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<Paper uid="E93-1041">
  <Title>A Tradeoff between Compositionality and Complexity in the Semantics of Dimensional Adjectives</Title>
  <Section position="5" start_page="353" end_page="355" type="concl">
    <SectionTitle>
4 Conclusions
</SectionTitle>
    <Paragraph position="0"> The results of the previous section yield Tables 4 and 5 as the complexity of reasoning with the Waltz algorithm under the non-compositional and compositional approaches, respectively. These results depend in part on the fact that there is a maximum number of parameters in each constraint in the linguistic application. Measurements are modelled as predicate constraints, i.e. they simply impose interval bounds on some parameter. Intervals are also assumed to model the range of measurement values for the physical property that is typical for members of a category (e.g. the typical width of refridgeratots), thus accounting for the norm used in the interpretation of positives. An important property of such &amp;quot;norm intervals&amp;quot; is that they may not be refined, at least not too much. This may be achieved by adding constraints imposing absolute upper and lower bounds on their ranges (cf. \[Simmons, 1992\]).</Paragraph>
    <Paragraph position="1"> Although the worst-case time complexity in all cases turns out to be the same, the compositional approach is more complex for two reasons. First, the system is prone to enter infinite loops under the compositional approach if the starting state is inconsistent, or if the solution is inadmissible. Consistency cannot generally be guaranteed in the linguistic application under consideration, since the sentences in  p = number of parameters, c = number of constraints * May not terminate if the starting state is inconsistent tTerminates in arbitrarily long (finite) time if the system is inconsistent fMay not terminate if the solution is inadmissible a text may contain errors. Second, reasoning under the compositional approach is incomplete in all but the trivial case of measurements, whereas the non-compositional approach guarantees at least assimilation completeness for a subset of the parameters in the system. This means that under the compositional approach, the reasoner does not refine some intervals as tightly as it could have under the non-compositional approach.</Paragraph>
    <Paragraph position="2"> These results may be taken as grounds for rejecting the compositional approach to the semantics of dimensional adjectives in the design of an NL interface to a KR system for quantitative knowledge.</Paragraph>
    <Paragraph position="3"> However, I do not believe that the compositional approach is contraindicated for all conceivable systems.</Paragraph>
    <Paragraph position="4"> In addition to the general theoretical appeal of compositional semantics, the compositional formation of meaning representations may be computationally more attractive in some cases (e.g. in unification-based formalisms). Thus if the non-compositional formation of semantic representations turns out to be too expensive, it may defeat the computational advantage gained in the reasoning process.</Paragraph>
    <Paragraph position="5"> This is especially true if the weaknesses of the compositional approach do not turn out to be highly relevant in the specific application. For example, if the domain of physical properties being represented is such that a set of constraints requiring some parameter to be set to \[0, 0\] or \[c~, co\] is unlikely to be encountered, and hence the solution is likely to be admissible, then the risk of infinite loops is reduced. Moreover, if Davis' heuristic for terminating infinite loops turns out to be reliable (which might be determinable by experimentation within the specific application), then inconsistencies need not be very damaging.</Paragraph>
    <Paragraph position="6"> The incompleteness of reasoning under the compositional approach is unacceptable for an application if it is crucial that the inferred intervals contain precisely those values that are warranted by the constraints and the initial labelling. If a superset of those values can be accepted, however, then the compositional approach can be taken. Both approaches suffer a lack of what Davis calls query completeness: if the value of a term T is to be determined during the querying stage (i.e. after assimilation),  the system may return a superset of the values for T that are warranted by the constraints.</Paragraph>
    <Paragraph position="7"> Thus an engineer building an NL interface to a system for reasoning about uncertain quantitative knowledge of physical properties must make a number of design decisions: * How important are difference and factor terms in the linguistic material to be processed? If difference and factor terms are so marginal that they may not occur at all, then the non-compositional approach is probably the better choice, due to its guarantee of termination and assimilation completeness.</Paragraph>
    <Paragraph position="8"> * Does the compositional generation of lexical semantic representations have a significant advantage (computational or otherwise) over the non-compositional approach? * Is it possible or likely for the measurement of some physical property to be exactly zero? While there is probably no natural application in which the magnitude of some property can be infinitely large, there are different philosophies about the treatment of zero. In a system of temporal reasoning, for example, saying that some event has zero duration may be a way of saying that the event does not exist. But another policy might be to insist that no physical property is represented if it is not exhibited to a positive degree. If this assumption can be made, then the intervals \[0, 0\] and \[cC/, oo\] are truly inadmissible, and hence one weakness of the compositional approach is diminished.</Paragraph>
    <Paragraph position="9"> * Is it important that the precise range of permissible measurement values be inferred for each parameter, or can a superset of those values be useful? If a superset of the possible values is acceptable, then the compositional approach can be chosen. Otherwise, the non-compositional approach must be taken. By weighing the various answers to these questions, an engineer can stake out a position on the tradeoff and design a system with the power and efficiency most appropriate to his or her needs.</Paragraph>
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