations: p, comp, E_, r, amt, ... To structure the set of entities E, we require permissible models to satisfy various axioms on the binary relations.</Paragraph> <Paragraph position="1"> Roughly following Eberle (1990) and Jackendoff (1991), we assume postulates enforcing the (nonexhaustive) sort hierarchy shown in Figure 1. We also assume that certain sorts cut across the hierarchy, in particular the disjoint sorts Kind and Individual. These sorts partition the sorts Material, Eventuality, Space and Time. Some of the resultant sorts are named in Figure 1; these equivalences are shown below:</Paragraph> <Paragraph position="3"> Following Schubert and Pelletier, we map predicates to kinds using the operator p. To map kinds to their realizations, we employ a relation comp(osed of) inspired by Jackendoff's (1991) conceptual function of the same name. As this relation is central to the present account, its sortal requirements are shown below: (5) Vxy. comp(z)(y) --* Kind(x) A Individual(y) (6) For all S in {Material, Eventuality,...}: Vxy. comp(z)(y) -* S(z) A S(y) In the spirit of Krifka (1989) and Eberle (1990), we also employ a partial order ff (part of) on the sort Individual, as well as total orderings ~ and < on the sorts Amount and Number, respectively. F\]-nally, we employ spatio-temporal trace functions r mapping from Eventuality to Space and to Time, as well as a function am(oun)t mapping from Individual to Amount.</Paragraph> <Paragraph position="4"> We relate the preceding binary relations as follows. First, formal kinds and their realizations are required to satisfy the following axiom: 3 (7) VPz. comp(p(P))(z) ~ P(z) Second, we require the spatio-temporal trace functions r to be homomorphisms preserving the part-of relation, as shown below: (8) Vele2 * el_e2 ~ v(el)__.v(e2) Third, we also require the spatio-temporal trace functions to preserve the composed-of relation, at least when they map processes to kind-level entities, as shown in (9); in the case of the temporal trace function rt, this requirement is strengthened to hold generally, as shown in (10): (9) Veal. comp(e)(el) ^ Kind(r(e)) --* comp(r(e))(r(el )) (10) Veel. comp(e)(ea) --* comp(rt(e))(rt(el)) Fourth, as a correlate of referential divisiveness, we assume that the set of individuals composed of a given kind is closed under the part-of relation; that is, whenever an individual y= is composed of a certain kind z, then all subparts Yl of y~ are also composed of z, as shown in (11). 4 (11) Vxyly2. comp(z)(y2) A ylff_y2 -* C/omp(z)(yl) Finally, we require the function amt and unit measures such as minutes' to satisfy various fairly obvious postulates concerning the preservation of the orderings __, _ and _<.</Paragraph> </Section> <Section position="3" start_page="414" end_page="414" type="sub_section"> <SectionTitle> 3.3 Syntax </SectionTitle> <Paragraph position="0"> The rudimentary categorial grammar given in Figure 2 suffices to derive all of the logical forms in the next section. Note that lexemes such as slime are paired with syntactic categories such as n and semantic functions such as slime ~ (where the category vp abbreviates s \ np). Three e-rules are also employed, one for introducing p in a bare np, one for SNote that not all kinds need involve #; presumably, conventional kinds such as Coke or Heineken are named directly.</Paragraph> <Paragraph position="1"> 4Because of the notorious MINIMAL PARTS PROBLEM (i.e., how little beer is still beer?), this postulate is not quite correct as stated; amending it would require adding a condition that yl be &quot;large enough ~ for the kind z. lifting a vp to apply to a generalized quantifier, 5 and one for adding an existential quantifier to the sentence radical (ignoring tense and mood).</Paragraph> </Section> <Section position="4" start_page="414" end_page="416" type="sub_section"> <SectionTitle> 3.4 Aspeetual Composition </SectionTitle> <Paragraph position="0"> Manner-of-motion verbs such as run, wa&, etc. are interesting insofar as the telicity of the expressions in which they are used is dependent upon both the subject NP and an optional trajectory-specifying PP: (12) John ran along the river for 20 minutes.</Paragraph> <Paragraph position="1"> (13) John ran to the bridge in 20 minutes.</Paragraph> <Paragraph position="2"> (14) Slime oozed into the urn for 20 minutes.</Paragraph> <Paragraph position="3"> (15) Two liters of slime oozed into the urn in 20 minutes.</Paragraph> <Paragraph position="4"> Let us assume that such verbs take material entities as arguments and describe eventualites (either events or processes). To capture their aspectual behavior, we stipulate the following preliminary postulate: an eventuality e, where A ranges over run e, ooze ~, etc., then e is an event (an individual eventuality) if and only if its spatial trace rs(e) is an individual trajectory and x is a thing (i.e., an individual material). If we assume that the expression to the bridge only describes individual trajectories, then postulate (16) forces John run to the bridge to describe an event. In contrast, if we assume that the expression along the river is not restricted in this way, then John run along the river may describe a process as well. To capture this formally, the following meaning postulate is needed: (17) Vzp. to'(x)(p) --* Individual(p) Given the categories listed in Figure 2, the expressions John run along the river and John run to the bridge receive the following translations: (18) Ae. run'(j)(e ) A along'(the'(river'))(rs(e)) (19) Ae. run'(j)(e) A to'(the'(bridge'))(rs(e)) From meaning postulates (16) and (17), it follows that the latter expression must describe events; with no analogous meaning postulate for along, the former expression is free to describe processes as well. Before continuing, it is worth explaining why postulate (17) is a reasonable one. Recall that a given process stands in the composed-of relation to multiple events. If these events differ in their spatial extents, then the spatial trace of the process cannot sensibly be an individual-level entity, assuming SThis rule is a simplified version of a more general rule which introduces an existential quantifier over the eventuality variable.</Paragraph> <Paragraph position="5"> : ~nmP. B~. comp(m)(x) ^ amt(~) = liters'(n) ^ P(~) : Az. z : slime' : g : the' : run' : APQe.Q(Az.P(:r)Ce)) : AnPxe. P(z)(e) ^ amt(rs(e)) = miles'(n) : AyPze. P(z)(e) ^ to'(y)(rs(e)) : AdPxel. Be. P(z)(e) h comp(e)(el) ^ amt(rt(el)) = d : ,~dPze. P(z)(e) A amt(rt(e)) _ d : minutes' : AP.Be.P(e) unique amounts (distances) for individual trajectories; instead, it should be a kind-level trajectory, standing in the composed-of relation to the various individual trajectories corresponding to these multiple events -- as per postulate (9). It is in this sense that the spatial trace of a process may not be &quot;delimited&quot; in extent. Of course, this does not mean that the spatial trace of a process cannot be bounded in any absolute sense; in the case of along the river, for example, no resultant trajectory is allowed to continue (very far) past the river's end. l~eturning now to to the river, we may note that this expression describes the end point of a trajectory; as such it is naturally restricted to describing individual trajectories, which always have defined endpoints. Next we turn to slime and two liters of slime. Given the categories listed in Figure 2, the expressions Slime ooze into the urn and Two liters of slime ooze into the urn receive the following translations:</Paragraph> <Paragraph position="7"> Now, if we assume a sortal meaning postulate for into analogous to that of to, then it follows from the sortal requirements on p and comp that (20) can only describe processes, whereas (21) can only describe events.</Paragraph> <Paragraph position="8"> At this point we are ready to consider the temporal adverbials. Not surprisingly, the relation comp is crucial to the present account of the for- vs. in-adverbial test data, as can be seen from comparing their semantics: whereas for-adverbials measure out a process using comp and a given amount of time, in-adverbials simply require that an event take place within a given amount of time.</Paragraph> <Paragraph position="9"> Let us first consider how the machinery developed so far can be used to account for examples (14) and (15), augmented below: (22) Slime oozed into the urn {for} * in twenty minutes.</Paragraph> <Paragraph position="10"> (23) Two liters of slime oozed into the urn {*for t in twenty minutes.</Paragraph> <Paragraph position="11"> The respective translations of the two possibilities in (23) follow: 3zeel. comp(p(slime'))(z) A</Paragraph> <Paragraph position="13"> Since the entity e in (24) is required to be an event, comp(e)(el) turns out undefined, s making (24) semantically anomalous. In contrast, lacking comp, the translation in (25) is unproblematic. Similar reasoning shows that (22) can only be compatible with for-adverbials, assuming durations (i.e., amounts of temporal traces) are not defined for processes. Furthermore, these same considerations lead to the correct predictions in examples (12) and (13) as well. T Finally, without further ado the theory makes the correct predictions in (26) below, as distances (amounts of spatial traces) are only defined for events: sI-Iere I am assuming for expository purposes that the interpretation of a function is undefined if any of its argument terms are not of the appropriate sort, or are undenned themselves.</Paragraph> <Paragraph position="14"> ZNote, however, that the theory as it stands cannot rule out ? John ran along the river in PS0 minutes, which comes out meaning the same thing as John ran some distance along the river in ~0 minutes.</Paragraph> <Paragraph position="15"> * for ~ twenty (26) John ran four miles in j &quot; minutes.</Paragraph> <Paragraph position="16"> Up until this point we have relied (in part) on the stipulated postulate (16) to capture the temporal adverbial data. We consider now how we may derive this postulate from more basic assumptions, beginning with the following one: For all A in {run', ooze' .... } :</Paragraph> <Paragraph position="18"> the intuition that a A process e must be &quot;measured out&quot; either by its trajectory Ts(e) or by its material argument x (cf. Krifka, 1989, Dowty, 1991, Tenny, 1992, Verkuyl and Zwarts, 1992). It does so by requiring that all individual events el composed of e be A events with either an individual trajectory %(el) composed of %(e) or an individual material argument x~ composed of x (or possibly both). From (27) follows the only-if (~--) part of (16), as follows: if both x and rs(e) are individual-level entities, then neither of the alternatives in the. consequent of (27) can be true, since the composed-of relation is not defined for individual-level entities; therefore, by way of contradiction, e cannot be a process (at least if we assume all kind-level entities are in the domain of comp).</Paragraph> <Paragraph position="19"> To make the if(--+) part of (16) follow too, we may employ the following postulate: For all A in {run', ooze',...} : (28) We. A(x)(e) ^ Individual(e) R(amt(rt(e) ) )(amtO'Je) ) )(amt(x) ) Postulate (28) relates the duration of a A event to the length of its trajectory and the quantity of its material argument by some unspecified relation R (which might limit speeds to acceptable ranges, for example). Since amounts are only defined for individual-level entities, this forces the trajectory and material argument of a A event to be individual-level as well.</Paragraph> </Section> <Section position="5" start_page="416" end_page="416" type="sub_section"> <SectionTitle> 3.5 Referential Homogeneity Revisited </SectionTitle> <Paragraph position="0"> While the property of referential homogeneity does not play a part in capturing the for- vs. in-adverbial test data in the present approach, it is nevertheless necessary to account for certain desired inferences.</Paragraph> <Paragraph position="1"> In particular, we shall need a version of referential divisiveness in order to make the first but not the second inference below a valid one: (29) John ran along the river for five minutes.</Paragraph> <Paragraph position="2"> John ran along the river for four minutes.</Paragraph> <Paragraph position="3"> (30) -, John ran to the bridge in five minutes.</Paragraph> <Paragraph position="4"> John ran to the bridge in four minutes.</Paragraph> <Paragraph position="5"> Given the translation of John ran to the bridge in n minutes in (31) below, it is easy enough to see why (30) is not a valid inference: all that is needed is a model in which there is an event of John running to the bridge that takes more than four minutes but takes place within five minutes.</Paragraph> <Paragraph position="7"> Turning now to (29), consider the translations below:</Paragraph> <Paragraph position="9"> Note here that the variables have been (equivalently) renamed to indicate which we shall take to be the same and which different: that is, we shall take e2 and el to be two events of different durations composed of the same process e. To get (29) to follow in this way, we need the following two postulates: For all A in {run', ooze',...} :</Paragraph> <Paragraph position="11"> ration amt(rt(e2)), then for all lesser durations dl, e2 has subevents el of that duration; postulate (35) states that r trajectory predicates are preserved by the composed-of relation. From postulate (34) it follows that the running event e2 of duration five minutes must have a subevent el of duration four minutes, which we know by (11) to be composed of the same process e; finally, postulate (35) ensures that el is also located along the river, thus validating (29).</Paragraph> <Paragraph position="12"> In addition to accounting for the downward entailments above, the machinery developed so far also accounts for existential entailments such as the one in (36), assuming the translation of the consequent given in (37): Slime oozed into the urn for ten minutes.</Paragraph> <Paragraph position="13"> (36) Some amount of slime oozed into the urn in ten minutes.</Paragraph> <Paragraph position="15"> The inference (36) follows by postulates (27) and (35). Since Some amount of slime ooze into the urn turns out to be referentially homogeneous, (36) concomitantly shows how the present approach dis-</Paragraph> </Section> </Section> <Section position="6" start_page="416" end_page="417" type="metho"> <SectionTitle> solves THE ACCIDENTAL REFERENTIAL HOMOGENE- ITY PROBLEM. </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="417" end_page="417" type="sub_section"> <SectionTitle> 3.6 Repetitions </SectionTitle> <Paragraph position="0"> So far we have been careful to exclude from consideration the iterative readings that for-adverbials can induce (cf. Moens and Steedman, 1988, Jackendoff, 1991). Here we consider some extensions to the approach developed above which permit these to be captured as well.</Paragraph> <Paragraph position="1"> Let us begin by adding retried sets to the domain of individuals, along the lines of Link (1983) or Krifka (1989). We do so by partitioning the sort Individual using disjoint sorts Atom and Non-Atom and introducing a new relation __.i (individual part of) isomorphic to the subset relation over the power set of the atoms, minus the empty set (to avoid confusion, we might rename the other part of relation E_q, for quantity part of). We also add a cardinality function \[ * \] mapping individuals to numbers, and an operator plur(al) mapping predicates over atoms to predicates over non-atoms. Naturally enough, we require the operator plur to satisfy the following postulate, where __.~i is equal to ___i with its domain restricted to the atoms: (38) VPzlz2. plur(P)(z2) A zl__.aiz2 -&quot;* P(Zl) Given this additional machinery, we may account for the iterative readings induced by for-adverbials by simply positing a lexical ambiguity between the reading for for given in Figure 2 and the one below: (39) for: ~dPxel. 3e. t~(plur(P(z))) = e ^ comp(e)(el) ^ amt(rt(e)) = d Note that in reading (39), the process e measured out by the for-adverbial is not the one described by P(z), but rather the one equal to/~(plur(P(z))), which has as its realizations collections of P(z) events of varying cardinalities; note also that the sortal requirements on plur and comp ensure that the two readings off or-adverbials are in complementary distribution, insofar as only one can ever be defined for a given eventuality predicate p.8 Finally, we may observe that these same extensions can be used to give a natural account of frequency adverbials such as twice or n times: (40) twice: APze. plur(P(x))(e) ^ l e 1= 2</Paragraph> </Section> </Section> <Section position="7" start_page="417" end_page="419" type="metho"> <SectionTitle> 4 Application </SectionTitle> <Paragraph position="0"> In this section we turn to an implemented system based on the above theoretical treatment which determines whether a specified sequence of events is or is not possible under varying situationally supplied constraints. The domain is limited to trajectory-of-motion events specified by the verbs run, jog, sit is worth noting that as an alternative to positing a lexical ambiguity, one could just as easily invoke a coercion operator on an event predicate P(z) mapping it to the process predicate he. #(plur(P(x))) = e, which would bring the present treatment more in line with Moens and Steedman (1988) and Jackendoff (1991).</Paragraph> <Paragraph position="1"> plod, and walk; the locative prepositions to, towards, from, away from, along, eastwards, westwards, and to and back; various landmarks; the distance adverbials n miles; the frequency adverbials twice and n times; and finally the temporal adverbials for and in. Trajectory-of-motion events are modeled as continuous constant rate changes of location in one dimension of the TRAJECTOR relative to one or more LANDMARKS (following Regier 1992 in his use of Langacker's 1987 terminology).</Paragraph> <Paragraph position="2"> Briefly, the system takes a set of landmark locations (which are assumed to remain constant) and an input string from which it derives all possible logical forms for the given sentences; it then extracts a set of constraint equations from the derived logical forms and solves them according to a best-value metric. If a solution is found, it is displayed as a space-time diagram as shown in Figure 3. Note that distances are in miles, durations are in minutes, and the range of rates associated with the verbs are appropriate for a serious athlete.</Paragraph> <Paragraph position="3"> The best-value metric currently employed is proximity to the median rate for the given manner of motion, summed across successive events. According to this metric, an event such as Guy running to the bar takes a default amount of time according to the distance and the median rate; however, an event of Guy running to the bar in n minutes may take less time if this duration is less than the default -at least up to the point where the specified duration requires exceeding the given maximum running rate, thus making the constraint equations unsatisfiable.</Paragraph> <Paragraph position="4"> Likewise, an event of Guy running along the river (towards the bar, say) for n minutes will yield a default distance according to the amount of time and the median rate; this distance may vary according to more demanding distance requirements imposed by succeeding sentences, again up to a certain point.</Paragraph> <Paragraph position="5"> The times of successive repetitive events are summed, so that scope differences between frequency and temporal adverbials may be adequately treated; that is, the system correctly determines when one but not the other of Guy jogged to the care and back in ten minutes twice and Guy ... twice in ten minutes is possible. The summing of the durations of successive events also allows the system to determine an appropriate number of iterations for Guy jogged to the cafe and back for 30 minutes. 9 The system is implemented in SCREAMER, Siskind and McAllester's (1993) portable, efficient version of nondeterministic Common Lisp augmented with a general-purpose constraint satisfaction package.</Paragraph> <Paragraph position="6"> Taking advantage of SCREAMER'S compatibility with the COMMON LISP OBJECT SYSTEM, constraints are specified in a declarative, hierarchical fashion. As an example, Figure 4 shows how variables associ9Note that the system cannot find a solution for Guy ran to the bar \]or 30 minutes, since there is no provision for adding unspecified events (such as leaving the bar). minutes. Then he jogged from the cafe to the museum. Next he ran to the bar and back three times in 20 minutes. Finally he plodded to the inn.&quot; Note that for 20 minutes could have been used instead of three times in 20 minutes.</Paragraph> <Paragraph position="7"> fication in SCREAMER.</Paragraph> <Paragraph position="8"> ated with the trajectory-of-motion class of events are constrained according to the formula distance = rate x time; it also shows how a further constraint on rates is associated with the running specialization of this class.</Paragraph> <Paragraph position="9"> Because the domain is so simple, adequate constraints on trajectories are trivial to specify. Somewhat more imaginatively, processes are modeled by their constrained but unsolved-for realizations; they are distinguished from them solely (and efficiently!) by the value of the feature delimited, as justified by the sortal approach advocated in the last section.</Paragraph> <Paragraph position="10"> Likewise, kind- and individual-level trajectories are distinguished by the same feature, in such a way as to maintain postulate (16). Lest the reader miss the point for its simplicity, it is worth emphasizing (recalling Figure 3) that this feature is crucial for determining whether single instances or repetitions are involved in sentences such as Guy walked eastwards along the river/or ~0 minutes and Guy ran to the bridge and back for ~0 minutes.</Paragraph> </Section> class="xml-element"></Paper>