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PLIN0009 Semantic Theory
创建日期：2024-09-06 15:17:52
所属分类：语言学linguistics
标签： PLIN0009
Semantic Theory

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PLIN0009 Semantic Theory

Coursework 2

Instructions

-  Answer all questions in entirety. Label your answers on your document by section number + letter (e.g., ‘1a)’ for question a) in section 1).

-  Pay careful attention to all instructions. If anything is unclear, please post your question on the Moodle forum.

-  You  may handwrite  (part of) your answers, as long as you scan them and submit the file on Moodle, but please make sure that they are legible and display correctly on Turnitin.

-  Do not use AI to answer the questions.

-  If you consult other sources, please indicate them in a bibliography and in the text.

1 - Properties of Quantifiers

Conservativity

The conservativity of a natural language quantifier Q can be defined as follows: given two sets A and B, ∈ [Q]M  iff   ∈ [Q]M.

As an example, consider the following sentence:

(1)       Every child plays.

This sentence is true in M iff <[child]M, [plays]M> ∈ [every]M. If every is conservative, we also expect that <[child]M, [child]M ∩ [plays]M> ∈ [every]M. This could be paraphrased as Every child is a child that plays.

a) Show that every is conservative by constructing a model M in which <[child]M, [plays]M> ∈ [every]M (i.e., in which (1) is true). To do so, provide the extensions of [child]M and [plays]M in list notation, and briefly explain why <[child]M, [plays]M> ∈ [every]M  holds. (You will need to go back to the extension of the quantifier). Then, explain why it also holds that <[child]M, [child]M ∩ [plays]M> ∈ [every]M.

b) Show that some is conservative. Assume that the following sentence is true in M:

(2)       Some books are interesting.

c) Show that no is conservative. Assume that the following sentence is true in M:

(3)       No book is boring.

d) Now consider the following hypothetical quantifier:

[wug]M  = { : |X| = |Y|}

Discuss whether wug is conservative, taking as a starting point the following sentence:

(4)       Wug book is interesting.

Hint: consider both conditions that must be met for wug to be conservative.

I.e., for any two sets X and Y, it must hold that  ∈ [wug ⟧M and that  ∈ [wug ⟧M. If you can come up with a model in which one of the two conditions holds but the other does not, then you have shown that wug is non-conservative.

e) Consider  another  hypothetical   quantifier  (notice  a  crucial  difference  with   respect  to  the denotation of every):

[wis⟧M  = { : Y ⊆ X}

Discuss whether wis is conservative, following the same hint provided for wug and taking as a starting point the following sentence:

(5)       Wis student left.

Monotonicity

Determine the monotonicity patterns of the following quantifiers. To do so, for each quantifier Q construct a model M such that given an arbitrary NP and an arbitrary VP, <[NP ⟧M, [VP ⟧M> is a member of [Q⟧M. This implies that a certain relation must hold between [NP ⟧M and [VP ⟧M. To work on monotonicity, you may want to refer to a subset and a superset of [NP ⟧M and a subset and a superset of [VP ⟧M.

Then, determine whether the quantifier is ↑MON, ↓MON, MON↑, or MON↓ . Remember that it is generally easier to prove that a certain property does not hold. For the purposes of this assignment, it will be sufficient to show that a given relation does hold in at least one situation to show that the relevant quantifier is monotonic in the relevant direction (e.g. ↑MON).

As an example:

(i) Every student left.

NP

NP subset

NP superset

[student⟧M = {a}

[undergraduate student⟧M = ∅

[person ⟧M = {a, b, c}

VP

VP subset

VP superset

[left⟧M = {a, b}

[left early⟧M = ∅

[moved⟧M = {a, b, c}

↑MON: every is not ↑MON. Every student left does not entail every person left. There may be a situation in which some people who are not students did not leave.

↓MON: every is ↓MON. Every student left entails every undergraduate student left.

MON↑: every is MON↑ . Every student left entails every student moved.

MON↓: every is not MON↓ . Every student left does not entail every student left early. There may be a situation in which all students left late.

f) exactly two

There is no need to construct another model;  simply refer to your intuitions. You  can use the sentence Exactly two students left as a starting point.

g) between five and ten

There is no need to construct another model;  simply refer to your intuitions. You  can use the sentence Between five and ten students left as a starting point.

h) wug

Remember: [wug ⟧M   = { : |X| = |Y|}. For this one, you need think of what the cardinality of subsets and supersets of X andY could be. You can use Wug student left as a starting point.

Conjunction and disjunction of QPs

Consider the following sentences:

(6)       Every woman but no man agreed with the president.

(7)       *A man but every woman agreed with the president.

i) Based on the above data, what generalisation can you make about two QPs coordinated by the conjunction but? Provide a short explanation and cite any relevant source you may have found.

(Hint: consider the rightward monotonicity of the quantifiers.)

2 - Negative Polarity Items (NPIs)

Licensing of any

The Fauconnier-Ladusaw Hypothesis  states that NPIs  are  licensed  in  downward-entailing  (DE) environments.

a) Consider the following sentence:

(8)       Exactly two people saw anything. Is this unexpected? Explain briefly why.

Licensing environment and their negative strength

We have seen that different NPIs require licensers with different negative strengths (non-veridical, DE, anti-additive, antimorphic).

b) Consider the distribution of either in English:

(9)       a.         Mary didn’t come either. b.         Mary never came either.  c.         *Did Mary come either?

For comparison with any:

(10)     a.         Mary didn’t eat any chocolate. b.         Mary never ate any chocolate. c.         Did Mary eat any chocolate?

What generalisation can you make about the type of licenser that either requires, based on the data?

c) Consider the following contrast between English and Japanese:

(11)     a.         I didn’t see any students.                                 (English) b.         If you see any student, inform. me.

(12)     a.         Watasi-wa        gakusei-o hito-ri-mo mi-nakat-ta.                 (Japanese) I-top                student-acc one-cl-MO see-neg-past

‘I didn’t see any students. ’

b.         *Gakusei-o hito-ri-mo mita-ra             siras-ero.

student-acc one-cl-MO see-if              inform.IMP

Intended: ‘If you see any student, inform. me. ’

How can you explain the contrast between any in English and hito-ri-mo in Japanese?

3 - Quantifier Scope

The following sentence is ambiguous:

(13)     Every student read a French novel.

a) Represent the two readings in predicate logic, using the following predicate letters: S = student      R = read (2-place)       N = novel        F = French

b) Does the surface scope reading entail the inverse scope reading? If it does not, briefly present a situation in which the surface reading is true but the inverse reading is false.

c) Does the inverse scope reading entail the surface scope reading? If it does not, briefly present a situation in which the inverse reading is true but the surface reading is false.

Now consider the following ambiguous sentence:

(14)     Every politician is not corrupt.

Here the scope relations are between the quantifier and negation.

d) Represent the two readings in predicate logic; assume that P = politician and C = corrupt.

e) Does the surface scope reading entail the inverse scope reading? If it does not, briefly present a situation in which the surface reading is true but the inverse reading is false.

f) Does the inverse scope reading entail the surface scope reading? If it does not, briefly present a situation in which the inverse reading is true but the surface reading is false.

4 - Tense and Aspect

a) Based on the following data:

(15)     a.         ?Mary builds a house.

b.         Mary is building a house.

(16)     a.         Mary knows French.

b.         *Mary is knowing French.

What  generalisation  can  you  make  about  a  verb’s  ability  to  appear  in  the  present  tense  ((a) sentences)  or in the progressive  ((b)  sentences)  depending  on  that verb’s Aktionsart (aspectual class)?

b) In the Reichenbach-Klein theory of tense-aspect, there are three main coordinates: Utterance Time (UT), Reference Time (RT), and Event Time (ET).

In the present tense, we can assume that UT = RT and RT = ET. In the simple past, on the other hand, RT < UT and RT = ET:

(17)     [Assume now = 6pm]

Mary ate at 4pm.         UT: now; RT: 4pm; ET: 4pm

Now consider the following tenses:

(18)     At 4pm, Mary had eaten.

(19)     At 4pm, Mary will have eaten.

What precedence (<) relations between ET and RT, and between RT and UT, can be established in

(18) and (19), respectively?

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MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A PHIL2617 PHYS3116 MIE250 BCPM0008 ECN 620 QBUS6830 ECSE-415 ECON5102 MGMT20005 MAT 653 ECO 480 COMP 5/600 CSSE 5600 ME 571 7CCMMS61 CS 550 COMP2865 MATH3075 STATS 506 QTM 220 ISYS2120 FIT5106 STAT 153 MKTG3112 ECON2102 ELE2018 COMP3031 MSIN0010 SCC461 MATH237 CS246 CSC3065 CSE 101 ICTWEB411 COMP9313 ECOS 2025 FN620 MATH11111 MATH 3018 KE1068 FINA 6112 C++ MISM 6202 MSIN0105 CSC8631 MECO6935 COMP4121 ACCT2011 DPBS1150 EEL 3701C F19PL OPM 661 CSE 310 CS918 BIOL30001 ACCT3563 BANK3600 MET CS622 MATH367 ACCT5907 Continuing COMP5048 COMP61021 CS3334 GSOE9210 CSCI-570 COMP 5322 HW 2 ALY-6020 IEOR 4706 DATA 200 EBUS504 CGE12412 COMP4108 7SSMM800 ECMM171P MATE50002 CS225 RS 6003 BH2274 ELEC3111 MAT6669 ECON-UA 227 PHIL 1012 7SSMM603 TB028A P6 ECS708 CSC 427 CS6476 CSE 250A A1A2 ITS61504 EECS 376 model HW6 UV0010 ECON 6074 MG4F7 CMP-7030Y INFO3008 BFIP013 ECON 5068 MATH6002 CS3483 PSTAT 131 C31FM CSOR W4246 AAEC 5307 DATA ELEC362 COMSM0047 ECN6006 MA20224 BST351 MATH 323 MATH323 AA2021 COMP3811 COMP2013 IB9X60 INVP001 EMATM0051 COMP220 BLAW1002 E20 TCP8001 ECON61001 EART40005 ECONM1022 MATH 365 MATH 367 ELEC6218 COMP 5812M EDUC 5061M ELEC ENG 1101 equation MATH6174 ST334 C4 EC9570 A33648 EBUS603 ECON47815 stata WFMS0001 PEM102 INF6060 ionically ELECTRICAL MATH 375 MMW 12 MKTG860 ECON60401 ALY6010 SOST20131 Introduction COM3524 MME2 GGR305 JNB 538 EECS101 COMM5030 IEOR E4601 2B CSC336 EN2315 LAW 432 CSC263 MATH2001 OLET1143 CSCB63 SIT772 COMM1170 STAT 441 MS930 INFT3050 GLBH0030 Stat 120B MAST10007 MGEC61 Machine GGR 252H1S ECON7030 Financial Marketing MGMT30019 ECON5120 SDSC 8009 CSC165H1S DSCI 551 3081W ACM41000 ECA 5304 MATH 1064 ECSE444 DATA 604 COMP7105 MIE1615 ECON4004 ENV200H1S EC481 MKT 306 EC1B1 MATH08051 ALY6140 CS260C CSE30 MSIN0226 CS4103 CSC3064 AM16 COMP11212 CSE4101 PSTAT 174 Math 380W CNT 5106C STAT 310 FIN2028 CS5014 STAT 425 COMP 4102A ELEC2140 MANF9544 QRM 9 QRM 8 ECON 457 COMPSCI 4091 MATH 523 DNSC-4211 PEAS 6000 MSIN0180 COMP2119 A2A HT 2022 IB93F0 MAS316/414 ACCT2522 MSIN0181 ATMS 201 COMP3425 MATH7861 SOLA2060 MA 325 7CCEMCTH ECON 432 INFT2051 SOLA 2060 ECOS2002 Stats141XP BIOA02H3 S2022 MA4601 K5 COMP5329 EG 284 IB3A70 WECO1020 COMP3027 Energy ACS61011 MAST20026 STAT 533 MATA31 ENVS257 BEM2031 EC 486 COMP0172 CS3214 EECE5644 IB2B20 COSC2536 COSC1147 COMP6214 5CCM242A COMP0130 AMME2000 MTMG50: EG238 ACF6006 QBUS2810 COSC2391 ECON7560 MATH377 STA305 CS 486 COMP1117B EL648 ELEC3909 ECON 241 COMP 4901W BUSI4428 ENEN20002 ENGN4524 ELEC3115 CSC 413 PSYC 100B ECON1002 MATH256 ANSC20005 MTHS2008 MATH40082 COSC 2406 FIT3174 STA 238 CMT202 Differential Equations MTHM017 GARCH 101 MATH2069 CSC336S ACSC12 ETF2121 CEME 2001 DB B474F ARHT1001 EECS 3311 3220 STATS 786 CS 484 COMP20008 MATH4091 ECE 455 CSCI 204 BUS B200F BA 875 BU5562 COSC 1147 X11 GEOG 101 IMM250F CSE 584A MATH38172 LAB 4 ELEC5882M FINS5523 EE 430 COMP 465 6CCS3PRE 7CCSMNSE FINANCE ACMB02H3 ENGG2112 ELEC5616 SCM B371 CHEM3120 CS22 ECMT2130 MAST30011 ADSPBF706 CENG0013 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