Presented in defense of my 2011 dissertation.

1. The Ontological Semanticsof English QuantifiersDissertation Defense Whitney Vandiver Linguistics, Purdue University April 13, 2011

2. Outline Motivations Ontological Semantic Technology Semantic Behavior of Quantification in English Conclusion 2

3. Outline Motivations Ontological Semantic Technology Semantic Behavior of Quantification in English Conclusion 3

4. Motivations: Categorical Criteria for Quantification Questions to consider… Which lexical items exhibit quantifier behavior? Determiners (Montague, 1973; Keenan and Stavi, 1986; Keenan, 1996; Greenbaum, 1996; Quirk et al., 1985) Adverbs (Quirk et al., 1985) Adjectival forms (Jespersen, 1969; Aldridge, 1982; Higginbotham, 1995) Pronouns (Jespersen, 1933; Quirk et al., 1985) What patterns can be derived from quantification? “category of determiner or pronoun used to express quantity” (McArthur, 1996, p. 747) How should quantification be classified? 4

5. Outline Motivations Ontological Semantic Technology Semantic Behavior of Quantification in English Conclusion 5

6. Ontological Semantic Technology Ontology language independent Hierarchy of concepts and their relationships Lexicon Language dependent Inventory of individual word senses Meaning of quantification represented with each quantifier’s independent sem-struc Text-Meaning Representation (TMR) shows processing of sentence with specific quantification 6

7. Outline Motivations Ontological Semantic Technology Semantic Behavior of Quantification in English Conclusion 7

8. Outline Semantic Behavior of Quantification in English Types of Quantification Definite Quantification Absolute Quantification Anchored Quantification Relative Quantification Stationary Quantification Drifting Quantification Composites Intensification Taxonomy of Quantifier Polarity Range-Restricting Intensification Comparative Intensification Set Quantification Logical Quantification 8

9. Types of Quantification Parameters Concept being quantified Object Time Iteration Frequency Temporal Segmentation Duration Relativity of a quantifier’s value Absolute Relative Stationary Drifting Set Individual Whole set Each new combination describes a new type of quantification 9

10. Definite Quantification Gives precise values and measurements (Jespersen, 1933, 1969; Quirk et al., 1985) Divided into two primary types Absolute Definite single value Consists of: Numerical quantification Singular quantification Determiners Generic forms Proportional quantification Anchored Range of possible values is anchored to single definite value Consists of: Anchored phrases Plural quantification 10

11. Definite: Absolute Quantification Numerical Number property Objects Single item: seven days Phrasal: a dozen Restriction: thousandths of an inch, half a dozen Iteration Occurs with time(s) Single: once, twice, never Cardinal: three times Ordinal: second time Frequency Iteration with a repeating timeframe Number + timeframe: once a week, three times a year 11

12. Definite: Absolute Quantification Numerical Number property Temporal Segmentation Length of time between two events Occurs with lexical tense markers: ago, since, until, later, after, before Three hours later, ten days after, yesterday Duration How long an event occurs with temporal unit measurement Lasted for forty-five minutes, from Holy Thursday to Good Friday Ordinal + temporal unit + of [progressive verb]: ninth day of studying 12

13. Absolute Quantification seven daysthousandths of an inch (day (inch (number(equal-to(7))) (number(equal-to(0.0001))) ) ) one die tossed three times he shaved for the second time that day (toss (shave … … (iteration(equal-to(3))) (iteration(equal-to(2))) ) (time-frame(sem(day (number(equal-to(1)))))) ) twice a month the editorial staff meets in New York it happened two weeks ago (meet (occur … … (frequency(equal-to(2))) (point-in-time(value(week (time-frame(sem(month (ordinality(value(-2)))))) (number(equal-to(1)))))) …for two weeks … …(duration(equal-to(2)) ) (value(week))) 13

14. Definite: Singular Quantification English marks with zero morph—no overt marking Default value of one he raised a/the bird (nurture (agent(sem(human))) (theme(sem(bird (number(equal-to(1)))))) ) 14

15. Definite: Determiners Indicates singular quantification Distributive properties of a/an with plurality The determiner should be interpreted as equivalent with one for distribution across the entire group (Aldridge, 1982) …many a local church… (agent(sem(religious-group (relative-distance(less-equal(0.2))) (number(greater-than(1)))))) ) Generic interpretation Bare form Coffee is made from the roasted and ground seeds of the coffee tree Lions are a fierce predator Determiners: …with which the student of comparative literature must be frequently concerned A lion is a fierce predatory Beadle is even that rare scientist who takes an interest in money matters 15

16. Definite: Proportional Quantification Fractions, percentages, and number+ of +number , number + out of (every) + number, and every + ordinal phrases Distinguish parts from wholes Phrases The group lost one-third of its members …thirty-three percent of its members …three of nine of its members …three out of nine of its members …one out of every three of its members …every third member (lose (experiencer(sem(organization))) (theme(sem(participant (member-of(sem(organization))) (number(equal-to(0.333)))))) ) 16

17. Definite: Anchored Quantification Permanently set endpoint at an exact, consistent value to which all possible quantifications are dependent Anchored phrases At least, more than, no more than, less/fewer than, no less/fewer than Followed by an exact value More than 5 million tons, no less than eighty acres, fewer than 600 boats (size(value(acre (number(greater-than(80)))))) (^$var1 (number(greater-than(600))) 17

18. Definite: Plural Quantification Indicated morphologically in English with –s suffix Creates value of at least one (give … (theme(sem(container (number(greater-than(1))) ) Exceptional forms will have lexical entries (children-n1 … (sem-struc(human (relative-age(greater-than(0.2))) (number(greater-than(1))) ) 18

19. Relative Quantification Gives vague values or imprecise measurements (Bradburn and Miles, 1979) Does not have consistent numerical equivalents (Routh, 1994; Wright et al., 1994; Sanford et al., 1994) Divided into two primary types—both of which quantify objects and temporal subclasses Stationary Quantification Has a definite range of possible values on a given scale, which represents the domain to which quantification applies Drifting Quantification Comparative or contextual amount is anchor for one endpoint of quantificational range, relative to domain and another value to which it is compared 19

20. Relative: Stationary Quantification Aldridge (1982) on several observes …its chief current usage is…and indeterminate number, which, though generally thought of as exceeding two or three, is not felt to be large… many…feel that [it] is very frequently used to suggest that, although the number of objects involved is not literally great, it is not small. (p. 251) Overlapping values in the sem-strucs distinguish the values in the TMRs Figure 1. Overlap of relative values 20

21. Relative: Stationary Quantification Objects: a few, little, few, a little, some, several, many, much, a lot (sem-struc(^$var1(rel-number(greater-than(0)))(less-equal(0.2)) (rel-up-to(0.3))))) (sem-struc(^$var1(rel-number(rel-down-to(0.2))(greater-equal(0.3))(less-equal(0.6))(rel-up-to(0.7))))) (sem-struc(^$var1(rel-number(rel-down-to(0.5))(greater-equal(0.6))(less-equal(0.7))(rel-up-to(0.8))))) Some municipal agencies will pay… (pay (agent(sem(organization (official-attribute(value(1))) (rel-number(rel-down-to(0.2))(greater-equal(0.3)) (less-equal(0.6))(rel-up-to(0.7)))))) ) 21

22. Relative: Stationary Quantification Some uses of few and little require a precondition Few states make effective use… (use (success(equal-to(1))) (agent(sem(state (rel-number(greater-than(0)))(less-equal(0.2)) (precondition(value(^$var1)))))) ) Few things are more perilous… (exist (theme(sem(object (rel-number(greater-than(0))(less-equal(0.05))(rel-up-to(0.1)))))) ) 22

23. Relative: Stationary Quantification Iteration—relquant + times Several times…I voted the Socialist ticket… (vote (agent(sem(human))) (iteration(rel-down-to(0.5))(greater-equl(0.6))(less-equal(0.7))(rel-up-to (0.8))) (theme(sem(candidate (member-of(pnd(Socialist-Party)))))) ) Frequency—use of object quantifiers creates iteration with timeframe He rarely has a muffin for breakfast (eat (agent(sem(human (theme(sem(bread (theme-of(sem(eat (time-frame(value(morning (frequency(greater-than(0)(less-equal(0.5))(rel-up-to(0.1))) ) 23

24. Relative: Stationary Quantification Temporal segmentation includes momentarily, shortly, a short time, a bit, a little, a few, some, several, a while, and a long time Makes use of rel-ordinality and start-time/end-time to compare order of events We have to wait a while until the concert (wait (agent(sem(human (number(greater-than(1))) (effect(sem(perform (start-time(value(temporal-unit(relative-ordinality(rel-down-to(0.3))(greater-equal(0.4)) (less-equal(0.6))(rel-up-to(0.7)))))) ) Duration includes relative object quantifiers and relative temporal segmentation quantifiers We went to the Louvre for a few hours (move-location (agent(sem(human (number(greater-than(1)))))) (goal-location(pnd(Louvre (has-locale(pnd(France)))))) (relative-duration(greater-than(0))(less-equal(0.2))(rel-up-to(0.3))(value(hour))) ) 24

25. Relative: Drifting Quantification Refers to the “extremely common practice of indicating proportional judgments by means of comparative constructions” (Aldridge, 1982, p. 245). Includes more, fewer, fewest, less, and least May be viewed as comparative and superlative forms of stationary quantifiers few, little, much, and many (Quirk et al., 1985) Figure 1. Anchored value of drifting quantification 25

26. Relative: Drifting Quantification Two interpretations of more This time more of them hurdled the barrier At least one already jumped and a greater number are jumping now (jump (agent(sem(animate (number(greater-than(1)))))) (theme(sem(barrier))) (point-in-time(ordinality(value(0))) ) The total number that have jumped over the fence, the amount jumping this time is unknown (jump (agent(sem(animate (number(greater-than(3)))))) (theme(sem(barrier))) (point-in-time(ordinality(value(0))) ) 26

27. Relative: Drifting Quantification Anchored vs. Relative quantification dependent on whether comparative value is known The second performance had the least attendance (receive (experiencer(sem(performance (ordinality(value(2)))))) (theme(sem(attend (agent(sem(human (number(less-than(10))))))))) ) (receive (experiencer(sem(performance (ordinality(value(2)))))) (theme(sem(attend (agent(sem(human (relative-number(greater-than(0))(less-equal(0.1))(rel-up- to(0.2))))))))) ) 27

28. Relative: Drifting Quantification Two senses of most John has the most points (own (agent(pnd(John))) (theme(sem(point (number(greater-than(^$var1(should-be-a(sem(number)))))) ) The most this room can hold is fifty people (accommodate (modality(value(possibility))) (agent(sem(room (number(equal-to(1)))))) (theme(sem(human (number(less-equal(50)))))) ) 28

29. Relative: Drifting Quantification Iteration—makes use of more and fewer/less and introduces again Bob visited the hospital more times than Jerry (visit1 … (rel-iteration(greater-than(^$var1 (should-be-a(number))) (relative-iteration-of(sem(visit2 (theme(sem(hospital))) (agent(pnd(Jerry)))))) ))) ) He again began to play the violin (play-music (play-music … … (iteration(greater-equal(2))) (iteration(equal-to(13))) ) ) 29

30. Relative: Drifting Quantification Frequency more and less with and without other quantifiers Each day he found himself thinking less often of Ann (know (experiencer(value(human1))) (theme(sem(information (has-topic(sem(consider-information (agent(value(human1))) (beneficiary(pnd(Ann, human2))) (relative-frequency(less-than(^$var1 (should-be-a(sem(number))) (time-frame(value(day (member-of(sem(group))) (number(value(unknown)))))) ))) ))) ))) ) 30

31. Relative: Drifting Quantification Temporal Segmentation—More time until Time between A and B is greater than time between A and C The reception is first, so we will still have more time until the dinner (exist (experiencer(sem(party (ordinality(vaule(1))) (effect(sem(experience (experiencer(sem(human))) (theme(sem(dinner (ordinality(greater-than(1)))))) ))) ))) ) Duration—More/less time The meeting will take a lot more time than his presentation (require1 (agent(sem(gathering))) (theme(sem(time (duration(greater-than(^$var1(value(temporal-unit)) (should-be-a(sem(number))) (duration-of(sem(require2 (theme(sem(time (theme-of(sem(present))))))))) ))) ))) ) 31

32. Composites Combination of quantifiers to create more restricted values One quantifier acting on the range of another quantifier Classes cannot always combine freely Twenty of the many volunteers helped with registration (assist (agent(sem(human (agent-of(sem(volunteer))) (number(equal-to(20))) (member-of(sem(group (has-members(sem(human (rel-number(rel-down-to(0.6))(greater-equal(0.7))(less-equal (0.8))(rel-up-to(0.9))))))))) ))) ) *Many of the twenty volunteers helped with registration Stationary and drifting may combine to act on each other or their own classes Stationary restricting stationary Stationary restricting drifting Drifting restricting stationary 32

33. Intensification: Taxonomy of Quantifier Polarity Relative quantifiers may be intensified to various degrees (Quirk et al., 1985) Intensification is directional and dependent on the quantifier being intensified Figure 2. Scale for polarity 33

34. Intensification: Range-Restricting Intensifies upward or downward within a definite range without necessarily relating to another known value—very and quite (very-quant1 …very little sugar is used in cooking … (use-physical-object (sem-struc(rel-number(value(^$var1^(2))))) (theme(sem(sugar ) (rel-amount(greater-than(0))(less-equal(0.04)) (rel-up-to(0.09))) (instrument-of(sem(cook)))))) ) (very-quant2 …very many large branch stores are uneconomical … (exist (sem-struc(rel-number(value(^$var1^(1/2))))) (theme(sem(store ) (relative-size(greater-than(0.8))(less-equal(1))) (rel-number(rel-down-to(0.774))(greater-equal (0.836))(less-equal(0.894))(rel-up-to(0.948))) (relative-efficiency(less-equal(0.5)))))) ) Quite varies with a few and a little, creating larger intensifications 34

35. Intensification: Comparative Intensifies to show a quantifier’s relationship with a limit—drifting (too) and alternate (almost and not quite) subclasses Drifting intensification A range of possible values is created in relation to a quantifier’s endpoint Polarity of the intensified quantifier There are too many people (exist (theme(sem(human (rel-number(greater-than(^$var1(should-be-a(sem(number)))))) ))) ) Figure 3. Anchored drifting quantification 35

36. Intensification: Comparative Alternate intensification (almost and not quite) Considers the minimum endpoint of a quantifier’s range and creates a new range of values with the lesser values Single exception of 0 value quantifiers, i.e. never Does not take polarity into account (almost-quant1 (almost-quant2 … … (sem-struc(rel-quant(less-than(^$var1 (syn-struc((root($var0))(cat(quant))(modifier((root (should-be-a(sem(number minimum-value))) (never no none))(cat(quant)))) (greater-equal(0.95))(rel-down-to(0.9)))))) (sem-struc(rel-quant(greater-than(0))(less-equal ) (0.05))(rel-up-to(0.1)))) ) The children he painted were almost always in rags (paint (agent(sem(human))) (theme(sem(child (number(greater-than(1))) (agent-of(sem(wear (theme(sem(clothing (relative-value(less-than(0.1)))(rel-up-to(0.15)))))) (frequency(rel-down-to(0.9))(greater-equal(0.95))(less-than(1)))))) ))) ) 36

37. Set Quantification Unity interpretation emphasize the entire set or group, while distributive interpretation focuses on a collection of distinct members (Aldridge, 1982). (each-quant1 … (sem-struc(^$var1 (member-of(sem(group (has-member(sem(^$var1 (number(greater-equal(1)))))))))))) ) (every-quant1 … (sem-struc(^$var1 (member-of(sem(group (has-member(sem(^$var2 (should-be-a(sem(^$var1)))))))))))) ) 37

38. Set Quantification Any At least one at a time but up to a large amount Only one from a group (any-quant1 … (sem-struc(^$var1 (number(greater-equal(1))) (member-of(sem(group)))))) ) (any-quant2 … (sem-struc(^$var1 (number(equal-to(1))) (member-of(sem(group)))))) ) 38

39. Set Quantification All Universal reading (Sapir, 1930; gives seven different meanings of totality) Ambiguous between unitary and distributive (Aldridge, 1982) (all-quant1 … (sem-struc(^$var1 (member-of(sem(group))) (rel-number(equal-to(1)))))) ) all members will contribute all twelve members will contribute (expand-information (expand-information (agent(sem(member (agent(sem(member (agent-of(sem(join-organization))) (agent-of(sem(join-organization))) (member-of(sem(group))) (number(equal-to(12))) (rel-quant(equal-to(1))) (member-of(sem(group ))) (has-member(sem(human ) (number(equal-to(12)))))) ))) ))) ) 39

40. Logical Quantification “Logical quantifiers” cannot contain all of the quantification of natural language (Barwise and Cooper, 1985) Universal quantification: “‘All men are mortal’ says no more than ‘Men are mortal’…or ‘Every man is mortal’ or ‘Any man is mortal’ or ‘Any men are mortal’ or ‘A man is mortal’” (Sapir, 1930, p. 17). Existential quantification Captured in each TMR “Dave ate two pieces of pie” 40

41. Outline Motivations Ontological Semantic Technology Semantic Behavior of Quantification in English Conclusion 41

42. Conclusion The difference in quantification of both absolute and relative quantifiers can be distinguished with exact and ranges of variable values The representative powers of logical notation and lambda abstraction are not broad enough to fully capture natural language quantification These differences can be represented in a machine-tractable formal language for use in computational applications OST offers a formal language for adequate representation of the differences in quantificational meaning 42

43. Appendix—Absolute Quantification seven daysthousandths of an inch (day (inch (number(equal-to(7))) (number(equal-to(0.0001))) ) ) one die tossed three times he shaved for the second time that day (toss (shave (theme(sem(die (agent(sem(human))) (number(equal-to(1)))))) (iteration(equal-to(2))) (iteration(equal-to(3))) (time-frame(sem(day ) (number(equal-to(1)))))) ) twice a month the editorial staff meets in New York it happened two weeks ago (meet (occur (agent(sem(group (theme(value(^$var1 (agent-of(sem(evaluate-info))) (should-be-a(sem(event)))))) (frequency(equal-to(2))) (point-in-time(value(week (time-frame(sem(month (ordinality(value(-2)))))) (number(equal-to(1)))))) …for two weeks (location(pnd(New-York))) …(duration(equal-to(2)) ) (value(week))) 43

44. Appendix—Relative: Stationary Quantification Some municipal agencies will pay… (pay (agent(sem(organization (official-attribute(value(1))) (rel-number(rel-down-to(0.2))(greater-equal(0.3)) (less-equal(0.6))(rel-up-to(0.7)))))) ) There are…organizations representing several of the denominational groups (indicate (agent(sem(organization))) (theme(sem(group (member-of(sem(religious-organization))) (rel-number(rel-down-to(0.5))(greater-equal(0.6))(less-equal (0.7))(rel-up-to(0.8)))))) ) 44

45. Appendix—Relative: Stationary Quantification Frequency—use of object quantifiers creates iteration with timeframe Tony Blair attends Mass a few times a weekHe rarely has a muffin for breakfast (attend (eat (agent(pnd(Blair (agent(sem(human))) (theme(sem(religious-event (theme(sem(bread (experiencer(sem(human (theme-of(sem(eat (has-religion(sem(catholic))))))))) (time-frame(value(morning (frequency(greater-than(0))(less-equal(frequency(greater-than(0) (0.1))(rel-up-to(0.2))) (less-equal(0.5))(rel-up-to(0.1))) (time-frame(value(week))) ) ) 45

46. Appendix—Relative: Stationary Quantification He dropped it off a short time agoWe have to wait a while until the concert (give (wait (agent(sem(human))) (agent(sem(human (theme(sem(object))) (number(greater-than(1))) (end-time(value(temporal-unit(relative-ordinality (effect(sem(perform (rel-down-to(0.2))(greater-equal(0.3)) (start-time(value(temporal-unit (less-equal(0.4))(rel-up-to(0.5))))))(relative-ordinality(rel-down-to(0.3)))) (greater-equal(0.4))(less-equal (0.6))(rel-up-to(0.7)))))) ) 46