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<Paper uid="C82-1068">
  <Title>TEST-SCORE SEMANTICS FOR NATURAL LANGUAGES</Title>
  <Section position="2" start_page="0" end_page="425" type="intro">
    <SectionTitle>
INTRODUCTION
</SectionTitle>
    <Paragraph position="0"> Test-score semantics represents a break with the traditional approaches to semantics in that it is based on the premise that almost everything that relates to natural languages is a matter of degree. The acceptance of this premise entails an abandonment of bivalent logical systems as a basis for the analysis of natural languages and suggests the adoption of fuzzy logic (Zadeh (1975), Bellman and Zadeh (1977), Zadeh (1979)) as the basic conceptual framework for dealing with natural languages.</Paragraph>
    <Paragraph position="1"> In fuzzy logic, as in natural languages, almost everything is a matter of degree. To put it metaphorically, the use of fuzTy logic may be likened to writing with a spray-can, rather than with a ball-point pen. The spray-can, however, has an adjustable orifice, so that one may write, if need be, as finely as with a ball-point pen. Thus, a commitment to fuzzy logic does not preclude the use of a bivalent logic when it is appropriate to do so. In effect, such a con~itment merely provides a language theorist with a much more flexible framework for dealing with natural languages and, especially, for representing meaning, knowledge and strength of belief.</Paragraph>
    <Paragraph position="2"> An acid test of the effectiveness of a meaning-representation system is its ability to provide a basis for inference from premises expressed in a natural language.</Paragraph>
    <Paragraph position="3"> In this regard, an indication of the capability of test-score semantics is provided by the following examples, in which the premises appear above the line and the question which may be answered is stated below it.</Paragraph>
    <Paragraph position="4"> (a) During much.of the past decade Pat earned far more than all of his close friends put together How much did Pat earn during the past decade? (b) Most tall men are not fat Many fat men are bald Big is tall and fat  426 L.A. ZADEH How many big men are bald? (c) If X is large then it is not likely that Y is small</Paragraph>
    <Paragraph position="6"> How likely is it that Y is more or less small? In fuzzy logic, the answer to a question is, in general, a possibility distribution (Zadeh (1978)). For example, in the case of (a) the answer would be a possibility distribution in the universe of real numbers which associates with each number u the possibility, ~(u), o ~(u) ~ I, that u could be the cumulative income of Pat given (i) the premise, and (ii) the information resident in a database.</Paragraph>
    <Paragraph position="7"> In test-score semantics, a semantic entity such as a proposition, predicate, predicate-modifier, quantifier, qualifier, command, question, etc., is represented as a system of elastic constraints on a collection of objects or derived objects in a universe of discourse. Simple examples of semantic entities whose meaning can be represented in this manner are the following:  I. Anca has a young son. (Proposition.) 2. When Dan is tired or tense, he smokes a lot. (Conditional proposition.) 3. It is not quite true that John has very few close friends. (Truth-qualified proposition.) 4. It is very likely that Marie will become well-known. (Probability-qualified proposition.) 5. It is almost impossible for Manuel to be unkind. (Possibility-qualified proposition.) 6. Expensive car. (Fuzzy predicate.) 7. Very. (Modifier) 8. Several large apples. (Second-order fuzzy predicate.) 9. More or less.(Modifier/Fuzzifier.) I0. Not very true. (Qualifier.) II. Very unlikely. (Qualifier) 12. Much taller than most. (Fuzzy predicate.) 13. Bring me several large apples. (Fuzzy command.) 14. /Who are Edie's close friends. (Question.)  Although test-score semantics has a much greater expressive power than the meaning-representation systems based on predicate, modal and intensional logics, its expressiveness is attained at the cost of downplaying, if not entirely severing, the connection between syntax and semantics. In particular, the homomorphic connection between syntax and semantics which plays a central role in Montague semantics (Montague (1974), Partee (1976) and attributed grammars for programming languages (Knuth (1968)), plays a much lesser role in test-score semantics-a role represented in the main by a collection of local translation rules governing the use of modifiers, qualifiers, quantifiers and connectives. In effect, the downplaying of the connection between syntax and semantics in test-score semantics reflects our belief that, in the case of natural languages, the connection is far too complex and far too fuzzy to be amenable to an elegant mathematical formulation in the style of Montague semantics, except for very small fragments of natural languages in which the connection can be formulated and exploited.</Paragraph>
    <Paragraph position="8"> The conceptual framework of test-score semantics is closely related to that of PRUF (Zadeh (1978)), which is a meaning-representation system in which an essential use is made of possiblity theory (Zadeh (1978))- a theory which is distinct from the bivalent theories of possibility related to modal logic and possible-world semantics (Cresswell (1973), Rescher (1975)).</Paragraph>
    <Paragraph position="9"> In effect, the basic idea underlying both PRUF and test-score semantics is that most of the imprecision and lack of specificity which is intrinsic in natural languages is possibilistic rather than probabilistic in nature, and hence that possi-</Paragraph>
  </Section>
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