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<Paper uid="E89-1028">
  <Title>COMPUTATIONAL SEMANTICS OF MASS TERMS</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
INTRODUCTION
</SectionTitle>
    <Paragraph position="0"> A formal semantics for a part of a natural language attempts to describe the truth conditions for sentences, or propositions expressed by sentences, in model theoretic terms, and thereby also the relation of valid inferences between sentences. From the point of view of computational linguistics and natural language understanding, it is important whether this relation of entailment can be made computational. In general, the question must be answered in the negative. All proposed formal semantics of, say, English are at least as complex as first order logic and hence at best semi-decidable, which means that if a sentence 13 is a logical consequence of a set of sentences Y., then there exists a proof for \[3 from ~, but no effective way to find such a proof. Several proposals use even more complex logics, like the higher order intensional logic used in Montague grammar, which has no deductive theory at all.</Paragraph>
    <Paragraph position="1"> We will not oppose to the view that English incorporates at least the power of first order logic and that even more complex formalisms may be needed to represent the meaning of all aspects of English.</Paragraph>
    <Paragraph position="2"> But we believe there are two different possible strategies when one is to study one particular semantic phenomenon in natural languages. The first one is to try to interpret the particular phenomenon into a system that attempts to capture all semantic aspects of the natural language. The other slrategy is to try to isolate the particular semantic phenomenon one wants to study and to build a semantic interpretation suited for this particular phenomenon.</Paragraph>
    <Paragraph position="3"> By following the latter strategy it might be possible to find systems simpler than even first order logic that reflect interesting semantic phenomena, and in particular to come up with systems that are computationally tractable.</Paragraph>
    <Paragraph position="4"> Quantified mass noun phrases is one such phenomenon that can be easily isolated. The properties particular for the semantics of quantified mass terms have been difficult to capture in extensions of systems already developed for count terms, like first order logic. However, if one isolate the mass terms and tries to interpret only them, it is possible to build a model where their typical properties fall out naturally. We have earlier proposed such a system and shown it to have a decidable logic (L0nning, 1987). We repeat the key points in the two following sections. The main point of this paper is a description of an algorithm for deciding validity of sentences and inferences involving quantified mass terms.</Paragraph>
    <Paragraph position="5"> The strategy of isolating parts of a natural language and giving it a semantics that can be computational is of course the strategy underlying all computational uses of semantics. For example, in queries towards data bases one disregards all truly quantified sentences, and use only atomic sentences and pseudo quantified sentences where e.g. for all means for all individuals represented in the data base.</Paragraph>
    <Paragraph position="6"> The system we present here contains genuine quantifiers like all water and much water, but contain other restrictions compared to full first order logic.</Paragraph>
    <Paragraph position="7"> In particular the mass quantifiers behave simpler with respect to scope phenomena than count quantifiers. null</Paragraph>
  </Section>
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