Boolean AND and the Semantic Correlates of Gradable Adjectives
|
|
- Joleen Morton
- 5 years ago
- Views:
Transcription
1 Boolean AND and the Semantic Correlates of Gradable Adjectives Alan Bale September 13 th, Introduction General Issues: 1. What are the semantic properties correlated with being syntactically categorized as a Gradable Adjective? Are Gradable Adjectives inherently linked to degrees or rather are degrees a creation of the comparative and equative morphemes? 2. How should conjunction be interpreted? Should the interpretation of conjunction be a boolean operator (specifically a boolean meet operator)? Specific Issue: Traditional views on the interpretation of gradable adjectives (as degree functions or relations between individuals and degrees) and the interpretation of conjunction (as boolean meet or intersection) have difficulties accounting for the sentences in (1). (1) a. Jen is more beautiful and intelligent than Morag is. b. Jen is as tall and wide as Morag is. In this talk I argue that sentences such as those in (1) are inconsistent with interpreting gradable adjectives as involving degrees while maintaining a boolean interpretation of conjunction. One of the two interpretations must be given up. I will explore and evaluate the following possible solution: * Gradable adjectives are interpreted as relations between individuals (much like the classical interpretation of transitive verbs). This interpretation of adjectives can account for the sentences in (1) while maintaining a traditional interpretation of conjunction. (Possible Alternative: Conjoined phrases are interpreted as structured meanings as proposed by Winter, We will not be able to explore this alternative in this talk.) 2 Are Gradable Adjectives Measure Functions? Sentences like those in (2) can easily be given an analysis using degrees (or structured equivalents such as extents and delineations). 1
2 (2) a. This table is longer than the door-frame is wide. b. This table is longer than the couch is. TWO THEORIES OF DEGREES 1. ADJECTIVES AS MEASURE FUNCTIONS * Kennedy (1999), following Bartsch & Vennemann (1972), suggests that adjectives should be interpreted as functions form individuals to degrees. (3) a. Jen is taller than Morag. b. MAX{d : d T [tall ](j)} > MAX{d : d T [tall ](m)} = [tall ](j) > [tall ](m) 2. ADJECTIVES AS RELATIONS BETWEEN INDIVIDUALS AND DEGREES * Cresswell (1976) proposes that adjectives should be interpreted as relations between individuals and degrees. (4) a. Jen is taller than Morag. b. MAX{d : [tall ](j, d)} > T MAX{d : [tall ](m, d)} Simplifying: I will collapse the two theories into one shorthand... x is d-adj. This form will represent both possible interpretations of the adjective. * Measure Function Approach: x is d-adj will translate as d ADJ [ADJ ](x). * Degree Relation Approach: x is d-adj will translate as [ADJ ] (x, d). The sentences in (5a) and (6a) can be given the truth conditions in (5b) and (6b). (5) a. Jen is more beautiful than Morag is. b. M AX{d : Jen is d-beautiful} > M AX{d : Morag is d-beautiful} (6) a. Jen is as tall as Morag is. b. MAX{d : Jen is d-tall} MAX{d : Morag is d-tall} BACK TO THE SENTENCES PRESENTED IN (1): the interpretation of the sentences in (1) do not yield a meaning that is consistent with intuitions. (7) a. Jen is more beautiful and intelligent than Morag is. b. M AX{d : Jen is d-beautiful and d-intelligent} > M AX{d : Morag is d-beautiful and d-intelligent} (8) a. Jen is as tall and wide as Morag is. b. MAX{d : Jen is d-tall and d-wide} MAX{d : Morag is d-tall and d-wide} 2
3 The problem is two-fold: 1. By assumption, there are no degrees that are both degrees of beauty and intelligence. Thus the set of degrees in (7b) would be empty. MAX would be undefined. The sentence is predicted to be anomalous. * Under both theories of degrees: [beautiful ] [intelligent] = 2. The adjectives tall and wide do share a scale of lengths. However, there are still problems for conjoining these adjectives: * {d : Jen is d-tall and d-wide} is equivalent to {d : Jen is d-wide} since like most human beings Jen is taller than she is wide. * Similarly {d : Morag is d-tall and d-wide} is equivalent to {d : Morag is d-wide}. Consequently, (8b) is equivalent to... MAX{d : Jen is d-wide} MAX{d : Morag is d-wide}. This formula specifies the truth conditions of (9). (9) Jen is as wide as Morag is. BUT this is not what the sentence in (8a) means! 2.1 Reasons to think there is no ellipsis. Sentences with conjoined adjectives have the same truth conditions as sentences with conjoined comparative phrases. This raises the question of whether ellipsis might account for the data presented above. (10) a. Jen is more beautiful and more talented than Pat is. b. Jen is more beautiful and talented than Pat is. Reasons to think that there is no ellipsis (gapping). * As (11) demonstrates, with canonical gapping constructions, the felicity of the ellipsis/gap is not affected by the addition of other material between the two conjoined phrases as long as parallelism is maintained. (11) a. John fought with Betty and Fred with Suzan. b. John fought with Betty on Tuesday and Fred with Suzan on Wednesday. c. John fought with Betty in the mountain park on Tuesday and Fred with Suzan in the fountain park on Wednesday. 3
4 * Also, consider non-canonical gapping constructions. The agreement facts in (12a) suggest that a determiner is elided in the second half of the conjunct. It is reasonable to suspect that (12a) underlyingly has the same syntactic form as (12b). (12) a. This fork and knife are gifts from my mother. b. This fork and this knife are gifts from my mother. * As with canonical gapping constructions, non-cannonical constructions are not affected by the addition of material between the first and second half of the conjunct. This is demonstrated in (13). (13) a. This fork and knife that I used this morning are gifts from my mother. b. This fork that I used yesterday and knife that I used this morning are gifts from my mother. * HOWEVER, the addition of material DOES affect the conjoined Gradable Adjectives. (14) a. Jen is more beautiful and intelligent than Morag is. b. Jen is as tall and wide as Morag is. (15) a. Jen is more beautiful than Betty is and more intelligent than Morag is. b.? Jen is more beautiful than Betty is and intelligent than Morag is. (16) a. Jen is as tall as Betty is and as wide as Morag is. b.?? Jen is as tall as Betty is and wide as Morag is. (17) a. Jen is less intelligent and beautiful than Morag is. b. Jen is less intelligent than Betty is and less beautiful than Morag is. c.?? Jen is less intelligent than Betty is and beautiful than Morag is. * FURTHERMORE, in canonical gapping constructions, the comparative and equative morpheme cannot be elided without also eliding the adjective it modifies. (18) a. Morag and Patricia are quite beautiful and intelligent but [Jen is more beautiful than Morag] and [Betty more intelligent than Patricia]. b. Morag and Patricia are quite intelligent but [Jen is more intelligent than Morag] and [Betty than Patricia]. c. * Morag and Patricia are quite beautiful and intelligent but [Jen is more beautiful than Morag] and [Betty intelligent than Patricia]. (19) a. Morag and Patricia are quite tall and wide but [Jen is as tall as Morag] and [Betty as wide as Patricia]. 4
5 b. Morag and Patricia are quite intelligent but [Jen is more intelligent than Morag] and [Betty than Patricia]. c. * Morag and Patricia are quite tall and wide but [Jen is as tall as Morag] and [Betty wide as Patricia]. SUMMARY: An ellipsis or gapping account encounters two problems Constructions with conjoined adjectives do not have the same properties as other constructions with ellipsis or gapping. 2. In other canonical gapping constructions, the comparative can never be elided/gapped without also eliding/gapping the adjective. 3 Are Gradable Adjectives Binary Relations? SOLUTION: A potential solution to this problem involves rejecting the idea that Gradable Adjectives are inherently linked to degrees and adopting a position where adjectives are interpreted as binary relations between individuals... * Transitive and reflexive relations such as [beautiful ] = { x, y : x has as much beauty as y} 2. [intelligent] = { x, y : x has as much intelligence as y} 3. [wide] = { x, y : x has as much width as y} 4. [tall ] = { x, y : x has as much height as y} * These relations are called Pre-orders or Quasi Orders (QOs). Consequences: * In such a theory, scales and degrees would be derived from the Gradable Adjectives by the comparative morpheme. * Combining Gradable Adjectives with boolean and allows for the creation of compounded scales that would give the correct truth conditions for the sentences in (1). Aside: Worries about the the QOs leading to semantic circularity: * In constructing scales from QOs, it seems as if one is defining a semantics for comparatives using a relation specified in terms of comparative and equative sentences. * BUT, there is a difference between the concept of comparison and the semantics of how comparative and equative sentences are given truth values. 5
6 * CONCEPT OF COMPARISON WITHOUT LANGUAGE: The underlying QO does not require an analysis of comparatives to define the relation. All it assumes is that given two individuals, speakers can tell if one has as much of a certain property as the other. * Even those without language (monkeys, cats, dogs) are able to compare two objects or individuals in terms of a certain property (to tell which food bowl has more, or which potential mates are more suitable/beautiful). DETAILS OF THE SOLUTION 1. Deriving Scales From QOs (cf. Cresswell, 1976; Klein, 1991): The quotient structure of the QO can be used as a scale. * Building a quotient structure involves two steps: (a) Individuals that are reflexively related are collapsed into equivalence classes. (b) The equivalence classes are ordered in a way that is congruent to the original QO, thus creating a scale. (An equivalence class A is ranked above an equivalence class B iff for all x that are members of A and all y that are members of B, x, y is a member of the QO but not y, x.) (20) Quasi Order Quotient Structure Conventional Representation a {a} d 1 = {a} b c {b, c} d 2 = {b, c} d {d} d 3 = {d} e f g {e, f, g} d 4 = {e, f, g} h i {h, i} d 5 = {h, i} j {j} d 6 = {j} 2. Deriving Compounded Scales: If beautiful and intelligent are both interpreted as QOs that encode relations between individuals, then their intersection would also be a QO (transitivity and reflexivity are preserved under intersection). 6
7 * The nature of this intersected QO can be described in the following way: *** x, y ( [beautiful ] [intelligent]) iff ( x, y [beautif ul ]) AND ( x, y [intelligent]) ** * This entails that x, y is a member of the intersected quasi-order iff x has as much beauty as y and x has as much intelligence as y. (21) B I = B I a c a b a b c b = c d f f e g d f h e g e g h d h * When this intersected QO is converted into a scale, the equivalence classes (and hence degrees) are ordered with respect to both properties.(an equivalence class X will be greater than Y iff every member of X has more beauty and more intelligence than every member of Y.) 7
8 (22) d a d b d c d f d d d e d g d h 3. Interpreting the Comparative: The comparative morpheme is a function that takes three arguments: a QO, a degree and an individual (symbolized by the variables P, d, and x respectively). The details of such an interpretation are given in (23) and (24). * Representing Degrees as ordered pairs (cf. Cresswell,1976): Any degree d is represented as an ordered pair d n, P, where d n is an equivalence class and P is an ordering relation that ranks equivalence classes in a scale. (23) a. MORE( d 1, P, d 2, Q ) is defined iff P = Q, when defined: MORE( d 1, P, d 2, Q ) = 1 iff (d 1 P d 2 )& (d 2 P d 1 ). b. AS( d 1, P, d 2, Q ) is defined iff P = Q, when defined: AS( d 1, P, d 2, Q ) = 1 iff (d 1 P d 2 ). (24) a. [more] = λp λd λx MORE( x P /, P /, d) b. [as] = λp λd λx AS( x P /, P /, d) 4. THAN-CLAUSES: Than-clause can be interpreted as a degree (the exact degree being determined by the adjective and individual in the clause). * The than-clause in (1) than Morag is can be assigned the degree m (B I )/, (B I ) /, where (B I) / is the intersection of the two quasi-orders [beautiful ] and [intelligent] and m B I is the equivalence class containing Morag (m) relative to the 8
9 intersection. * Likewise the second as-clause in the equative in (1) as Morag is can be assigned the degree m (T W )/, (T W )/, where T W is the intersection of the two quasiorders [tall ] and [wide]. * NOTE: Like others, I assume that the than-clause and as-clause contain a copy of the AP in the main clause ([beautiful and intelligent] and [wide and tall] respectively). 5. EXAMPLES: The interpretation of the sentences in (1) can be represented as in (25) and (26). (25) a. [ Jen is more beautiful and intelligent than Morag is ] = ( ( ( [more] [beautiful and intelligent]) [than Morag is...] ) [Jen] ) = ( ( ( ( (λp λdλx MORE( x P /, P /, d) ) B I ) m (B I )/, (B I )/ )j ) =MORE( j (B I )/, (B I )/, m (B I )/, (B I )/ ) (Let the equivalence class containing Jen and the one containing Morag j (B I )/ and m (B I )/ be represented by d j and d m respectively. Let the partial order based on the relation (B I) / be represented by with no subscripts.) =MORE( d j,, d m, ) = 1 iff (d j d m ) & (d m d j ) b. INTERSECTING ADJECTIVES B I B I (B I) / h j h d h i h i d i j i j k m m d m l n k d k m o l d l d j n l n d n o k o d o (26) a. [Jen is as tall and wide as Morag is] = ( ( ( [as] [tall and wide]) [as Morag is...] ) [Jen] ) 9
10 = ( ( ( ( (λp λdλx AS( x P /, P /, d) ) T W ) m (T W )/, (T W )/ )j ) =AS( j (T W )/, (T W )/, m (T W )/, (T W )/ ) (Let the equivalence class containing Jen and the one containing Morag j (T W )/ and m (T W )/ be represented by d j and d m respectively. Let the partial order based on the relation (T W ) / be represented by with no subscripts.) =AS( d j,, d m, ) = 1 iff d j d m b. INTERSECTING ADJECTIVES T W T W (T W) / h h h d h i l i d i j i j d j k j l d l l n k d k m k m n m n d n o o o d o 4 What About Disjunction? Not only can adjectives be combined with and, they also can be combined with or... (27) a. Jen is more intelligent or beautiful than Morag is. b. Jen is as tall or wide as Morage is. Potential Problem: A boolean interpretation of disjunction cannot account for these sentences. * Combining two Quasi Orders with set-union does not always yield a quasi order. Transitivity is not preserved. * Without a Quasi Order, one cannot form a scale. Scales require transitivity. HOWEVER: As many others have pointed out (Alonso-Ovalle, 2006; Larson, 1985; Schwarz, 1999; Simons, 2005, 2006; Zimmermann, 2001), there are many contexts where disjunction seems to take wider scope than its surface position. 10 d m
11 (28) Everybody thinks that Mary insulted Patrick or Dan. a. Compatible situation with potential narrow scope: Half of the people think that Mary insulted Patrick and the other half think she insulted Dan. b. Compatible situation with potential wide scope: Either everybody thinks that Mary insulted Patrick or they think that Mary insulted Dan (I can t remember which). FURTHERMORE, the wide scope of disjunction cannot be completely reduced to ellipsis/gapping (contrary to the proposal of Schwarz, 1999). * Gapping remnants must have a correlate in the antecedent. (29) a. Some talked about politics and others about music. (Schwarz ex.40c) b. *Some talked about politics and others with me about music. (Schwarz ex.40b) * Wide scope of disjunction does not require this kind of parallelism. (30) John thinks that Mary talked about politics or about music with her brother (I can t remember which). (Note, this judgment is contrary to those reported in Schwarz, 1999.) The non-boolean interpretations of disjunction can derive the correct truth conditions for the sentences in (27) no matter how the adjective is interpreted. BUT is there an asymmetry between the two types of coordinations? Is conjunction Boolean but not disjunction? (Evidence presented by Husley 2006 suggests that there is indeed such an asymmetry. The work of Winter, 1995, is also relevant with respect to this issue.) 5 Tentative Conclusions? I have argued that popular views on the interpretation of and (as Boolean Meet) and the interpretation of gradable adjectives (as a measure function/relation) encounters empirical problems. One way to address this problem is to alter the interpretation of gradable adjectives. I have explored this option in this talk, suggesting... Gradable Adjectives are interpreted as binary relations between individuals and do not directly involve degrees. Another alternative that was not explored in this talk was to alter the interpretation of conjunction. Acknowledgments: I would like to thank Brendan Gillon, Danny Fox, Irene Heim, Kai von Fintel, Heather Newell, Bernhard Schwarz, and all the participants in the LF-Reading Group at MIT. 11
12 References [1] Alonso-Ovalle, L. (2006). Disjunction in Alternative Semantics. PhD dissertation, UMass Amherst. [2] Bartsch, R. and Vennemann, T. (1972). Semantic Structures. Athenaum, Frankfurt. [3] Cresswell, M. (1976). The Semantics of Degree. In: B. Partee (ed.), Montague Grammar. Academic Press, New York. [4] Cresswell, M. (1985). Structured Meanings. MIT Press. [5] Hendriks, H. (1993). Studied Flexibility. Ph.D. diss., University of Amsterdam. [6] Hulsey, S. (2006). An Argument from Gapping for a Hamblin Semantics for Disjunction. Presentation given at NELS 37. [7] Johnson, K. (2004). In Search of the English Middle Field. Manuscript. UMASS. Kennedy, C. (1999) Projecting the Adjective. Ph.D Dissertation, UCSC. [8] Klein, E. (1991). Comparatives. In: A. von Stechow, D. Wunderlich (eds.), Semantik/Semantics: An International Handbook of Contemporary Research. Waler de Gruyter. [9] Larson, R. (1985). On the syntax of disjunction scope. Natural Language and Linguistic Theory 3, pp [10] Schwarz, B. (1999). On the syntax of either...or. Natural Language and Linguistic Theory, 17: [11] Simons, M. (2005). Dividing things up: The semantics of or and the modal/or interaction. Natural Language Semantics 13, [12] Winter, Y. (1995). Syncategorematic conjunction and structured meanings. Proceedings of Semantics and Linguistic Theory (SALT) 5. [13] Zimmermann, T.E. (2000). Free choice disjunction and Epistemic Possibility. Natural Language Semantics 8(4), pp
Gradable Adjectives, Compounded Scales, Conjunction and Structured Meanings
Gradable Adjectives, Compounded Scales, Conjunction and Structured Meanings Alan Bale (alanbale@mit.edu) Winter, 2007 1 Introduction General Issues: 1. What are the semantic properties correlated with
More informationa. Rachel is {taller / more intelligent} than Stephanie (is). a. Rachel is the {tallest / most intelligent} (student in my class).
Degree semantics1 1 Gradability Certain predicates allow us to specify to what extent the predicate holds; we call them gradable. There are many constructions which only apply to gradable predicates. (1)
More informationSeminar in Semantics: Gradation & Modality Winter 2014
1 Subject matter Seminar in Semantics: Gradation & Modality Winter 2014 Dan Lassiter 1/8/14 Handout: Basic Modal Logic and Kratzer (1977) [M]odality is the linguistic phenomenon whereby grammar allows
More informationScales and comparison classes
Noname manuscript No. (will be inserted by the editor) Scales and comparison classes Alan Clinton Bale the date of receipt and acceptance should be inserted later Abstract This paper evaluates three accounts
More informationA Universal Scale of Comparison
A Universal Scale of Comparison Alan Clinton Bale December 12, 2007 Abstract. Comparative constructions form two classes, those that permit direct comparisons (comparisons of measurements as in Seymour
More informationBreaking de Morgan s law in counterfactual antecedents
Breaking de Morgan s law in counterfactual antecedents Lucas Champollion New York University champollion@nyu.edu Ivano Ciardelli University of Amsterdam i.a.ciardelli@uva.nl Linmin Zhang New York University
More informationIntroduction to Pragmatics
Introduction to Pragmatics Summer 2016 Tuesdays 2:30--4:00pm @ 2321.HS 3H INSTRUCTOR Todor Koev (Todor.Koev@uni-duesseldorf.de) Presupposition projection Presupposition is a prevalent type of inference
More informationAntonymy and Evaluativity
Antonymy and Evaluativity SEMANTICS AND LINGUISTIC THEORY 17 MAY 11, 2007 Jessica Rett hughesj@rutgers.edu A construction is evaluative if it makes reference to a degree that exceeds a contextuallyvalued
More informationHedging Your Ifs and Vice Versa
Hedging Your Ifs and Vice Versa Kai von Fintel and Anthony S. Gillies MIT and Rutgers November 21 University of Latvia Ramsey s Test If two people are arguing If p will q? and are both in doubt as to p,
More informationTwo sets of alternatives for numerals
ECO5 @ Harvard April 11, 2015 Teodora Mihoc, tmihoc@fas.harvard.edu Alexander Klapheke, klapheke@fas.harvard.edu Two sets of alternatives for numerals Contents 1 Preliminaries 1 2 Horn-style alternatives:
More information564 Lecture 25 Nov. 23, Continuing note on presuppositional vs. nonpresuppositional dets.
564 Lecture 25 Nov. 23, 1999 1 Continuing note on presuppositional vs. nonpresuppositional dets. Here's the argument about the nonpresupp vs. presupp analysis of "every" that I couldn't reconstruct last
More informationSemantics and Generative Grammar. Quantificational DPs, Part 3: Covert Movement vs. Type Shifting 1
Quantificational DPs, Part 3: Covert Movement vs. Type Shifting 1 1. Introduction Thus far, we ve considered two competing analyses of sentences like those in (1). (1) Sentences Where a Quantificational
More informationQuantifiers in Than-Clauses *
Quantifiers in Than-Clauses * revised July 2009 Abstract The paper reexamines the interpretations that quantifiers in than-clauses give rise to. It develops an analysis that combines an interval semantics
More informationThe Semantics of Questions Introductory remarks
MIT, September-October 2012 1 1. Goals for this class The Semantics of Questions Introductory remarks (1) a. Which boy (among John, Bill and Fred) read the book? Uniqueness presupposition (UP): exactly
More informationSeminar in Semantics: Gradation & Modality Winter 2014
Seminar in Semantics: Gradation & Modality Winter 2014 Dan Lassiter 1/15/14 Handout Contents 1 Sign up to present a reading and lead discussion 1 2 Finishing up Kratzer 1991 1 3 Klein 1980 4 4 Orders and
More informationQuantifiers in than-clauses
Semantics & Pragmatics Volume 3, Article 1: 1 72, 2010 doi: 10.3765/sp.3.1 Quantifiers in than-clauses Sigrid Beck University of Tübingen Received 2009-01-13 / First Decision 2009-03-17 / Revised 2009-06-17
More informationDEGREE QUANTIFIERS, POSITION OF MERGER EFFECTS WITH THEIR RESTRICTORS, AND CONSERVATIVITY
DEGREE QUANTIFIERS, POSITION OF MERGER EFFECTS WITH THEIR RESTRICTORS, AND CONSERVATIVITY RAJESH BHATT AND ROUMYANA PANCHEVA University of Texas, Austin bhatt@cs.utexas.edu University of Southern California
More informationQUANTIFICATIONAL READINGS OF INDEFINITES
QUANTIFICATIONAL READINGS OF INDEFINITES WITH FOCUSED CREATION VERBS * Tamina Stephenson, Massachusetts Institute of Technology tamina@mit.edu Abstract This paper looks at sentences with quantificational
More informationDegree equatives: The same as comparatives?
Degree equatives: The same as comparatives? Zukunftskolleg & Department of Linguistics Workshop Equative Constructions Unversität zu Köln 15 December 2016 Equatives in degree semantics Degree semantic
More informationPresuppositions (introductory comments)
1 Presuppositions (introductory comments) Some examples (1) a. The person who broke the typewriter was Sam. b. It was Sam who broke the typewriter. c. John screwed up again. d. John likes Mary, too. e.
More information127: Lecture notes HT17. Week 8. (1) If Oswald didn t shoot Kennedy, someone else did. (2) If Oswald hadn t shot Kennedy, someone else would have.
I. Counterfactuals I.I. Indicative vs Counterfactual (LfP 8.1) The difference between indicative and counterfactual conditionals comes out in pairs like the following: (1) If Oswald didn t shoot Kennedy,
More informationTwo Reconstruction Puzzles Yael Sharvit University of Connecticut
Workshop on Direct Compositionality June 19-21, 2003 Brown University Two Reconstruction Puzzles Yael Sharvit University of Connecticut yael.sharvit@uconn.edu Some constructions exhibit what is known as
More informationRelational Reasoning in Natural Language
1/67 Relational Reasoning in Natural Language Larry Moss ESSLLI 10 Course on Logics for Natural Language Inference August, 2010 Adding transitive verbs the work on R, R, and other systems is joint with
More informationPropositional Logic. Testing, Quality Assurance, and Maintenance Winter Prof. Arie Gurfinkel
Propositional Logic Testing, Quality Assurance, and Maintenance Winter 2018 Prof. Arie Gurfinkel References Chpater 1 of Logic for Computer Scientists http://www.springerlink.com/content/978-0-8176-4762-9/
More informationTwo kinds of long-distance indefinites Bernhard Schwarz The University of Texas at Austin
Amsterdam Colloquium 2001, December 17-19, 2001 Two kinds of long-distance indefinites Bernhard Schwarz The University of Texas at Austin 1. Introduction Indefinites can often be interpreted as if they
More informationGeneralized Quantifiers Logical and Linguistic Aspects
Generalized Quantifiers Logical and Linguistic Aspects Lecture 1: Formal Semantics and Generalized Quantifiers Dag Westerståhl University of Gothenburg SELLC 2010 Institute for Logic and Cognition, Sun
More informationlist readings of conjoined singular which -phrases
list readings of conjoined singular which -phrases Andreea C. Nicolae 1 Patrick D. Elliott 2 Yasutada Sudo 2 NELS 46 at Concordia University October 18, 2015 1 Zentrum für Allgemeine Sprachwissenschaft
More informationCHAPTER THREE: RELATIONS AND FUNCTIONS
CHAPTER THREE: RELATIONS AND FUNCTIONS 1 Relations Intuitively, a relation is the sort of thing that either does or does not hold between certain things, e.g. the love relation holds between Kim and Sandy
More informationInternal and Interval Semantics for CP-Comparatives
Internal and Interval Semantics for CP-Comparatives Fred Landman Linguistics Department, Tel Aviv University, landman@post.tau.ac.il Abstract. The interval degree semantics for clausal (CP)-comparatives
More informationBasics of conversational implicatures
Semantics I, Rutgers University Week 12 Yimei Xiang November 19, 2018 1. Implication relations Basics of conversational implicatures Implication relations are inferential relations between sentences. A
More informationTruth-Functional Logic
Truth-Functional Logic Syntax Every atomic sentence (A, B, C, ) is a sentence and are sentences With ϕ a sentence, the negation ϕ is a sentence With ϕ and ψ sentences, the conjunction ϕ ψ is a sentence
More informationExtensions to the Logic of All x are y: Verbs, Relative Clauses, and Only
1/53 Extensions to the Logic of All x are y: Verbs, Relative Clauses, and Only Larry Moss Indiana University Nordic Logic School August 7-11, 2017 2/53 An example that we ll see a few times Consider the
More information1 Introduction to again
Additive again Introduction to again Cara Feldscher March 9, 206 Michigan State University Examples from the Oxford English Dictionary go back as far as 523 in (5a). (5) a. It is worthe halfe as moche
More informationPlural Superlatives and Distributivity
Plural Superlatives and Distributivity Natalia Fitzgibbons, Yael Sharvit and Jon Gajewski University of Connecticut 1. The Distributivity Problem and the Cut-off Problem In this paper we propose a unified
More informationLing 98a: The Meaning of Negation (Week 5)
Yimei Xiang yxiang@fas.harvard.edu 15 October 2013 1 Review Negation in propositional logic, oppositions, term logic of Aristotle Presuppositions Projection and accommodation Three-valued logic External/internal
More informationLecture 7. Logic. Section1: Statement Logic.
Ling 726: Mathematical Linguistics, Logic, Section : Statement Logic V. Borschev and B. Partee, October 5, 26 p. Lecture 7. Logic. Section: Statement Logic.. Statement Logic..... Goals..... Syntax of Statement
More informationDistributing the disjuncts over the modal space. Luis Alonso-Ovalle. University of Massachusetts, Amherst
Distributing the disjuncts over the modal space Luis Alonso-Ovalle University of Massachusetts, Amherst 1. The distribution requirement Time for dessert. Nobody can have anything unless Mom has explicitly
More informationAntecedents of counterfactuals violate de Morgan s law
Antecedents of counterfactuals violate de Morgan s law Lucas Champollion champollion@nyu.edu Joint work with Ivano Ciardelli and Linmin Zhang Fourth Workshop on Natural Language and Computer Science (NLCS
More informationSpring 2017 Ling 620. An Introduction to the Semantics of Tense 1
1. Introducing Evaluation Times An Introduction to the Semantics of Tense 1 (1) Obvious, Fundamental Fact about Sentences of English The truth of some sentences (of English) depends upon the time they
More informationPeter Hallman, University of Vienna
All and Every as Quantity Superlatives Peter Hallman, University of Vienna peter.hallman@univie.ac.at Summary An analysis is proposed that captures similarities between most and all in English bytreatingall
More informationThe Puzzles of Deontic Logic
The Puzzles of Deontic Logic 04.09.12 William Starr Phil 6710 / Ling 6634 Spring 2012 For now, we won t place any constraints on R Notation: R(w) := {w R(w, w )} Models M = R, W, v A model says what the
More informationTOPICS IN DEGREE SEMANTICS: 4 LECTURES HANDOUT 1: DEGREES
TOPICS IN DEGREE SEMANTICS: 4 LECTURES HANDOUT 1: DEGREES ARNIM VON STECHOW, TÜBINGEN 1. Plot of the Lectures...1 2. Reading...2 3. What are degrees?...3 4. Comparative as relation between degrees...4
More informationIntensional semantics: worlds, modals, conditionals
Intensional semantics: worlds, modals, conditionals 1 Limitations of the actual world Recall some assumptions we have followed in this class: Sentences are conditional truth values ( 1 iff truth condition]
More informationVacuous and Non-Vacuous Behaviors of the Present Tense
Vacuous and Non-Vacuous Behaviors of the Present Tense Laine Stranahan Department of Linguistics, Harvard University stranahan@fas.harvard.edu 88 th Annual Meeting of the Linguistic Society of America
More informationCS1021. Why logic? Logic about inference or argument. Start from assumptions or axioms. Make deductions according to rules of reasoning.
3: Logic Why logic? Logic about inference or argument Start from assumptions or axioms Make deductions according to rules of reasoning Logic 3-1 Why logic? (continued) If I don t buy a lottery ticket on
More informationLess. the set of degrees that satisfy y the set of degrees that satisfy f
1 Less 1. Summary from last week (1) adjective meanings: relational (Rullmann's 'at least' interpretation), i.e. [[tall]] = ld.lx. TALL(x) d Functional ('exactly') meanings were equivalent for almost all
More informationSpring 2017 Ling 620. The Semantics of Modals, Part 2: The Modal Base 1
1. On Our Last Episode The Semantics of Modals, Part 2: The Modal Base 1 (1) The Failure of a Lexical Ambiguity Account Postulating separate lexical entries for all the different readings of a modal misses
More informationComparative superlatives in relative clauses
SynSem, Fall 2017 Comparative superlatives in relative clauses Nico(letta) Loccioni 1 Introduction Languages like Italian and Spanish extensively use relativization as a strategy to form relative interpretations
More informationComparatives and quantifiers
Empirical Issues in Syntax and Semantics 7 O. Bonami & P. Cabredo Hofherr (eds.) 2008, pp. 423 444 ØØÔ»»ÛÛÛº ÔºÒÖ º Ö» Comparatives and quantifiers Robert van Rooij 1 Introduction A traditional issue in
More informationSemantics and Generative Grammar. The Semantics of Adjectival Modification 1. (1) Our Current Assumptions Regarding Adjectives and Common Ns
The Semantics of Adjectival Modification 1 (1) Our Current Assumptions Regarding Adjectives and Common Ns a. Both adjectives and common nouns denote functions of type (i) [[ male ]] = [ λx : x D
More informationFirst-Degree Entailment
March 5, 2013 Relevance Logics Relevance logics are non-classical logics that try to avoid the paradoxes of material and strict implication: p (q p) p (p q) (p q) (q r) (p p) q p (q q) p (q q) Counterintuitive?
More informationSemantics 2 Part 1: Relative Clauses and Variables
Semantics 2 Part 1: Relative Clauses and Variables Sam Alxatib EVELIN 2012 January 17, 2012 Reviewing Adjectives Adjectives are treated as predicates of individuals, i.e. as functions from individuals
More informationPropositional Logic Truth-functionality Definitions Soundness Completeness Inferences. Modal Logic. Daniel Bonevac.
January 22, 2013 Modal logic is, among other things, the logic of possibility and necessity. Its history goes back at least to Aristotle s discussion of modal syllogisms in the Prior Analytics. But modern
More informationPropositions. Frequently, we will use the word statement instead of proposition.
Propositional Logic Propositions A proposition is a declaration of fact that is either true or false, but not both. Examples and non-examples: One plus two equals four (proposition) Mozart is the greatest
More informationINTRODUCTION TO LOGIC. Propositional Logic. Examples of syntactic claims
Introduction INTRODUCTION TO LOGIC 2 Syntax and Semantics of Propositional Logic Volker Halbach In what follows I look at some formal languages that are much simpler than English and define validity of
More informationChristopher Kennedy University of California, Santa Cruz
C omparison and Polar Opposition Christopher Kennedy University of California, Santa Cruz 1. Introduction The focu s of this paper is a phenomenon that I will refer to as "cross-polar anomaly", which is
More informationConsequence Relations and Natural Deduction
Consequence Relations and Natural Deduction Joshua D. Guttman Worcester Polytechnic Institute September 9, 2010 Contents 1 Consequence Relations 1 2 A Derivation System for Natural Deduction 3 3 Derivations
More informationE-type interpretation without E-type pronoun: How Peirce s Graphs. capture the uniqueness implication of donkey sentences
E-type interpretation without E-type pronoun: How Peirce s Graphs capture the uniqueness implication of donkey sentences Author: He Chuansheng (PhD student of linguistics) The Hong Kong Polytechnic University
More informationKratzer on Modality in Natural Language
Kratzer on Modality in Natural Language 1 Modal Logic General Propositional modal logic: Syntax: 02.06.12 William Starr Phil 6710 / Ling 6634 Spring 2012 Atomic formulas: P, Q, R,..., Connecties:,,,,,,
More informationA Little Deductive Logic
A Little Deductive Logic In propositional or sentential deductive logic, we begin by specifying that we will use capital letters (like A, B, C, D, and so on) to stand in for sentences, and we assume that
More informationA statement is a sentence that is definitely either true or false but not both.
5 Logic In this part of the course we consider logic. Logic is used in many places in computer science including digital circuit design, relational databases, automata theory and computability, and artificial
More informationSingleton Indefinites (re. Schwarzschild 2000)
MIT Syntax-Semantics Reading Group November 15, 2000 Kai von Fintel Singleton Indefinites (re. Schwarzschild 2000) 1. If a (particular) friend of mine from Texas had died in the fire, I would have inherited
More informationSyllogistic Logic and its Extensions
1/31 Syllogistic Logic and its Extensions Larry Moss, Indiana University NASSLLI 2014 2/31 Logic and Language: Traditional Syllogisms All men are mortal. Socrates is a man. Socrates is mortal. Some men
More informationFocus in complex noun phrases
Focus in complex noun phrases Summary In this paper I investigate the semantics of association with focus in complex noun phrases in the framework of Alternative Semantics (Rooth 1985, 1992). For the first
More informationAdjectives and Negation: deriving Contrariety from Contradiction
Adjectives and Negation: deriving Contrariety from Contradiction Karen De Clercq & Guido Vanden Wyngaerd FWO/U Gent & KU Leuven Linguistic Society of Belgium, Spring Meeting Universiteit Antwerpen 5 May
More informationAgainst generalized quantifiers (and what to replace them with)
Against generalized quantifiers (and what to replace them with) Udo Klein SFB 732 Stuttgart, 06.11.08 Generalized quantifier theory the basic idea The sentence Exactly three students smoke. is true if
More informationComparative-induced event measure relations
Comparative-induced event measure relations James Kirby University of Chicago 10 Jan 2009 In Vietnamese quantity comparison structures, differentials are prohibited from appearing phraseinternally. I argue
More informationHardegree, Formal Semantics, Handout of 8
Hardegree, Formal Semantics, Handout 2015-04-07 1 of 8 1. Bound Pronouns Consider the following example. every man's mother respects him In addition to the usual demonstrative reading of he, x { Mx R[m(x),
More informationTwo Reconstruction Puzzles Yael Sharvit University of Connecticut
Workshop on Direct Compositionality June 19-21, 2003 Brown University Two Reconstruction Puzzles Yael Sharvit University of Connecticut yael.sharvit@uconn.edu Some constructions exhibit what is known as
More informationThe semantics of yuè V yuè A in Mandarin Chinese: Coercion and the necessarily temporal reading
Proceedings of CLS 51 (2015), 381-395 c Chicago Linguistic Society 2016. All rights reserved. 381 The semantics of yuè V yuè A in Mandarin Chinese: Coercion and the necessarily temporal reading Xiao Li
More informationBar-Hillel and the Division of Labor in Language
Bar-Hillel and the Division of Labor in Language On the interaction of grammar, logic, and pragmatics Luka Crnič November 2, 2015 Language, Logic and Cognition Center http://scholars.huji.ac.il/llcc Luka
More informationKEYWORDS: Negative adjective; Transformation; Degree; Measure; Comparison; Ratio modifiers.
THE DEGREE FUNCTIONS OF NEGATIVE ADJECTIVES Galit Weidman Sassoon, ILLC, University of Amsterdam & Ben Gurion University of the Negev galitadar@gmail.com ABSTRACT This paper provides a new account of positive
More informationPropositional Logic: Review
Propositional Logic: Review Propositional logic Logical constants: true, false Propositional symbols: P, Q, S,... (atomic sentences) Wrapping parentheses: ( ) Sentences are combined by connectives:...and...or
More informationDegree pluralities : distributive, cumulative and collective readings of comparatives
Degree pluralities : distributive, cumulative and collective readings of comparatives Jakub Dotlačil (Groningen) & Rick Nouwen (Utrecht) February 14, 2014, Paris 1 John lifted the box. 1 John lifted the
More informationEpistemic Modals and Informational Consequence
Epistemic Modals and Informational Consequence [This is a penultimate draft. Please quote only from the published version. The paper is already available through Online First at http://www.springerlink.com/content/0039-7857]
More informationFirst Order Logic (FOL)
First Order Logic (FOL) CE417: Introduction to Artificial Intelligence Sharif University of Technology Spring 2013 Soleymani Course material: Artificial Intelligence: A Modern Approach, 3 rd Edition, Chapter
More informationContinuations for Comparatives
Volume 22 Issue 1 Proceedings of the 39th Annual Penn Linguistics Conference 1-1-2016 Continuations for Comparatives Todd Snider University of Pennsylvania Working Papers in Linguistics Article 28 This
More information7. Propositional Logic. Wolfram Burgard and Bernhard Nebel
Foundations of AI 7. Propositional Logic Rational Thinking, Logic, Resolution Wolfram Burgard and Bernhard Nebel Contents Agents that think rationally The wumpus world Propositional logic: syntax and semantics
More informationUniform Definability in Assertability Semantics
Uniform Definability in Assertability Semantics Institute for Logic, Language and Computation, Universiteit van Amsterdam S.N.M.Steinert-Threlkeld@uva.nl Abstract This paper compares two notions of expressive
More informationAI Programming CS S-09 Knowledge Representation
AI Programming CS662-2013S-09 Knowledge Representation David Galles Department of Computer Science University of San Francisco 09-0: Overview So far, we ve talked about search, which is a means of considering
More informationContinuations in Type Logical Grammar. Grafting Trees: (with Chris Barker, UCSD) NJPLS, 27 February Harvard University
Grafting Trees: Continuations in Type Logical Grammar Chung-chieh Shan Harvard University ccshan@post.harvard.edu (with Chris Barker, UCSD) NJPLS, 27 February 2004 Computational Linguistics 1 What a linguist
More informationHomogeneity and Plurals: From the Strongest Meaning Hypothesis to Supervaluations
Homogeneity and Plurals: From the Strongest Meaning Hypothesis to Supervaluations Benjamin Spector IJN, Paris (CNRS-EHESS-ENS) Sinn und Bedeutung 18 Sept 11 13, 2013 1 / 40 The problem (1) Peter solved
More informationSpring 2018 Ling 620 Introduction to Semantics of Questions: Questions as Sets of Propositions (Hamblin 1973, Karttunen 1977)
Introduction to Semantics of Questions: Questions as Sets of Propositions (Hamblin 1973, Karttunen 1977) 1. Question Meanings and Sets of Propositions (1) The Semantics of Declarative Sentence Dave smokes
More information5. And. 5.1 The conjunction
5. And 5.1 The conjunction To make our logical language more easy and intuitive to use, we can now add to it elements that make it able to express the equivalents of other sentences from a natural language
More informationTHE LOGIC OF COMPOUND STATEMENTS
CHAPTER 2 THE LOGIC OF COMPOUND STATEMENTS Copyright Cengage Learning. All rights reserved. SECTION 2.1 Logical Form and Logical Equivalence Copyright Cengage Learning. All rights reserved. Logical Form
More informationSemantics and Generative Grammar. A Little Bit on Adverbs and Events
A Little Bit on Adverbs and Events 1. From Adjectives to Adverbs to Events We ve just developed a theory of the semantics of adjectives, under which they denote either functions of type (intersective
More informationContexts for Quantification
Contexts for Quantification Valeria de Paiva Stanford April, 2011 Valeria de Paiva (Stanford) C4Q April, 2011 1 / 28 Natural logic: what we want Many thanks to Larry, Ulrik for slides! Program Show that
More informationFoundations of Artificial Intelligence
Foundations of Artificial Intelligence 7. Propositional Logic Rational Thinking, Logic, Resolution Joschka Boedecker and Wolfram Burgard and Bernhard Nebel Albert-Ludwigs-Universität Freiburg May 17, 2016
More informationPropositional Logic: Syntax
Logic Logic is a tool for formalizing reasoning. There are lots of different logics: probabilistic logic: for reasoning about probability temporal logic: for reasoning about time (and programs) epistemic
More informationProseminar on Semantic Theory Fall 2013 Ling 720 The Proper Treatment of Quantification in Ordinary English, Part 1: The Fragment of English
The Proper Treatment of Quantification in Ordinary English, Part 1: The Fragment of English We will now explore the analysis of English that Montague puts forth in his seminal paper, PTQ. As we ve already
More informationAn Introduction to Modal Logic. Ordinary logic studies the partition of sentences1 into two categories, true and false.
An Introduction to Modal Logic Ordinary logic studies the partition of sentences1 into two categories, true and false. Modal logic investigates a finer classification. A sentence can be either necessary
More informationON THE LOGIC OF VERBAL MODIFICATION DAVID BEAVER AND CLEO CONDORAVDI
ON THE LOGIC OF VERBAL ODIFICATION DAVID BEAVER AND CLEO CONDORAVDI Department of Linguistics University of Texas at Austin dib@mail.utexas.edu PARC and Department of Linguistics Stanford University condorav@csli.stanford.edu
More informationInquisitive semantics
Inquisitive semantics NASSLLI 2012 lecture notes Ivano Ciardelli University of Bordeaux Floris Roelofsen University of Amsterdam June 25, 2012 Jeroen Groenendijk University of Amsterdam About this document
More informationGrundlagenmodul Semantik All Exercises
Grundlagenmodul Semantik All Exercises Sommersemester 2014 Exercise 1 Are the following statements correct? Justify your answers in a single short sentence. 1. 11 {x x is a square number} 2. 11 {x {y y
More informationThe Formal Architecture of. Lexical-Functional Grammar. Ronald M. Kaplan and Mary Dalrymple
The Formal Architecture of Lexical-Functional Grammar Ronald M. Kaplan and Mary Dalrymple Xerox Palo Alto Research Center 1. Kaplan and Dalrymple, ESSLLI 1995, Barcelona Architectural Issues Representation:
More information5. And. 5.1 The conjunction
5. And 5.1 The conjunction To make our logical language more easy and intuitive to use, we can now add to it elements that make it able to express the equivalents of other sentences from a natural language
More informationElla failed to drop the class. Ella dropped the class.
Propositional logic In many cases, a sentence is built up from one or more simpler sentences. To see what follows from such a complicated sentence, it is helpful to distinguish the simpler sentences from
More informationComparison Across Domains in Delineation Semantics
Noname manuscript No. (will be inserted by the editor) Comparison Across Domains in Delineation Semantics Heather Burnett Received: date / Accepted: date Abstract This paper presents a new logical analysis
More informationCompositionality Problems and How to Solve Them Thomas Ede Zimmermann, Goethe-Universität Frankfurt Hyderabad CogSci Colloquium, March 09
Compositionality Problems and How to Solve Them Thomas Ede Zimmermann, Goethe-Universität Frankfurt Hyderabad CogSci Colloquium, March 09 1. Compositionality Generalised Principle of Compositionality cf.
More informationPredicative superlatives. 1 Superlatives can have a purely predicative construal
Topics in Syntax and Semantics, Spring 2018 Predicative superlatives Nico(letta) Loccioni 1 Superlatives can have a purely predicative construal Predicative = non attributive modifier, that is no nominal
More information