University of Toronto, Department of Computer Science CSC 485H/2501H: Computational linguistics, Fall 2024
Assignment 3
Due date: 17:00 on Thursday, December 4, 2024.
Late assignments will not be accepted without a valid medical certificate or other documentation of an emergency.
For CSC485 students, this assignment is worth 30% of your final grade.
For CSC2501 students, this assignment is worth 25% of your final grade.
• Read the whole assignment carefully.
• What you turn in must be your own work. You may not work with anyone else on any of the problems in this assignment. If you need assistance, contact the instructor or TA for the assignment.
• Any clarifications to the problems will be posted on the Piazza forum for the class. You will be responsible for taking into account in your solutions any information that is posted there, or discussed in class, so you should check the page regularly between now and the due date.
• ThestartercodedirectoryforthisassignmentisdistributedviaMarkUs.Inthishandout,code files we refer to are located in that directory.
• When implementing code, make sure to read the docstrings as some of them provide impor- tant instructions, implementation details, or hints.
• Fillinyourname,studentnumber,andUTORidontherelevantlinesatthetopofeachfilethat you submit. (Do not add new lines; just replace the NAME, NUMBER, and UTORid placeholders.)
Overview: Symbolic Machine Translation
In this assignment, you will learn how to write phrase structure grammars for some different lin- guistic phenomena in two different languages: English and Chinese. You can use the two grammars to create an interlingual machine translation system by parsing in one, and generating in the other. Don’t panic if you don’t speak Chinese, and also don’t cheer up yet if you can speak the language — it won’t give you much of an advantage over other students. A facility with languages in general will help you, as will the ability to learn and understand the nuances between the grammars of two different languages. In particular, you will start by working on agreement. Then, you will need to analyse the quantifier scoping difference between the two languages.
TRALE Instructions The instructions to setup and launch TRALE on teach.cs can be found in:
https://www.cs.toronto.edu/~niu/csc485/trale/setup/
1. Agreement: Determiners, Numbers and Classifiers [10 marks]
English expresses subject–verb agreement in person and number. English has two kinds of number: singular and plural. The subject of a clause must agree with its predicate: they should be both singular or both plural. However, the number of a direct object does not need to agree with anything.
(1) (2) (3) (4)
A programmer annoys a dolphin.
Two programmers annoy a dolphin.
* Two programmers annoys two dolphins. * A programmer annoy two dolphins.
Chinese, on the other hand, does not exhibit subject–verb agreement. As shown in the examples below, most nouns do not inflect at all for plurality. Chinese does, however, have a classifier (CL) part of speech that English does not. Semantically, classifiers are similar to English collective nouns (a bottle of water, a murder of crows), but English collective nouns are only used when describing collectives. With very few exceptions, classifiers are mandatory in complex Chinese noun phrases. Different CLs agree with different classes of nouns that are sorted by mostly semantic criteria. For example, 学生 (xuesheng)1 student is a person and an occupation, so it should be classified by either 个 (ge) or 名 (ming) and cannot be classified by the animal CL 只 (zhi). However, the rules of determining a noun’s class constitute a formal system that must be followed irrespective of semantic similarity judgements. For example, while wolves and sheep are both animals and can both be classified by the animal CL 只 (zhi), 狼 (lang) wolf can take another classifier, 匹 (pi).
yi ge xuesheng
one ge-CL student
(6) 两 个 学生 liang ge xuesheng
two ge-CL student
(7) 三 个 学生
san ge xuesheng
three ge-CL student
san xuesheng
three student
(9) *三 只 学生
san zhi xuesheng
three zhi-CL student
You should be familiar by now with the terminology in the English grammar starter code for
1Use the Romanized form with no spaces or hyphens, e.g.,xuesheng, for multi-character lexical entries. 3
(10) 一只羊 yi zhi yang
one zhi-CL sheep
(11) 两只羊 liang zhi yang
two zhi-CL sheep
(12) 三只羊 san zhi yang
three zhi-CL sheep
(13) *三 匹 羊 san pi yang
three pi-CL sheep
(14)*三名 羊 san ming yang
three ming-CL sheep
this question. The Chinese grammar is fairly similar, but there is a new phrasal category called a classifier phrase (CLP), formed by a number and a classifier. The classifier phrase serves the same role as a determiner does in English.
The two grammars below don’t appropriately constrain the NPs generated. You need to design your own rules and features to properly enforce agreement.
English Grammar: Rules:
NP → Det N NP→NumN VP → V NP S → NP VP
three: Num student: N students: N wolf: N wolves: N sheep: N sheep: N see: V sees: V saw: V chase: V chases: V chased: V
Chinese Grammar: Rules:
CLP→NumCL NP→CLPN VP→VNP S→NPVP
一 yi one/a Num
两 liang two Num 三 san three Num
学生 xuesheng student N 狼 lang wolf N 羊 yang sheep N
追逐 zhuizhu chase V 看见 kanjian see V
个ge CL 名 ming CL 只zhi CL 匹pi CL
Det Num Num
Here is a list of all of the nouns in this question and their acceptable classifiers: • 狼langwolf:只zhi;匹pi;
• 羊 yang sheep: 只 zhi
• 学生 xuesheng student: 个 ge, 名 ming.
(a) (6 marks) Implement one grammar for each language pursuant to the specifications above. English: q1_en.pl and Chinese: q1_zh.pl.
Neither of your grammars need to handle embedded clauses, e.g., a student caught two wolves see a sheep. Similarly for Chinese, your grammar doesn’t need to parse sentences like example (15):
(15)一名学生 看见两匹狼追逐一只羊 yi ming xuesheng kanjian liang pi lang zhuizhu yi zhi yang
A student saw two wolves chase a sheep.
For the Chinese grammar, code the lexical entries in pinyin (the Romanized transcriptions of the Chinese characters).
(b) (4marks)Useyourgrammarstoparseandtranslatethefollowingsentences.Saveandsubmit all the translation results in the .grale format. The results of sentence (16) should be named q1b_en.grale and the results of sentence (17) should be named q1b_zh.grale.
(16) Two wolves saw one sheep
(17)两个学生 追逐三只羊 liang ge xuesheng zhuizhu san zhi yang
Operational Instructions
• Independently test your grammars in TRALE first, before trying to translate.
• Use the function translate to generate a semantic representation of your source sen- tence. If your sentence can be parsed, the function translate should open another gralej interface with all of the translation results.
| ?- translate([two,wolves,catch,one,sheep]).
• To save the translation results, on the top left of the Gralej window (the window with the INITIAL CATEGORY entry and all of the translated sentences listed), click File >> Save all >> TRALE format.
• Don’t forget to close all of the windows or kill both of the Gralej processes after you finish. Each Gralej process will take up one port in the server, and no one can use the server if we run out of ports.
2. Quantifier Scope [30 marks]
For this assignment, we will consider two quantifiers: the universal quantifier (every, 每 mei) and the existential quantifier (a, 一 yi). In English, both quantifiers behave as singular determiners.
(18) (19) (20)
A professor stole every cookie. * A professor stole every cookies. * A professors stole every cookie.
In Chinese, both of these quantifiers behave more like numerical determiners. In addition, when a universal quantifier modifies an NP that occurs before the verb (such as with a universally quanti- fied subject), the preverbal operator 都 (dou) is required. When a universally quantified NP occurs after the verb, the dou-operator must not appear with it.
(21) (22) (23)
Every professor stole a cookie.
A professor stole every cookie.
每个 教授 都偷了一块 饼干
mei ge jiaoshou dou tou-le yi kuai binggan ∀ ge-CL professor DOU stole ∃ kuai-CL cookie
*每个 教授 偷了一块 饼干 mei ge jiaoshou tou-le yi kuai binggan ∀ ge-CL professor stole ∃ kuai-CL cookie
一个 教授 偷了每块 饼干
yi ge jiaoshou tou-le mei kuai binggan ∃ ge-CL professor stole ∀ kuai-CL cookie
*一个 教授 都偷了每块 饼干
yi ge jiaoshou dou tou-le mei kuai binggan ∃ ge-CL professor dou stole ∀ kuai-CL cookie
Quantifier Scope Ambiguity In lecture, we talked about different kinds of ambiguity. In many English sentences, no matter what the order of the quantifiers, there is a quantifier scope ambiguity. For example, the sentence every student takes a course has two readings:
• (∃ > ∀) Every student takes a course. [The course is Math.]
• (∀ > ∃) Every student takes a course. [Some students take Math and some students take
The symbol (∃ > ∀) means the existential quantifier outscopes the universal quantifier in a logical form representation of the sentence.
NP LF:λP.∀x.(student(x) ⇒ P (x))
every student
VP LF:λz.∃y.(course(y) ∧ take(z, y))
takes a course
Figure 1: Beta Reduction. What should be the LF of S?
We can write the semantics of the two sentences in their logical forms (LF) to distinguish the two readings:
• ∃y.(course(y)∧∀x.(student(x)⇒take(x,y))) • ∀x.(student(x)⇒∃y.(course(y)∧take(x,y)))
English sentences (27, 28) are scopally ambiguous no matter what the linear order of the quan- tifiers is. But in Chinese, a sentence is scopally ambiguous only when the universally quantified NP precedes the existential NP: (29) is ambiguous, but (30) is unambiguous.2
(27) Every student takes a course Ambiguous: ∃ > ∀, ∀ > ∃
(28) A student takes every course Ambiguous: ∃ > ∀, ∀ > ∃
(29)每个学生都会上一种 课程 mei ge xuesheng dou huishang yi zhong kecheng ∀ ge-CL student DOU take ∃ zhong-CL course
Ambiguous: ∃ > ∀, ∀ > ∃
(30)一个学生会上每种 课程
yi ge xuesheng huishang mei zhong kecheng ∃ ge-CL student take ∀ zhong-CL course
Unambiguous: ∃ > ∀
How can we derive the LF of the two readings? We use a process called beta reduction. Recall the lambda-calculus notation: λx.x2 denotes a function that takes a variable x, and returns the square of its value (x2). After substituting the value for the bound variable x, we can reduce the function application in the body of the lambda term to a new expression. For example, applying 2 to λx.x2 will get us:
λx.x2(2) = 22
2The actual principles that determine the scopal readings of a Chinese sentence are still an active area of research, but this is obviously beyond the scope of this assignment. You only need to construct an analysis that explains every example mentioned in this assignment.
∀x.(student(x) ⇒ ∃y.(course(y) ∧ take(x, y))) NP VP
λP.∀x.(student(x) ⇒ P (x)) λz.∃y.(course(y) ∧ take(z, y)) Q N V NP
λF.λP.∀y.(F (y) ⇒ P (y))
λx.(student(x)) λQ.λz.Q(λx.(take(z, x)))
Figure 2: Beta reduction analysis of the sentence every student takes a course.
λP.∃y.(course(y) ∧ P (y))
λF.λP.∃y.(F (y) ∧ P (y)) λx.(course(x))
Code Help
This process is also known as beta reduction (denoted as ⇔β ). Note that beta reduction itself does not tell us that this equals 4. That is obtained by a subsequent process of arithmetic evaluation. But we can use beta reduction even if we don’t evaluate.
We can also perform beta reduction on variables for functions. For example, applying in λF.F (2) to λx.x2 will yield:
λF.F (2) (λx.x2) = (λx.x2)(2) = 22
Now, let’s look at an example that uses beta reduction to compute the LF of a sentence. For ex- ample, as shown in figure 1, we know that the LF of the NP every student is λP.∀x.(student(x) ⇒ P (x)) and the LF of the VP takes a course is λz.∃y.(course(y) ∧ take(z, y)). What is the LF of every student takes a course?
λP.∀x.(student(x) ⇒ P (x))(λz.∃y.(course(y) ∧ take(z, y))) ⇔β ∀x.(student(x)⇒λz.∃y.(course(y)∧take(z,y))(x))
⇔β ∀x.(student(x)⇒∃y.(course(y)∧take(x,y)))
Each step of repeatedly applying beta reduction to every subterm until we reach an irreducible statement is called beta normalisation.
Figure 2 shows the complete analysis of the sentence every student takes a course. Familiarize yourself with every part of the analysis. But this only generates one of the two readings – the surface reading (∀ > ∃). We will use a technique called quantifier storage to capture the scopal ambiguity and make both readings available.
Quantifier Storage If quantifier scoping is a semantic effect, how do we represent it in syntax? When there is no ambiguity, keeping track of the quantifier scope is pretty straightforward. To keep track of and resolve scope ambiguities, we will use a list called a quantifier store. The idea behind QSTORE is that, instead of consuming all of the LF components right away, we can choose to keep them in QSTORE and apply them later.
LF: ∀x.student(x) ⇒ take(x, z) QSTORE: ⟨z; λG.∃y.(course(y) ∧ G(y))⟩
LF: λP.∀x.(student(x) ⇒ P (x)) QSTORE: ⟨⟩
every student
Figure 3: Quantifier Storage. Storing the quantifier at (1), and retrieve it later at (2). 9
LF: λF.F(z) ⟩
z; λG.∃y.(course(y) ∧ G(y)) a course
Computer Science Tutoring
Let’s go back to the example, every student takes a course (figure 3). We first store the LF of the NP a course at (1) and replace the LF of the NP with a placeholder λF.F (z). The variable z in this expression is a free occurrence, and it is the same variable as the z in the store and in the LF of the sentence (the free occurrences of z are highlighted in red). We retrieve the logical form from the store at (2). The retrieval process consists of three steps:
1. First, we construct a function λz.LS , where LS is the current LF, and z is the variable paired in the QSTORE entry. In our particular case, this will yield λz.(∀x, student(x) ⇒ take(x, z)).
2. Then, we apply this function to the LF from the QSTORE entry.
3. Finally, we beta normalise. Using beta normalisation, we obtain the second reading of the sentence.
λG.∃y.(course(y) ∧ G(y))(λz.(∀x, student(x) ⇒ take(x, z))) ⇔β ∃y.(course(y)∧(λz.(∀x.student(x)⇒take(x,z))(y))
⇔β ∃y.(course(y)∧(∀x.student(x)⇒take(x,y))
Topicalization and Movement Topicalization is a linguistic phenomenon in which an NP appears at the beginning of a sentence in order to establish it as the topic of discussion in a sentence or to emphasize it in some other way. It plays an important role in the syntax of fixed-word-order courses because grammatical function is mainly determined by word order. Both Chinese and En- glish exhibit topicalization. The entire object NP, for example, can be moved to the beginning of the sentence in either course. But in Chinese, object topicalization is more restricted when the subject is quantified: it can happen when the subject is universally quantified, but not when it is existentially quantified (33-36).
(31) A course, every student takes. ∃ course ∀ student take
Ambiguous: ∀ > ∃ and ∃ > ∀ (32) Every course, a student takes.
∀ course ∃ student take
Ambiguous: ∀ > ∃ and ∃ > ∀
(33)一种 课程每个学生都会上
yi zhong kecheng mei ge xuesheng dou huishang ∃ zhong-CL course ∀ ge-CL student dou take
Unambiguous: ∃ > ∀
(34)每种 课程每个学生都会上 mei zhong kecheng mei ge xuesheng dou huishang ∀ zhong-CL course ∀ ge-CL student dou take
(35) *一种 课程 一个 学生 会上
yi zhong kecheng yi ge xuesheng huishang ∃ zhong-CL course ∃ ge-CL student take
(36) *每 种 课程 一个 学生 (都) 会上 mei zhong shu yi ge xuesheng (dou) huishang
ben-CL course ∃ ge-CL student dou take
Q N Q N V NP a course every student takes ε
Figure 4: English topicalization parse tree: example (31).
Q CL N Q CL N D VP
In English, neither subject–verb agreement nor quantifier scope ambiguity is generally affected by movement. In particular, the number and person of the subject should always agree with the predicate no matter where it occurs. Here, you can assume that Chinese also follows subject–verb agreement (regarding the requirement of dou) in the same way that English does. But whereas in English, both readings are still available after the sentences are topicalised (31, 32), this is not the case in Chinese. Compared to its untopicalised counterpart (29), the topicalised sentence (33) is no longer ambiguous.
Figures 4 and 5 show the parse trees of sentences (31) and (33). Topicalization is generally analysed with gaps. An empty trace is left in the untopicalized position of the object NP, where the gap is introduced. The gapped NP then percolates up the tree, and is finally unified with the topicalized NP at the left periphery of the sentence.3
3Although Chinese is an SVO (Subject-Verb-Object) course, there is a means of performing “double movement.” 11
种 课程 每 个 学生 都 V NP zhong kecheng mei ge xuesheng dou
zhong-CL course ∀ ge-CL student dou 会上 huishang
Figure 5: Chinese topicalization parse tree: example (33).
(a) (2marks)Manuallyconvertallreadingsofthesentences(28)and(30)tologicalexpressions. Put your logical forms in section 2(a) of analysis.txt. Use exists and forall for the quantifiers, and use => and the caret symbol ^ for implication and conjunction.
(b) (10marks)Implementgrammarsforthesyntaxofquantifierscopeambiguity.Youdon’tneed to account for meanings, or for ambiguity in meanings (there should be no syntactic ambigu- ities). At this point, a correct grammar will produce exactly one parse for every grammatical sentence. Test your implementation before you move on to the next step.
(c) (10 marks) Augment your grammars to represent meaning and quantifier scope ambiguity. Marks for question 2(b) will be deducted if your work on this part causes errors in the syn- tactic predictions. Your grammar should generate more than one parse for each ambiguous sentence.
(d) (4 marks) Translate sentences (28) and (30), as you did in the first question. Operational Instructions
• Use the function translate to generate semantic representations of your source sen- tences. If your sentences can be parsed, translate should open another gralej win- dow and with all of the translation results.
| ?- translate([a,student,takes,every,course]).
• You will be prompted as follows to see the next parse.
ANOTHER? y
ANOTHER? y
Answer y to see the next parse until you reach the end. Each time TRALE will open a new Gralej window. You need to store all of your translation results by repeating the previous step. A no will be returned when you reach the end of your parses.
• Saveyourtranslationsofsentence(28)asq2d_28_1.grale,q2d_28_2.grale…and your translations of sentence (30) as q2d_30_1.grale, q2d_30_2.grale …
• Submit a zip file q2d.zip containing all the translation results. You can use this com- mand: zip -r q2d.zip q2d_*.grale to create the zip file.
• Again, don’t forget to close all the windows and kill your Gralej processes after you finish.
(1)一个学生每种 课程都会上
yi ge xuesheng mei zhong kecheng dou huishang
∃ ge-CL student ∀ zhong-CL course dou take
A student every course take. We will ignore these.
Programming Help
(e) (4marks)LargecourseModels(LLMs)havegainedquitealotofpopularityrecently.Inthis question, you will explore the question of whether LLMs such as ChatGPT4 “understand” quantifier scope.
There are several approaches to this exploration: You can ask ChatGPT to translate sentences and compare its translations to your grammar’s translations. Or, you can directly interrogate ChatGPT about quantifier scope readings and analyse its responses. You can also design some clever linguistic tasks that involve quantifier scope and catch how ChatGPT handles them. Be both creative and precise in your experimentation.
In your write-up, report at least one case where GPT’s behaviour differs from that of your grammar. Document the prompts you used and describe your experimental design. Reflect on the differences observed and share your thoughts on why these differences may have occurred.
Your analysis should be submitted as section 2(e) in analysis.txt.
4https://chat.openai.com/
What to Submit
This assignment is submitted electronically via MarkUs. You should submit a total of eight (8) required files as follows:
• q1_en.pl The (entire) q1_en.pl with your implementations filled in.
• q1_zh.pl The (entire) q1_zh.pl with your implementations filled in.
• q1b_en.grale The translation result saved in .grale format for the English sentence in question 1(b).
• q1b_zh.grale The translation result saved in .grale format for the Chinese sentence in question 1(b).
• analysis.txt Logical expressions for question 2(a).
• q2_en.pl The (entire) q2_en.pl with your implementations filled in.
• q2_zh.pl The (entire) q2_zh.pl with your implementations filled in.
• q2d.zip The translation results saved in .grale format (and compressed into a .zip file) for question 2(d).