This document provides an outline and overview of Whitney Vandiver's dissertation defense on the ontological semantics of English quantifiers. The defense will cover motivations for studying quantification, ontological semantic technology used to represent quantification, and the semantic behavior of quantification in English. Key points covered include different types of definite and relative quantification, how quantification is represented using semantic structures and text-meaning representations, and categorization of quantifiers based on parameters like the concept being quantified, time, iteration, and relativity.
L'année 2015 sera marquée par des événements "remarquables".
Le social, le sociétal et l'environnemental sont trois maître-mots en tête de gondole d'une société en plein doute, questionnement.
Serait-ce alors l'année du retour aux valeurs nobles et fortes, au dépassement du "moi" (pour aller vers "l'autre"), à "l'être" (non au "paraître") ?
L'Humain veut recouvrer de l'espoir, redevenir passionné (enthousiaste), ressentir un esprit d'unité, de vérité et d'équité.
Au-delà des "étiquettes" (politiques, sociales et syndicales), un mouvement de fond (ie de "front") émerge progressivement, véhément à "faire bouger les lignes".
Qu'il se nomme "rouge (social)-rose (sociétal)-vert (environnemental)", qu’il opte pour le dialogue via une conférence européenne vers une coopération internationale entre les peuples, une transition écologique ambitieuse, attentive (impacts tant sur notre Univers que sur les "vivants") et une refondation (un renouveau) démocratique, pour une démocratie directe, ou qu’il mène une large réflexion pour une république et une écologie plus sociale et solidaire, il recherche avant tout à faire preuve d’un engagement unitaire "juste et vrai", "fort et courageux".
Alors que certains parlent d’uberisation de la classe politique et syndicale, d’autres agissent pour reconstruire les liens avec les citoyens, pour co-construire l’avenir à force de propositions (et non d’opposition), au-delà des clivages (des chapelles) traditionnels…
La France doit prendre cet "instant de responsabilité", prouver sa force authentique à rassembler (et non à diviser), à mélanger les "origines" pour affronter les mutations du XXIe siècle.
1) The document discusses the benefits of meditation for reducing stress and anxiety.
2) It states that meditating for just 10 minutes per day using focused breathing can help calm the mind and lower stress levels within a few weeks.
3) Meditation has also been shown to have additional health benefits like reducing blood pressure and improving overall well-being over time with regular practice.
Este documento descreve um evento sobre morte assistida organizado por um Núcleo de Estágio de Filosofia. Ele fornece detalhes sobre a data, hora e local do evento, bem como sugestões de filmes, documentários e obras para o tema. O documento também discute os limites da ciência, a bioética e alguns dos principais temas da bioética, incluindo eutanásia.
This document outlines key topics in consumer behavior that are covered in Chapter 5, including the model of consumer behavior, characteristics affecting consumer behavior like culture, personality, and motivation, different types of buying decisions, and the consumer decision process of need recognition, information search, evaluation, purchase, and post-purchase evaluation. It provides an overview of the chapter's content through a slideshow format.
L'année 2015 sera marquée par des événements "remarquables".
Le social, le sociétal et l'environnemental sont trois maître-mots en tête de gondole d'une société en plein doute, questionnement.
Serait-ce alors l'année du retour aux valeurs nobles et fortes, au dépassement du "moi" (pour aller vers "l'autre"), à "l'être" (non au "paraître") ?
L'Humain veut recouvrer de l'espoir, redevenir passionné (enthousiaste), ressentir un esprit d'unité, de vérité et d'équité.
Au-delà des "étiquettes" (politiques, sociales et syndicales), un mouvement de fond (ie de "front") émerge progressivement, véhément à "faire bouger les lignes".
Qu'il se nomme "rouge (social)-rose (sociétal)-vert (environnemental)", qu’il opte pour le dialogue via une conférence européenne vers une coopération internationale entre les peuples, une transition écologique ambitieuse, attentive (impacts tant sur notre Univers que sur les "vivants") et une refondation (un renouveau) démocratique, pour une démocratie directe, ou qu’il mène une large réflexion pour une république et une écologie plus sociale et solidaire, il recherche avant tout à faire preuve d’un engagement unitaire "juste et vrai", "fort et courageux".
Alors que certains parlent d’uberisation de la classe politique et syndicale, d’autres agissent pour reconstruire les liens avec les citoyens, pour co-construire l’avenir à force de propositions (et non d’opposition), au-delà des clivages (des chapelles) traditionnels…
La France doit prendre cet "instant de responsabilité", prouver sa force authentique à rassembler (et non à diviser), à mélanger les "origines" pour affronter les mutations du XXIe siècle.
1) The document discusses the benefits of meditation for reducing stress and anxiety.
2) It states that meditating for just 10 minutes per day using focused breathing can help calm the mind and lower stress levels within a few weeks.
3) Meditation has also been shown to have additional health benefits like reducing blood pressure and improving overall well-being over time with regular practice.
Este documento descreve um evento sobre morte assistida organizado por um Núcleo de Estágio de Filosofia. Ele fornece detalhes sobre a data, hora e local do evento, bem como sugestões de filmes, documentários e obras para o tema. O documento também discute os limites da ciência, a bioética e alguns dos principais temas da bioética, incluindo eutanásia.
This document outlines key topics in consumer behavior that are covered in Chapter 5, including the model of consumer behavior, characteristics affecting consumer behavior like culture, personality, and motivation, different types of buying decisions, and the consumer decision process of need recognition, information search, evaluation, purchase, and post-purchase evaluation. It provides an overview of the chapter's content through a slideshow format.
This document discusses tensor decomposition with Python. It begins by explaining what tensor decomposition and factorization are, and how they can be used to represent multi-dimensional datasets and perform dimensionality reduction. It then discusses matrix and tensor factorization methods like NMF, topic modeling, and CP/PARAFAC decomposition. The remainder of the document provides examples of tensor decomposition using Python tools and libraries, and discusses applications to analyzing temporal network and sensor data.
Ejercicios de estilo en la programaciónSoftware Guru
El escritor francés Raymond Queneau escribió a mediados del siglo XX un libro llamado "Ejercicios de Estilo" donde mostraba una misma historia corta, redactada de 99 formas distintas.
En esta plática realizaremos el mismo ejercicio con un programa de software. Abarcaremos distintos estilos y paradigmas: programación monolítica, orientada a objetos, relacional, orientada a aspectos, monadas, map-reduce, y muchos otros, a través de los cuales podremos apreciar la riqueza del pensamiento humano aplicado a la computación.
Esto va mucho más allá de un ejercicio académico; el diseño de sistemas de gran escala se alimenta de esta variedad de estilos. También platicaremos sobre los peligros de quedar atrapado bajo un conjunto reducido de estilos a lo largo de tu carrera, y la necesidad de verdaderamente entender distintos estilos al diseñar arquitecturas de sistemas de software.
Semblanza del conferencista:
Crista Lopez es profesora en la Facultad de Ciencias Computacionales de la Universidad de California en Irvine. Su investigación se enfoca en prácticas de ingeniería de software para sistemas de gran escala. Previamente, fue miembro fundador del equipo en Xerox PARC creador del paradigma de programación orientado a aspectos (AOP). Crista es una de las desarrolladoras principales de OpenSimulator, una plataforma open source para crear mundos virtuales 3D. También es fundadora de Encitra, empresa especializada en la utilización de la realidad virtual para proyectos de desarrollo urbano sustentable. @cristalopes
A Family of Reactive-Cognitive Architectures based on Natural Language Processing, as Decision-Making Helpers for IoT, in the Closed- or Open-World Assumption.
The document discusses arithmetic sequences, including defining them recursively or through an implicit linear equation, finding the common difference and nth term, and examples of determining terms and sums of arithmetic sequences given initial terms or the values of a and d. It also provides homework problems involving identifying arithmetic sequences, writing terms, and calculating sums of sequences.
Chapter 2 Mathematical Language and Symbols.pdfRaRaRamirez
This document discusses mathematical language and symbols. It defines key concepts such as sets, relations, functions, and binary operations. Sets are collections of distinct objects that can be defined using a roster or rule. Relations pair elements between two sets. A function is a special type of relation where each input is paired with exactly one output. Binary operations take two inputs from a set and return an output in that same set. Common properties of binary operations include commutativity and associativity.
This document provides information about sequences and series in mathematics. It defines a sequence as a function whose domain is the set of natural numbers and whose range is a set of term values. Examples of finding the next term in sequences are provided. Summation notation is introduced to write the terms of a series and evaluate its sum. Convergent and divergent sequences are defined. Properties of sequences and summation are outlined, including using Desmos to list terms of a sequence. Examples are provided to demonstrate evaluating finite and infinite series using summation notation and properties. Exercises for students are listed at the end.
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The document discusses the origins and evolution of fuzzy logic, beginning with fuzzy set theory proposed by Zadeh in 1965 which aimed to represent vagueness in natural language using fuzzy sets with non-crisp boundaries. It explains key concepts in fuzzy logic like membership functions, fuzzy set operations, fuzzy relations and compositions. The document also compares classical sets with crisp boundaries to fuzzy sets and contrasts crisp logic with fuzzy logic which allows for degrees of truth between 0 and 1.
The document discusses the history of object-oriented programming. It describes early computing projects like Project Whirlwind that used interactive computing. It then discusses Ivan Sutherland's 1963 PhD thesis called Sketchpad, which is considered a precursor to object-oriented programming. Sketchpad used the concept of objects and components to allow for interactive drawing with a light pen on a computer screen. The general functions developed in Sketchpad gave it the ability to operate on different types of entities, laying the foundations for object-oriented programming.
This document provides examples of different R data structures including vectors, matrices, lists, and data frames. Vectors are one-dimensional arrays that can contain only one data type. Matrices are two-dimensional arrays that can contain only one data type. Lists are collections of elements that can contain different data types. Data frames are two-dimensional structures similar to tables or spreadsheets that can contain different data types across rows and columns. The document demonstrates how to create, subset, and manipulate each of these structures through examples.
The document discusses the key differences between the English and mathematics languages, including how words, symbols, and concepts have different meanings or representations. It explains how mathematics has developed a precise symbolic language to concisely express relationships, operations, and concepts in a way that is internationally understood regardless of spoken language. Precise definitions and notations are provided for important mathematical concepts like sets, relations, functions, and equations.
A Psychophysical Investigation of Size as a Physical VariableYvonne Jansen
This document summarizes a psychophysical study that investigated how accurately people can estimate the relative sizes of elementary physical shapes. The study presented participants with pairs of bars and spheres of varying sizes and asked them to estimate size ratios using two methods. For bars, estimates were highly accurate and linear regardless of encoding method. For spheres, encoding by volume led to misleading underestimates, while surface area encoding produced more accurate overestimates. The study provides insights into how different physical variables influence size perception and recommendations for effectively encoding data physically.
Python 101++: Let's Get Down to Business!Paige Bailey
You've started the Codecademy and Coursera courses; you've thumbed through Zed Shaw's "Learn Python the Hard Way"; and now you're itching to see what Python can help you do. This is the workshop for you!
Here's the breakdown: we're going to be taking you on a whirlwind tour of Python's capabilities. By the end of the workshop, you should be able to easily follow any of the widely available Python courses on the internet, and have a grasp on some of the more complex aspects of the language.
Please don't forget to bring your personal laptop!
Audience: This course is aimed at those who already have some basic programming experience, either in Python or in another high level programming language (such as C/C++, Fortran, Java, Ruby, Perl, or Visual Basic). If you're an absolute beginner -- new to Python, and new to programming in general -- make sure to check out the "Python 101" workshop!
- R is a free software environment for statistical computing and graphics. It has an active user community and supports graphical capabilities.
- R can import and export data, perform data manipulation and summaries. It provides various plotting functions and control structures to control program flow.
- Debugging tools in R include traceback, debug, browser and trace which help identify and fix issues in functions.
The document discusses various techniques for representing text for classification tasks, including bag-of-words representations, term frequency-inverse document frequency (TF-IDF) weighting, and n-grams. It covers extracting unigram and bigram features to capture word and word-pair frequencies from documents. The document also discusses removing stopwords and using word histograms or one-hot encodings to transform text into numerical feature vectors.
This document provides an overview of statistical concepts and analysis techniques in R, including measures of central tendency, data variability, correlation, regression, and time series analysis. Key points covered include mean, median, mode, variance, standard deviation, z-scores, quartiles, standard deviation vs variance, correlation, ANOVA, and importing/working with different data structures in R like vectors, lists, matrices, and data frames.
The document summarizes a lecture on blending, compositing, and anti-aliasing in computer graphics. It discusses how colors are combined during rendering using blending operations, and how compositing operates on entire images rather than individual pixels. Porter-Duff models for digital image compositing are explained, along with how they relate to OpenGL blending functions.
The document discusses the Sphinx in ancient Egyptian and other cultures. It provides details about the Great Sphinx of Giza, including that it is the largest monolith in the world at 241 feet long. It describes the construction process for the Sphinx and highlights erosion damage to its walls and face over time.
Discussion of types of pyramids as they developed through Ancient Egypt to the common pyramid we think of today--and how they were built and used as tombs
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Please don't forget to bring your personal laptop!
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Computing the "Fuzziness" of Scalar Quantification in Ontological S...Whitney Vandiver
Whitney Vandiver presented a paper on computing the "fuzziness" of scalar quantification in ontological semantics. The paper discusses how scalar quantifiers like "a little", "some", and "many" have fuzzy boundaries that are context dependent. It proposes using ontological semantics to represent scalar quantification using scales and ranges. This allows quantifiers to be given relaxable ranges and handles composition of quantifiers. Representing quantification this way could benefit natural language processing by providing a flexible way to model relative concepts with fuzzy measurements.
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
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
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
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