An Ontological Semantic Account of Relative Quantification in English
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This document discusses an ontological semantic framework for understanding relative quantification in English, emphasizing the limitations of syntax-based linguistic accounts. It categorizes quantification into stationary and drifting types, analyzing the context-dependent nature of quantifier values and their relationships. The framework utilizes a formal language to represent quantifier meanings, suggesting that semantic phenomena can be systematically analyzed and machine-tractable.
An Ontological Semantic Account of Relative Quantification in English
- 1. An Ontological Semantic Account of Relative Quantification in EnglishWhitney VandiverPurdue University22nd MAICSApril 17, 2011
- 2. Need for semantic treatmentMajority of linguistic accounts are syntax-basedFails to distinguish between types of quantificationWill not apply cross-linguisticallyTend to use formal mathematical and logical representationsSemantic analysis providesSubclasses of quantificationMay be used cross-linguistically
- 3. Relative QuantificationVariable, inconsistent values that appear to be contextually dependent Values are in part reliant on other quantifiers’ values within the same domainTwo classesStationary—definite range that cannot be adjusted with a given scaleDrifting—range created in comparison to another known value
- 4. Relative quantification: Stationary(a) few, (a) little, (a) bitalways communicate smaller amounts regardless of domain(a) few and (a) little semantically synonyms—vary only with application to count nounsFew and little may also have an expectation being violated (i) Mary brought few books with her
- 5. Representation of semantic sensesSome provides broader rangeBordering on lower values of a few and higher values of manyCompare ranges in (ii), (iii), and (iv)(ii) Mary bought a few books, and John bought some (iii) Mary bought some books, but John bought a lot (iv) Mary bought some books, and John bought severalValue is determined by the co-occurring quantifier in the second clauseConjunction in (ii) and (iv) show smaller realm of quantification of someDisjunction in (iii) illustrates that the range must fall between a few and several
- 6. Representation of semantic sensesGrammatical combinations of conjunction and disjunction of some do not exhibit the same patterns Conjunction is always grammaticalDisjunction has requirement of comparative ranges not being overlapping except in higher ranges(v) Mary bought a few books and/*but John bought some books (vi) Mary bought several books and/*but John bought some books (vii) Mary bought some books and/*but John bought a few books (viii) Mary bought some books and/but John bought many/several/ a lot of booksSeveral, many, much, and a lotRepresent greater values bordering some and just shy of all (ix) Many/several students attended the workshop (x) Much attention was paid to the issueA lot may be used with both count and non-count nouns
- 7. Relative quantification: DriftingCreated in comparison to another known value rather than with respect to other vague quantifiersMore (than), less (than), fewer (than) (xi) John drank less tea than Mary (xii) John ate fewer cookies than Mary (xiii) John drank more coffee/cups of coffee than MaryRange of quantification may have one endpoint moved along a scale to represent a predetermined valueMinimum endpoint is set for more (than)Maximum endpoint is set for less/fewer (than)
- 8. IntensificationVery directionally strengthens quantification by restricting values within a rangeIncrease or decrease is determined by modified quantifier (xi) We had very few students attendDoes not grammatically combine with all relative quantifiers (xii) We didn’t have very many students attend (xiii) ?We had very many students attend (xiv) Did very many students attend the workshop?Too means that quantification occurs by surpassing a limit or expectation, such as minimum or maximum(xv) Too many students registered (xvi) We have too little coffee left
- 9. Ontological Semantic Technology (OST)Semantic-based computationInput of textOutput of text-meaning representation (TMR)Human-quality outputResourcesOntologyLanguage independentHierarchical relationships of conceptsHundreds of properties combinable for descriptionLexiconLanguage dependentSemantic description of lexical itemsSemantic structures(concept (property (facet (filler))))
- 10. Representation of semantic sensesEach quantifier is represented with a range of possible quantification of a property, i.e. number, relative-ordinalityThe scale of ranges is determined by the domain being quantifiedEach possible range of a quantifier remains fixed to a scaleRanges reveal consistent interpretation of each quantifier—and relationships between themFig. 1. Overlap of relative values
- 11. Representation of semantic sensesStationary quantificationA fixed range represented as a crisp set on a given scaleRange remains the same regardless of domainOST usesfacets greater-equal, greater-than, less-than, less-equal to create endpointsProperties relative-number and relative-amountA few can be represented as (sem-struc(^$var1(rel-number(greater-than(0))(less-equal (0.2)))Expectation of few (sem-struc(^$var1(rel-amount(greater-than(0))(less-equal(0.2)) (precondition(value(^$var1(should-be-a(sem(event)))))))))
- 12. Representation of semantic sensesThe broad range of some is captured similarly with a larger span of values between endpoints(sem-struc(^$var1(rel-number(greater-equal(0.3))(less-equal(0.6))))) (sem-struc(^$var1(rel-amount(greater-equal(0.3))(less-equal(0.6)))))No definitive answer for when a few ends and some beginsCaptured with relaxable-down-to and relaxable-up-to(sem-struc(^$var1(rel-amount(rel-down-to(0.2))(greater-equal(0.3))(less-equal(0.6))(rel-up-to(0.7)))))
- 13. Representation of semantic sensesLarger stationary quantifiersSeveral (sem-struc(^$var1(rel-number(rel-down-to(0.5))(greater-equal (0.6))(less-equal(0.7))(rel-up-to(0.8)))))Many(sem-struc(^$var1(rel-number(rel-down-to(0.6))(greater-equal (0.7))(less-equal(0.8))(rel-up-to(0.9)))))Much(sem-struc(^$var1(rel-number(rel-down-to(0.6))(greater-equal (0.7))(less-equal(0.8))(rel-up-to(0.9)))))A lot(sem-struc(^$var1(rel-number(rel-down-to(0.7))(greater-equal (0.8))(less-equal(0.9))(rel-up-to(0.95)))))
- 14. Representation of semantic sensesDriftingPredetermined value (^$var2) designates the anchored endpoint, which is contextually resolvedmore (sem-struc(^$var1(rel-number(greater-than(^$var2(should-be-a(sem (number))))))))less/fewer(sem-struc(^$var1(rel-number(less-than(^$var2(should-be-a(sem (number))))))))IntensificationOne sem-struc for positive quantification and negative quantification, in reverse relationship with polarityVery (sem-struc(^$var1(rel-number(value(^$var1^(2)(polarity(negative))))))) (sem-struc(^$var1(rel-number(value(^$var1^(1/2)(polarity(positive)))))))Too (sem-struc(^$var1(rel-number(value(^$var1^(1/2)(polarity(negative))))))) (sem-struc(^$var1(rel-number(value(^$var1^(2)(polarity(positive)))))))
- 15. ConclusionThe relationship of quantifiers can remain consistent despite relative natureThe formal language of OST provides a strong apparatus for representing quantifier meaningSemantic phenomena in natural language is not only describable but can be represented in a machine-tractable form
- 16. Questions?Whitney VandiverLinguistics ProgramPurdue Universitywvandive@purdue.edu