HSL747: Language Computations and Mental Architecture - Sem I, 2024-25 PDF

HSL747: Language Computations and Mental Architecture Sem I, 2024–25 Deepak Alok IIT Delhi  Syntax? o Syntax refers to the study of how words are arranged in sentences, clauses, and phrases to form grammatically correct express...

HSL747: Language Computations and Mental Architecture Sem I, 2024–25 Deepak Alok IIT Delhi  Syntax? o Syntax refers to the study of how words are arranged in sentences, clauses, and phrases to form grammatically correct expressions in a language.  More about ‘Word’ 1) a. The man loved the butter naan. b. The woman loved the butter naan. c. The dog loved the butter naan. d. The king loved the butter naan. 2) a. *The green loved the butter naan. b. *The in loved the butter naan. c. *The sing loved the butter naan. d. *The fastly loved the butter naan. o (1) & (2) show that we can substitute the word ‘man’ with various word types of nouns (e.g., woman, dog, king), but we cannot substitute words that are not nouns (green, in, sing, correctly). o Parts of speech/lexical category of a word tell us how the word functions in a sentence. 3 Parts of speech, Taught in School, Traditional definitions o Noun o Pronoun o Verb o Adjective o Adverb o Preposition o Conjunction o Interjection 4 Parts of speech: Traditional definitions o Traditional definitions of parts of speech (ones you learned in school) are based on semantic criteria (i.e., based on meaning): o Noun : A noun is a “person, place, or thing” o Verb : A verb is “an action, state, or state of being” 5 The problem with traditional definitions o They’re not very good for words you do know: Destruction : Noun ‘The destruction of the cities is bothering the Ukrainians.’ It describes an action. Assassination : Noun ‘The assassination of the president shocked the public.’ It describes an action. 6 The problem with traditional definitions ▪ Think : Verb ‘I think you are smart.’ It does not seem to describe an action. ▪ Believe : Verb ‘I believe you are smart.’ It does not seem to describe an action 7 The problem with traditional definitions 1. Sincerity is an important quality. Sincerity is an attribute, a general property of adjectives. However, it is used as a noun in (1) 8 The problem with traditional definitions o Many words change their parts of speech depending on where they appear in a sentence. 1. I have a Pen. (Pen as a noun) 2. She penned an application to the principal. (Pe as a verb) 3. She worked. (work as a verb) 4. She did the work. (Work as a noun) 9 The problem with traditional definitions o What’s the noun in (1)? What’s the verb? noun verb o What’s the noun in (2)? What’s the verb? noun verb 10 The problem with traditional definitions o Some words do not seem to have any meaning. 1. John heard that it was snowing. o It’s not clear what (if anything) that means! o So, hard to use that’s meaning to talk about its parts of speech. 11 The problem with traditional definitions o Useless for words you don’t know! Twas brillig, and the slithy toves Did gyre and gimble in the wabe; All mimsy were the borogoves, And the mome raths outgrabe. (a nonsense poem written by Lewis Carroll, Jabberwocky (1871)) o What is the part of speech of toves, wabe, and slithy? o How do we know toves and wabe are nouns? o How do we know slithy is an adjective? 12 The problem with traditional definitions ▪ The yikish dripner ▪ into the nindin ▪ with the pidibs o The underlined word would be unknown to you, but you know their parts of speech (and so you recognize this as grammatical English). yikish → Adjective nindin → Noun dripner → Noun pidibs → Noun o How do you do that? You know that what actually matters for a word’s part of speech is that word’s distribution. 13 Next class o Distributional criteria of parts of speech. o Words to phrases/constituents o Reading - start reading Carnie, Ch. 3 “Constituency, Trees and Rules (till section 1)” 14 HSL747: Language Computations and Mental Architecture Sem I, 2024–25 Deepak Alok IIT Delhi Parts of speech: A Problem with the Traditional definitions o Traditional definitions of parts of speech (ones you learned in school) are based on semantic criteria (i.e., based on meaning). o Could you recognize the part of speech of the underline words below? ▪ The yikish dripner yikish → Adjective nindin → Noun ▪ into the nindin ▪ with the pidibs dripner → Noun pidibs → Noun o The underlined word would be unknown to you, but you know their parts of speech (and so you recognize this as grammatical English). o How do you do that? You know that what actually matters for a word’s part of speech is that word’s distribution. 2 Parts of speech: Distributional criteria o Two ways to look at a word’s distribution: Morphological: What affixes a word has or could combine with. Syntactic: where a word can go in a sentence, what other words appear near the word. 3 Distributional Criteria: Main categories o Noun (N): Morphological distribution Can have derivational suffixes like –ment, -ness, -tion, -ation …. Can carry inflectional suffixes like the plural marker –s Syntactic distribution Occurs after a determiner: the/a (big) basement o Verb (V): Morphological distribution Can have derivational suffixes like –ize , -ate ….. Inflected for tense, aspect and agreement … Syntactic distribution Can follow an auxiliary (can), modal (might), or negation (See Carnie Ch 2 for details) 4  Distributional Criteria: Main categories o Adjectives (Adj): Morphological distribution: Can have derivational suffixes like -able, -ful, -ly... Can be used in degrees of comparison (-er, -est or more, most) Syntactic distribution: Can occur between a determiner and a noun, like ‘a big basement’ o Adverb (Adv): Morphological distribution: Can have derivational suffixes like –ly, -wise (clockwise), -ward(e) (downwards)… Modifies a verb, adjective, or adverb Syntactic distribution: Cannot occur between a determiner and a noun, like *a correctly answer (See Carnie Ch 2 for details) 5 A note on Adjectives and adverbs o Both take the suffix –ly (friendly vs. quickly). Both are modifiers-- attribute the properties to the item they modify but have different syntactic distributions. Adjectives Adverbs Adjectives modify nouns and generally occur Adverbs modify verbs and can appear elsewhere in the sentence. inside the noun phrase: 1. He runs quickly. 1. A good book 2. Yesterday, he ran. 2. A friendly dog 3. Bill is always late. Note: It can occur inside a noun phrase in the presence of an adjective. 1. A very nice book 2. A very friendly dog Can appear after the verb ‘to be’: Cannot appear after the verb ‘to be’ 1. That person is quick. 1. *That person is quickly/yesterday/always. 2. Ram is smart. o Complementary distribution: occurrences of adjectives and adverbs are entirely predictable. 6 Open vs. Closed and Lexical vs. Functional o The categories we saw so far, i.e., Nouns, Verbs, Adjectives, Adverbs, are all open They allow new coinages (e.g., Facebook in 2004, iPad in 2010). Open categories are also called lexical categories. o Other categories (we see in the next slide) are closed. Very hard, if not impossible, to expand them. Closed categories are also called functional categories. They encode grammatical information and are the “glue” that holds a sentence together. 7 Some closed/functional categories o Determiners: Articles: a/an, the, Quantifiers: all, every, some, many, most, three, two... Demonstrative: this, that, those, these.. possessive pronoun: my, his, her.. o Prepositions: in, near, on, by, over, under, for... o Complementizers: that, whether, if, for, … o Conjunctions: and, or, but, neither-nor, either-or,... o Tense: has, have, had, is, are, am, was, were... o Negation not/n’t (note: we will not talk about negation in this course) 8 Constituents: From words to phrases 9 What is in a sentence? 1. Cats meow. o What is in the sentence (1)? A noun and a verb? oWhat about (2) and (3)? 2. The cats meow. 3. The cats on the mat meow. o In the above sentences, ‘cats’, ‘the cats’, and ‘the cats on the mat’ all function as the subject of the respective sentences. o A group of words that functions together as a unit in the Syntax is called a constituent. o Phrase is a term that we use to capture constituency. o So, the subjects above are not just nouns but noun phrases. 10 What is in a sentence? o In the same way, the verb part of a sentence can be composed of multiple words. 1. Cats meow. 2. Cats like milk. 3. Cats like milk on their birthday. o A group of words created around a verb is called a ‘verb phrase’. o Phrases, not words, are used to make a sentence. o So, sentences are composed of a noun phrase (NP) and a verb phrase (VP), not only N and V. o Phrases are constituents. 11 Prepositional phrases (PP) o Some sentences we already encountered with PP 1. The cats on the mat meow. 2. Cats like milk on their birthday. 3. Stop for pedestrians in a crosswalk. 12 Zooming in on Phrases 13  Zooming in on the NP o What can occur in a noun phrase (NP) , and in what place? 1. Women 2. The woman 3. The woman with the telescope 4. The woman from India with the telescope 5. The smart woman from India with the telescope 6. The smart friendly woman from India with the telescope.. o What do you observe? 1. Noun (N) 2. Determiner (D) and N 3. D, N and prepositional phrase (PP) 4. D, N, PP, and PP 5. D, Adjective (Adj), N, PP, and PP 6. D, Adj, Adj, N, PP, and PP 14 Starting the observation as a rule o What do you observe? 1. N 2. D and N 3. D, N and PP 4. D, N, PP, and PP 5. D, Adj, N, PP, and PP 6. D, Adj, Adj, N, PP, and PP o An NP can consist of a noun, then optionally a determiner, any number of adjectives, and optionally any number of PPs. o Order among them is D > Adj > N > PP o The following rule captures our observation NP → (D) (AdjP+) N (PP+) (to be revised) 15 Starting the observation as a rule o The following rule captures our observation. NP → (D) (AdjP+) N (PP+) o This representation is called a phrase structure (PS) rule Read ‘→’ as ‘can consist of’ Treat everything in parentheses as optional Read ‘+’ as ‘more than one’ o A noun phrase (NP) can consist of an optional determiner, optionally more than one adjective, obligatory noun and optionally more than one prepositional phrase (PP). 16 Primary tree: NP o The PS rule can generate the following tree NP → (D) (AdjP+) N (PP+) NP (D) (AdjP) (AdjP) N (PP) (PP) 17  Zooming in on prepositional phrases (PP) o What can occur in a PP, and in what order? o Some PPs from India with the telescope on the mat in crosswalk o What is your observation? What can appear in PPs? a PP can consist of a P, then an NP o Stating the observation as a rule PP → P NP 18 Primary tree: PP o A PP can consist of a P, then an NP PP → P NP PP P NP 19 Zooming in on Adjective phrases o The NP rule mentions AdjP. What’s inside an AdjP? ▪ Minimally, an Adj: Yellow, friendly, intelligent AdjP → Adj ▪ But it can be complex: very yellow, incredibly stupid,... AdjP → (AdvP) Adj Note: ‘very’ in ‘very yellow’ is not an adjective but an adverb since it modifies an adjective. So ‘incredibly’ in ‘incredibly stupid’ 20 Primary tree: AdjP o An adjective phrase can have an adjective and optionally an adverb. AdjP → (AdvP) Adj AdjP (AdvP) Adj 21 Zooming in on Adverb Phrase o Adverbs work the same way. They can either be Simple: quickly or Complex: very quickly o This gives us the following rule for AdvP: AdvP → (AdvP) Adv o An adverb phrase can have an adverb and, optionally, an adverb Phrase. AdvP (AdvP) Adv 22 A note on Adjectives and Adverbs 1. A big yellow book 2. A very yellow book o What is the difference between (1) and (2) In (1), ‘big’ and ‘yellow’ both modify the noun ‘book’. So, both are adjectives. In (2), ‘yellow’ modifies the noun ‘book’. So, ‘yellow’ is an adjective. ‘very’, on the other hand, modifies the adjective ‘yellow’. So, ‘very’ is an adverb. Note: Adjectives only modify nouns. Adverbs modify adjectives or verbs but never nouns. o Principle of Modification: if X modifies Y, X and Y are sisters in a tree. 23 More on Adjectives and Adverbs 1. A big yellow book 2. a very yellow book o Two different structures o A tree like the left can’t be generated for ‘a very yellow book’. o A tree like the right can’t be generated for ‘a big yellow book’. 24  An NP with full-fledged AdjP o Putting all things together NP (D) (AdjP) (AdjP) N (PP) (PP) (AdvP+) Adj (AdvP) Adv 25 Next class More on phrase structure (PS) rules How to build tress for sentences Reading: Carnie, Ch. 3 section:2-3 26 HSL747: Language Computations and Mental Architecture Sem I, 2024–25 Deepak Alok IIT Delhi Announcements o No class this Friday. o The Brain and Cognitive Science colloquium is to be held on this Friday. o Please attend it. It starts at 9:30 in the Seminar room https://bcs.iitd.ac.in https://bcs.iitd.ac.in/schedule o Your graded answer script will be available for review on Tuesday. 2 Recap: NP PS rule and syntactic tree for NP: NP → (D) (AdjP+) N (PP+) NP (D) (AdjP) (AdjP) N (PP) (PP) 3 Recap: PP o PS rule and the syntactic tree of PP: PP → P NP PP P NP 4  Recap: NP o A NP so far (to be revised) NP (D) (AdjP) (AdjP) N (PP) (PP) (AdvP+) Adj P NP (AdvP) Adv 5 Recursion: A formal aspect o Recursion expressions of infinite length o A grammar is recursive if you can have an X inside of an X (here, X is a variable that stands for a phrase) o In ‘very very very tired’, we have AdvP that contains AdvPs. AdvP → (AdvP) Adv o Our simple rules for AdjP’s and AdvP’s generate big structures! 6 Recursion: NP and PP o Repeating our two phrase structure rules: NP → (D) (AdjP+) N (PP+) PP→ P NP o What do you notice? An NP can contain a PP, which will contain an NP, which can contain a PP, which...... The man in a house in the woods by the shed at the lake... o This is how we get recursion (a unique property of human language)! 7 Ambiguity at NP level: A formal aspect o A grammar is (syntactically) ambiguous if it generates multiple (syntactic) trees for a single string. Here’s an ambiguous NP: 1. A linguist with a book from Toronto (a) The linguist is from Toronto (b) The book is from Toronto NP → D N PP PP NP → D N PP PP → P NP PP → P NP 8 Ambiguity at NP level: A formal aspect o Two PPs in the same NP may lead to ambiguity. 1. The woman with the telescope from India (a) The telescope is from India (b) The woman is from India o Two ways to build (1), and our NP and PP rules can capture this. We could treat ‘from India’ as part of the NP ‘the telescope from India’, meaning NP → D N PP PP → P NP We could treat ‘from India’ as separate from ‘the telescope’ and only part of the larger NP, meaning (b). NP → D N PP PP PP → P NP 9  Ambiguity Tree-1 Tree-2 ‘from India’ as part of ‘from India’ as a part of ‘the telescope from India’ the larger NP’ o Remember? Principle of Modification: if X modifies Y, X and Y are sisters in a tree. 10 Exploring the verb phrases (VPs): NP Arguments o Verb phrases can just be a verb (Intransitive verb) John [left]. Thus, VP → V o Or a verb and an NP (transitive verb) John [read the book]. Thus, VP → V NP o Or a verb and two NPs. (ditransitive verb) John [gave the boy a book]. Thus, VP → V NP NP o A single rule that can capture all three sentences? VP → V (NP) (NP) 11 Exploring the verb phrases (VPs): A clausal argument o Some verbs take NP or a clause (CP) as an object 1. I asked [NP the question]. 2. I asked [CP if you knew the answer]. VP → V {NP/CP} o The second argument of a verb can also be clausal 3. John told [NP Mary] [NP a story]. VP → V {NP} {NP/CP} 4. John told [NP Mary] [CP that he is a linguist]. o This modifies our previous VP rule as: VP → V ({NP/CP}) ({NP/CP}) A VP can consist of a V, optionally followed by NPs or something we call CPs (complementizer phrase). o We’ll come back to CPs after we’re finished with VP. 12 Exploring the verb phrases (VPs): A PP argument o The second argument of a verb can also be a PP, as (2) 1. John gave [NP Mary] [NP a book]. VP → V NP NP 2. John gave [NP a book] [PP to Mary]. VP → V NP PP o This modifies our previous VP rule as: VP → V ({NP/CP}) ({NP/CP/PP}) Note: The ability to take the (syntactic) arguments of a verb/lexical item is called “subcategorization’. 13 Exploring the verb phrases (VPs): Modifiers/Adjuncts inside VPs o A verb can also be preceded by any number of AdvPs: Bill [often very very quickly ran]. VP → AdvP+ V o And followed by any number of PPs and AdvPs: I [bought an ice-cream at IIT happily for Rs.100 yesterday] VP → V NP PP AdvP PP AdvP oFull-fledged verb phrase VP → (AdvP+) V ({NP/CP}) ({NP/CP}) (AdvP+) (PP+) (AdvP+) 14 The full-fledged VP VP → (AdvP+) V ({NP/CP}) ({NP/CP}) (AdvP+) (PP+) (AdvP+) o Here’s a sentence making use of (almost) all these pieces: John frequently very happily told Mary that he majored in Linguistics loudly in the library yesterday. 15 Exploring CPs o ‘CP’ stands for ‘complementizer phrase’. It’s a sentence preceded by a complementizer (words like that, whether, if). John told Mary that he’s a linguist. What will you do if you miss the plane? I will see whether she is at home. o The C turns out to be optional in many cases: John told Mary (that) he was a linguist o Thus, we have the CP rule as follows CP → (C) S 16 Sentences: S or TP o We looked at many English sentences. All consist of NP and VP 1. [NP Cats] [VP meow]] 2. [NP The man] [VP walked]] 3. [NP John] [VP frequently very happily told Mary that he majored in Linguistics loudly in the library yesterday]] o Thus, a sentence (S) consists of a noun phrase and a verb phrase. We often call S’s another name, TP, which stands for ‘tense phrase’. S/TP → NP VP o You can use whichever label you like, but TP is more modern. 17 Sentences: S or TP o A sentence can have a CP as the subject. 1. That Mary was coming surprised John S/TP → {NP/CP} VP o Sometimes Tense (such as modal- can/might/could , etc. or auxiliary verbs- is/am/are/has/have/was/were/will/shall) can precede the main verb: 1. Mary might come. 2. Mary is eating a banana. 3. Bill will read the book. 4. Sue had read the book. o Summarizing these points, our final TP rule: S/TP → {NP/CP} (T) VP 18 Back to PP: The final rule o The PP rule so far: PP → P NP o The above PP rule explains set 1. o But set 2 shows that NP can be optional in PP. Set -1 Set-2 1. I threw the garbage out the window. 1. I threw the garbage out. 2. I bought a book from India. 2. I blew it up. 3. I saw a boy with a telescope. 3. I haven’t seen him before. o A PP can have a preposition and, optionally, an NP. PP → P (NP) 19 Tw0 more PSRs o Conjunction (lexical and phrasal) X → X conj X (to conjoin two words) XP → XP conj XP (to conjoin two phrases/sentences) Here, the X’s can be instantiated as any category whatsoever. 1. [Bill and Ethan] are reading the book. 2. The [blue and red] station wagon. 3. Bill [went and ate] a burger. 4. I am [drinking lemonade and eating a brownie]. 5. [I’ve lost my wallet, or I’ve lost my mind]. 6. We went [through the woods and over the bridge]. Summing up: Phrase structure rules developed today for English 1. CP → (c) TP 2. TP → {NP/CP} (T) VP 3. NP → (D) (AdjP+) N (PP+) (CP) 4. PP → P (NP) 5. AdjP → (AdvP) Adj 6. AdvP → (AdvP) Adv 7. VP → (AdvP+) V ({NP/CP}) ({NP/CP/PP}) (AdvP+) (PP+) (AdvP+) 8. X → X conj X 9. XP → XP conj XP Bonus PS rule and Over-generalization o Our VP rule VP → (AdvP+) V ({NP/CP}) ({NP/CP/PP}) (AdvP+) (PP+) (AdvP+) o How do you explain the ungrammaticality of the following sentences? 1. *John told 2. *John ate that Mary left. o (1) is ungrammatical because ‘tell’ is a ditransitive verb. It needs three arguments. However, there is only one argument, ‘John’, in (1). o (2) is ungrammatical because ‘eat’ cannot take a CP argument 23 Announcements o No class this Friday. o The Brain and Cognitive Science colloquium is to be held on this Friday. o Please attend it. It starts at 9:30 in the Seminar room https://bcs.iitd.ac.in https://bcs.iitd.ac.in/schedule o Your graded answer script will be available for review on Tuesday. 24 HSL747: Language Computations and Mental Architecture Sem I, 2024–25 Deepak Alok IIT Delhi Recap: Phrase structure rules in English 1. CP → (c) TP 2. TP → {NP/CP} (T) VP 3. NP → (D) (AdjP+) N (PP+) (CP) 4. VP → (AdvP+) V ({NP/CP}) ({NP/CP/PP}) (AdvP+) (PP+) (AdvP+) 5. PP → P (NP) 6. AdjP → (AdvP) Adj 7. AdvP → (AdvP) Adv 8. X → X conj X 9. XP → XP conj XP How to build trees 3 Parts of a tree o Consider the following tree o Some terminology that will be useful to know 1,2,3,4,5, and 6 are all nodes in the tree 1 and 3 are branching nodes (non-terminal node is a more modern term) 2,4,5, and 6 are leaves (terminal node is a more modern term) 1, the highest branching node, is the root of the tree 2 and 3 are sisters; so are 4, 5, and 6 1 is the mother node for 2 and 3 and 3 is the mother node for 4, 5 and 6 4 Parts of a tree A B C D E F G H I J Some Practice: What is the root note? A What are the nodes? A-J What are the terminal nodes? G,H,E,I,J What are the branching/non-terminal nodes? A,B,D,C,F What are the sisters/siblings? B,C; G,H; E,F; I,J 5 Practice: From Phrase structure rules to trees o Can you draw the tree that the following phrase structure rules generate? A→ BC B→D D→GH C→E A B C D E G H 6 Practice: From trees to Phrase structure rules o Can you write the phrase structure rules that generate the following tree? A B C D E F G H I J A→ BC B→D D→GH C→EF F→I J 7 PS rules and their relationship with Trees o Elements are ordered inside a phrase. o Phrase structure rules describe how trees can be built. o For example, based on TP → {NP/CP} (T) VP, we know that the tree in (1) is possible, and the tree in (2) and (3) are impossible: 1. 2. 3. TP *TP *TP NP T VP NP VP T T NP VP Note: Order matters 8 Building tree for sentences o Draw tree structure for A linguist from New York told Mary she won. o Begin with lexical categories, then start putting them together, keep doing this in ways consistent with our Phrase structure rules 9 Bottom-up TP NP VP NP CP PP TP NP NP VP D N P N V N N V A linguist from New York told Mary she won 10 Top-down TP NP VP NP PP CP TP NP VP NP D N P N V N N V a linguist from New York told Mary she won 11 Tree Representation 12 Practice with syntactic trees 1. John ran. 2. John ate a mango. 3. The boy surprised John. 4. Mary might come. 5. John will read the book. 6. That Mary was coming surprised John. 7. I often bought ice cream at IIT happily. 13 Next class o More on Constituency o Reading: Carnie, Ch. 3 section-4-5 14 HSL747: Language Computations and Mental Architecture Sem I, 2024–25 Deepak Alok IIT Delhi Recap: Phrase structure rules in English 1. CP → (c) TP 2. TP/S → {NP/CP} (T) VP 3. NP → (D) (AdjP+) N (PP+) (CP) 4. VP → (AdvP+) V ({NP/CP}) ({NP/CP/PP}) (AdvP+) (PP+) (AdvP+) 5. PP → P (NP) 6. AdjP → (AdvP) Adj 7. AdvP → (AdvP) Adv 8. X → X conj X 9. XP → XP conj XP Today o Phrase structures in other languages o More on “Constituents” Not all languages are like English: NPs o In English, determiner and adjective appear before the noun they modify o But not all languages are like English. Consider an NP in French 1. les gars beaux the.PL guys handsome.PL “The handsome guys" o Generally, in French, adjectives typically follow the noun they modify. *NP → D AdjP N NP → D N AdjP Not all languages are like English: PPs o In English, a preposition appears before the noun: PP → P NP o But not all languages are like English. Consider some PPs in Hindi 1. mez par 2. New York me table on New York in ‘on the table’ ‘in New york’ o In Hindi, prepositions appear after the noun phrase (called postpositions) *PP → P NP PP → NP P Not all languages are like English: objects inside VP o In English, object NPs follow the verb they are associated with (VP → V NP NP) but not in all languages. Consider a VP in Japanese and Hindi 1. John-ga [VP tegami-o yonda] (Japanese) John-SUB letter-OBJ read.PAST "John read the letter." 2. John-ne [VP chhithii parhii] (Hindi) John.SUB letter.OBJ read.PAST.3S "John read the letter." o The object comes before the verb VP → NP V  Practice with syntactic trees o Some sentences in Sinhala (spoken in Srilanka) o Let’s assume that an AdjP rule: AdjP → Adj What is the PP rule of Sinhala? PP → NP P What is the NP rule of Sinhala? NP → (D) (AdjP) N What is the VP rule of Sinhala? VP → (PP) (NP) V What is the TP rule of Sinhala? TP → NP VP  Practice with syntactic trees o Draw the tree for the first and second sentences. Next Class Constituency and some tests HSL747: Language Computations and Mental Architecture Sem I, 2024–25 Deepak Alok IIT Delhi Constituents  Constituents: intuitively o In the below example, we have an intuition that certain words and groups of words are tied together more closely than others. John told Mary that he was watching a nice movie.  Constituents, intuitively o In the below example, we have an intuition that certain words and groups of words are tied together more closely than others. John told Mary that he was watching a nice movie. that he was watching a nice movie but not that he was he was watching a nice movie but not that he watching a nice movie but not watching a a nice movie but not a nice Nice o The constituents in a sentence “hang together” in a way the non- constituents do not. Constituents: formally o A group of words that functions together as a unit in Syntax. o The natural groupings of the parts of a sentence are constituents. Phrases are constituents o Let’s see some properties that constituents share, which you can use as constituency tests. Constituency tests The fragment test Substitution/Replacement test Movement tests The fragment test: Stand alone o If a group of words can stand alone as an answer to a question, they form a constituent. 1. What did John buy? a red hat/*a red 2. Where are you? at the beach/*at the Q: What phrases are these constituents? NP in (1), PP in (2) Substitution/Replacement test o If a group of words can be replaced by a single word, by the same category, they form a constituent. 1. John bought three red hats. 2. John bought them. 3. The Republican candidate for president only eats fast food. 4. He only eats fast food. Q: What phrases are these constituents? NP o An NP can be replaced by a pronoun. o Keep in Mind: Pronouns are NPs Substitution/Replacement test o If a group of words can be replaced by a single word (by the same category), they form a constituent. 1. If Mary went to the park, then John went to the park 2. If Mary went to the park, then John did. Q: What phrases are these constituents? VP o A VP can be replaced by the verb ‘to do’; do, does, did. Movement test o If a group of words can be moved together, they form a constituent. Passivization: 1. The news surprised every student in the class. 2. Every student in the class was surprised __ by the news. Clefting: 1. I watched the parade from my window. 2. It was from my window that I watched the parade __. Topicalization: 1. I like nice people. (I don’t like mean people) 2. Nice people, I like ____. (Mean people, I don’t __.) How to test constituency: Our earlier example 1. John told Mary that he was watching a nice movie o Is ‘a nice’ a constituent in (1)? Fragment test: What did John tell Mary that he was watching? *a nice (failed the test) The replacement test: *John told Mary that he was watching it movie. (failed the test) Movement test: *A nice, John told Mary that he was watching ___ movie. (failed the test) o N0. ‘a nice’ is not a constituent. It fails all the constituency tests. How to test constituency: Our earlier example 1. John told Mary that he was watching a nice movie. Q: Is ‘a nice movie’ a constituent in (1)? Fragment test: What did John tell Mary that he was watching? Ans: A nice movie (passed the test) The replacement test: John told Mary that he was watching it. (passed the test ) Movement test: A nice movie, John told Mary that he was watching ___. (passed the test) Constituency arguments o Constituents will pass at least one constituency test. To prove that something’s a constituent, construct an example that shows it passes a constituency test. To be on the safe side, use at least two constituency tests. o Non-constituents will fail every constituency test. To argue that something’s not a constituent, check that it fails all the tests. Movement Yes-no question in English: Movement (Different word orders) Declarative/Statement Yes-no question 1. Mary could see the cat. Could Mary __ see the cat? 2. Mary is reading a book. Is Mary __ reading a book? 3. Mary was reading a book. Was Mary __ reading a book? 4. Mary will read the book. Will Mary __ read a book? oGeneralization: ‘Aux/tense’ is found in the front of the sentence. oHypothesis: A Yes-no question is derived from a declarative The ‘Aux/tense’ is moved to the front of the sentence. oBut where? The rule: T-to-C movement o Declarative sentences are TPs o ‘Yes-no question’ sentences are CPs o T0 make yes-no questions : Move T to C, leaving a trace The basic tree structure for (1) TP NP T VP could Mary V NP see the cat Step-1: create a CP note above TP CP C TP NP T VP Could Mary V NP see the cat Step-2 o Move T element to C, leaving a trace (t) CP C TP Couldi NP T VP ti Mary V NP see the cat Wh-question: Data Declarative/Statement Wh-question (of the object) 1. Mary can bake a bread. What can Mary __ bake__? 2. Mary will read the book. What will Mary __ read __? 3. Mary reads a book. What does Mary __ read __? o Generalization: ‘Aux/tense’ moves before the subject Wh-word moves before the aux/tense o But where? The rule for Yes-no question o Declarative sentences are TPs. o ‘wh-questions’ are CPs o The wh-question rule Draw a CP node above the TP. Move T to the C, leaving a trace. Move the wh-word to the left of the moved T, leaving a trace. The basic structure TP NP T VP can Mary V NP bake what The Final structure o Move the T element to C and the wh-word to CP CP NP C TP whatj cani NP T VP ti Mary V NP bake tj Some practice Is John going? Were you studying? Will you watch the movie? What will you read tomorrow? Where did you go yesterday? Next Class Some Semantics HSL747: Language Computations and Mental Architecture Sem 1, 2024-2025 Semantics Module Ojaswee Bhalla Post Doctoral Fellow, HUSS, IIT-D [email protected], [email protected] Laying the ground: Week 1: Introduction to Meaning Lexical Semantics: Word Sense, Word Reference, Meaning Relationships Compositional Semantics: Propositions and Truth Values, Relations between propositions Material - based on Fromkin et al., Language Files and Hurford et al. Unit 3 What is the meaning of meaning? As a language speaker, this is one part of what you know when you say you know a language: - You know what is said to you – whether a word is meaningful (light) or not (tribilit) – whether a sentence is meaningful or not (Colourless green ideas sleep furiously) - You can generate infinite new meaningful sentences using finite means (A class in LH620 at 11am makes me extremely happy) As a language speaker, this is one part of what you know when you say you know a language: - You know when a word has two meanings (bank) or when a sentence has two meanings (I saw a girl with binoculars) - You know when two words have the same meaning (sofa and couch) or when two sentences have same meaning (Jack put off the meeting and Jack put the meeting off) As a language speaker, this is one part of what you know when you say you know a language: - You know when two words or sentences have opposite meanings (alive or dead; Jack is a student v/s Jack is not a student) - You mostly know what real world object a word refers to (a bench near the wall), or if the thing doesn’t exist, we still have some sense of it (a unicorn, the Yeti) So you have a lot of intuition (and, hopefully now, insight) about your knowledge about linguistic meaning  Now let us think about …. What is the meaning of a sentence? The meaning of a sentence: - Its truth conditions – the circumstances under which the sentence is true or false - By knowing the meaning, one knows the kind of world knowledge that is needed – linguistic or nonlinguistic or both (All corpses are dead; Utah is in USA) - If one knows whether a sentence is true, they also know what sentence is entailed by that sentence (Kim kissed Lee passionately entails Kim kissed Lee) Knowledge about syntactic structure and knowledge about meaning – both part of the grammar of language Semantics → The study of linguistic meaning of morphemes, word, phrases and sentences Subfields → Lexical semantics and compositional semantics Lexical Semantics → Meaning of words and the meaning relationships amongst words Compositional Semantics → How the meanings of words are combined to form the meanings of larger syntactic units such as phrases and sentences Pragmatics (a related field) → the study of how context affects meaning (How was the movie? ~ I slept within 15 minutes) Two aspects of Linguistic Meaning: SENSE of an expression – some kind of mental representation of its meaning REFERENCE of an expression – relationship of that expression to the world Example: Hearing ‘cat’ might conjure up some image of a cat or a mental representation of what cats are (four-legged, furry, potentially allergy-causing etc.) To know the sense of an expression is to have some mental representation of its meaning. By virtue of knowing the sense of some expression, one knows its relationship to the world, the reference of that expression. Sense and Reference: A speaker indicates which things in the world (including persons) are being talked about by means of reference – the reference of a linguistic expression identifies or points towards a part of the world Ex: John smashed the car - identifies a person and a thing in the world The particular entities in the world to which some expression refers – REFERENT The collection of all referents of an expression – its REFERENCE Referent of an expression – a thing or a person in the world Sense of an expression – not a thing but an abstraction that the human mind understands Sense and Reference: Same linguistic expression can refer to different things outside the language – case of variable reference Ex: ‘Touch your nose’ – your nose can refer to 23 different noses in the class Case of an expression having constant reference Ex: The moon, Hailey’s Comet More than one expression can have the same referent Ex: The Morning Star and The Evening Star refer to planet Venus Sense and Reference: Not every linguistic expression has a reference Ex: almost, probable, if, above, and, not Phrases and sentences, besides words, can also have a sense. Ex: Bachelors prefer redheads Girls with red hair are preferred by unmarried men Same word can have more than one sense Ex: Bank of Maharashtra Bank of the river Sense and Reference: Same sentence can have different senses too Ex: The chicken is ready to eat Ex: He killed the king with long hair Expressions in different varieties of same language can have same sense Ex: friend/pal/buddy Meaning of a word is not just reference of a word. If that was the case, we wouldn’t understand the meaning of Unicorns are running outside the classroom → Semantic knowledge of a linguistic expression involves both its sense and its reference (German philosopher Gottlob Frege’s Sinn and Bedeutung) In order to know the reference of some expression, one must understand the sense it expresses. However, understanding its sense does not guarantee that one will be able to pick out all its referents correctly. Ex: Diamond To conclude: Notion of sense – underlies the intuition that there is mental component to linguistic meaning Notion of reference – relates this mental representation to the outside world In our next class: Lexical Semantics  HSL747: Language Computations and Mental Architecture Sem 1, 2024-2025 Semantics Module Ojaswee Bhalla Post Doctoral Fellow, HUSS, IIT-D [email protected], [email protected] 10/4/2024 1 Laying the ground: Week 1: Introduction to Meaning Lexical Semantics: Word Sense, Word Reference, Meaning Relationships Compositional Semantics: Propositions and Truth Values, Relations between propositions This lecture is based on Fromkin et al. & Language Files readings Also read – Hurford et al. unit 2 and unit 3 10/4/2024 2  LEXICAL SEMANTICS What exactly does it mean for a word to mean something? 10/4/2024 3  Common assumption – Dictionaries are the true source of word meanings - They are an authoritative source of word meanings - Definitions arrived at by studying language usage by speakers - Dictionary entries not fixed and immutable – undergo changes - Dictionaries model usage and usage is not modelled by dictionaries - Highest authority on word meaning – speech community itself 10/4/2024 4 Established in previous class linguistic expressions (including words) are associated with senses Senses are the mental representations of the meaning Next logical question – What is the form of these representations? How are word meanings stored in mental lexicon? 10/4/2024 5  Potential Answer 1: Dictionary-style definitions Potential Answer 2: Mental Image definitions Potential Answer 3: Usage-based definitions 10/4/2024 6 PA1: envision an imaginary idealized dictionary – changes with time – lists all words in a language at a given time – provides verbal definition of each word according to the speaker’s use of it Problems with this: - unending process of knowing the meaning of the words that constitute a definition, knowing the meaning of the words that constitute those words’ definitions - possible circularity in defining words (eg: pride-proud) - understanding one definition requires knowing content and function words (like the, of, to etc.) → Dictionaries – useful – can’t make theoretical claims about nature of meaning → They don’t explain meaning in basic terms but only paraphrase → Dictionary-style definitions – can’t be all there is to meanings of words in a language 10/4/2024 7 PA2: word’s meaning stored as mental image – goal of conversation to get addressee to have a mental image similar to one’s own – we do utilize this technique in some way to conceptualize reality Problems with this: - Different people’s mental images may be very different from each other without the word’s meanings varying very much from individual to individual Ex: ‘lecture’ seen from a student’s perspective v/s a teacher’s perspective - Hearing a word in isolation and hearing a word in context may mean different things –word may mean something more than what you think when heard alone Ex: mother v/s Mother Teresa - Default mental image – tends to be of typical example of the kind of thing the word represents – a prototype – but words can signify a range of ideas which may not be typical of its kind Ex: bird, ostrich - Many words have no clear mental images Ex: forget, useful → Mental image definitions cannot be all there is to how we store meanings in mind 10/4/2024 8 PA3: What exactly lexical sense is – still an open question – up for investigation What is agreed upon – when we know a word, we know when it is suitable to use that word in order to convey a particular meaning or grammatical relationship Ex: blanket - Something about a particular set of circumstances tells one whether it is suitable to use a word - Hearing a word- we know what circumstances must be like them to use it - True for both content words and function words 10/4/2024 9  Conclusion: Regardless of the form of mental representation of word meanings, if we know what a word means, we know under what conditions it is appropriate to use it 10/4/2024 10  All that was about word sense What about word reference? What kind of reference a word can have? 10/4/2024 11 Proper names – refer to specific entities in the world (people, places etc.) 10/4/2024 12 Common nouns – do not refer to specific thing by themselves Ex: Does Ravi have a dog? No, he doesn’t have a dog. ‘dog’ – restricts attention of the addressee to a certain set of things in the worlds – the things that are dogs Expressions that contain a common noun can have a specific referent – consequence of how noun meanings combine with other meanings 10/4/2024 13  What does an intransitive verb refer to? What does an adjective refer to? 10/4/2024 14 Meaning Relationship: Words can be related phonologically, morphologically, syntactically and semantically To analyze meaning relations among words – looking at word reference – specific things that word picks out in the world 10/4/2024 15 Meaning Relationship: 1. Hyponymy 2. Synonymy 3. Antonymy a. Complementary antonyms b. Gradable antonyms c. Reverses d. Converses 10/4/2024 16 Hyponymy – a word X is a hyponym of word Y if the set that is the reference of X is always included in the set that is the reference of Y – a relation of sense inclusion Ex: Dogs – Golden retriever, Poodle Homonym ~ Hypernym Sister terms – reference is on the same level of hierarchy, exactly same hypernyms This sense relation can be extended to sentences in the form of entailment Ex: I can speak English and Hindi entails I can speak English 10/4/2024 17 Synonyms – exactly same reference (sense may differ) - have same meaning in some or all contexts Ex: ancestry/lineage, couch/sofa, quick/rapid, groundhog/woodchuck Antonyms – being opposite in some sense, contrast with each other in a significant way – ‘opposite’ is vague 10/4/2024 18 Complementary antonyms – X and Y are complementary antonyms if everything in the world in either in X’s reference set or Y’s reference set or in neither of the sets but crucially not in both Ex: married/unmarried; alive/dead 10/4/2024 19 Gradable antonyms – represent points on a continuum so something can be one or the other or neither (but not both), one can be between the two too Ex: hot/cold; wet/dry; old/young tend to be relative; don’t represent absolute value often words to describe intermediate state possible to ask about extent of gradable antonym Ex: How hot?/ How old? 10/4/2024 20 Reverses- suggest some kind of movement; one word in the pair suggests movement that undoes the movement suggested by the other Ex: ascent, descent; expand/contract (Possible for something to expand without having anything contract) 10/4/2024 21 Converses- involves two opposing point-of-views or a change in perspective; for one member of the pair to have reference other must as well – also called relational opposites Ex: lend/borrow; employer/employee 10/4/2024 22 Other lexical relations: Homonymy – words that are pronounced the same but have different meanings Ex: bear-bare Polysemy – same word that has multiple meanings Ex: paper 10/4/2024 23 Semantic Features: Semantic features – properties that comprise some of the meaning of a word or morpheme – clarifies how words relate to each other Ex: pot – pan – ? floor Ex: woman – [HUMAN], [FEMALE] → Synonyms, hyponyms share most/some of the semantics features; antonyms must crucially differ in terms of some principle semantic feature →They are the conceptual elements that contribute to the meanings of words/sentences → Meaning of content words and some function words (like with, over) can be partially specified by such features 10/4/2024 24 Semantic Features of Nouns: Can be morphologically marked →In English, [FEMALE] sometimes indicated by suffix –ess as is goddess, princess etc. →In other languages, nouns occur with ‘classifiers’ – grammatical morphemes that indicate semantic class of the noun Ex: Swahili prefixes for human singular/plural distinction - mtoto (‘child’), watoto (‘children’) →Semantic features may have syntactic effects too Ex: [COUNT] or [MASS] feature of nouns (whether they can be enumerated and pluralized) controls determiner/quantifier choice *I have a rice/many rice *I has much dogs 10/4/2024 25 Semantic Features of Verbs: What is the common semantic feature in darken-kill ? Other potential features: [GO]-expresses change in location in swim, crawl; [BECOME] – expresses end state of the action of certain verbs like break Semantic features can have syntactic consequences →Stative/Eventive difference in verbs: Stative verbs: Mary knows John; Mary likes apples Eventive verbs: Mary kissed John; Mary ate an apple Asymmentry in syntactic construction grammaticality/acceptability when: Mary is kissing John/ ? Mary is knowing John Mary deliberately kissed John/ ? Mary deliberately knows John 10/4/2024 26 Semantic Features of Verbs: →Negation and Negative Polarity Items (NPIs) NPIs are a set of lexical items that require negation in their environment to be licensed. Ex: ever, anymore Mary will not ever smile/ *Mary will ever smile I cannot visit you anymore/ *I can visit you anymore Certain verbs have ‘negation’ as a component of their meaning – evidence comes from the fact that they can license NPIs: John doubts/*thinks that he will ever fly a plane again. John refuses/*hopes to ever fly a plane again. 10/4/2024 27 Verb and theta roles: Part of Verb Meaning – its argument structure Verb assigns semantic theta roles to its arguments Theta roles – agent, theme, goal, source, instrument, experiencer Ex: The boy ran. The ship sank. The boy threw the book at his friend 10/4/2024 28 Sense Properties of sentences: Sense properties of a sentence – analyticity, syntheticity and contradiction 1. Analytic sentence: one that is necessarily true as result of the sense of the words in it – it reflects an agreement by speakers of the language about the senses of the words in it Ex: Cats are animals Bachelors are unmarried 2. Synthetic sentence: one that is not analytic – one that may be either true or false, depending on the way world is. Ex: The ruling monarch of UK is a man. 3. Contradiction – sentence that is necessarily false as a result of the sense of the words in it – opposite of an analytic sentence Ex : This animal is a vegetable. John killed Bill, who remined alive for many days 10/4/2024 29  Next week: Compositional Semantics & Propositional Logic 10/4/2024 30 HSL747: Language Computations and Mental Architecture Sem 1, 2024-2025 Semantics Module Ojaswee Bhalla Post Doctoral Fellow, HUSS, IIT-D [email protected], [email protected] Laying the ground: Week 2: Principle of Compositionality Truth Conditions Semantic Rules Lecture Material - based on Fromkin et al. and Language Files readings 10/15/2024 2 Last week, we had been talking about words – the meaning they express (the sense) and that meaning’s relationship with the world (the reference) Word reference was seen in terms of specific entities in the world (for proper names) or in terms of sets of entities in the world (for verbs, adjectives). But there is more to sentence meaning than specific entities or sets of specific entities. 10/15/2024 3 Ex 1: Delhi is amongst the top polluted cities in the country. This sentence is not just picking out one entity (a city called ‘Delhi’) or a set of entities (denoted by ‘city’ or ‘country’) - but it is making an assertion about certain entities in the world. → This claim expressed by a sentence is called a Proposition → Words in isolation do make a claim or assert anything about entities → Proposition is the sense expressed by a sentence 10/15/2024 4 Defining characteristic of a proposition – it can be true or false The ability to be true or false – the ability to have a truth value → the truth value of a proposition can be enquired explicitly →one cannot enquire about the truth value of the meanings of nouns or proper names Proposition expressed by sentence 1 – happens to be true 10/15/2024 5 Ex 2: Shimla is amongst the top polluted cities in the country. Proposition expressed by sentence 2 – happens to be false 10/15/2024 6 What the contrastive pair 1 and 2 exhibit: – having truth value does not mean being true, but rather being either true or false – each proposition has to be evaluated with respect to the world to identify its truth value – truth values really do represent a relationship between the sense expressed by a sentence (a proposition) and the world Bottomline: Sentences express propositions and refer to truth values 10/15/2024 7 Understanding a proposition must involve being able to determine its reference, in principle – what the world would have to be like for the proposition to be true Truth Conditions – the conditions that would have to hold in the world in order for some proposition to be true Understanding a proposition = understanding its truth conditions 10/15/2024 8 Ex: IIT-Delhi’s campus festival recently concluded. - There should be a place called IIT-Delhi - That place should have a campus festival - That festival should be over by the time of utterance - The conclusion should have been in near past. 10/15/2024 9 It may be possible that we don’t have requisite knowledge about the actual world to determine a sentence’s reference in it Ex: Mekong river runs through Laos. → What is relevant is that we understand its truth conditions i.e. we know how the world should be like for that sentence to be true 10/15/2024 10 It could be the case that a proposition’s truth value is not definitively known by anyone Ex: Sometime in the future, another world war will occur. → So the truth value maybe unknown but that doesn’t mean the proposition doesn’t have one 10/15/2024 11 To conclude: in order to know the truth value of a proposition, it is necessary to understand its truth conditions. However, since no one has perfect information, it is possible to understand its truth conditions but still not know its reference 10/15/2024 12 Relationship between propositions vis-à-vis their truth values: What is the relationship between propositions where the truth of proposition expressed by one sentence guarantees the truth of proposition expressed by another sentence? Answer: Entailment Ex: (1) All dogs bark. (2) My dog barks. In a world where the truth conditions for (1) are satisfied, the conditions for (2) being true also hold obligatorily. 10/15/2024 13 Note: Reasoning about entailment is not concerned with the actual truth values of propositions Ex: (1) No dog barks. (2) My dog doesn’t bark. We know that the world we live in, (1) is not true. But still (1) entails (2) i.e. the world in which (1) is true, (2) has to be true too. 10/15/2024 14 When two propositions entail one another – this relationship is called mutual entailment (or also the sentences are synonymous) Ex: (1) I have a female sibling. (2) I have a sister. 10/15/2024 15 Two propositions can also be incompatible – both cannot be true at the same time in the same world – truth conditions of one are incompatible with truth conditions of the other. Ex: (1) All dogs bark. (2) No dogs bark. 10/15/2024 16 Next up: Principle of Compositionality and Semantic Rules 10/15/2024 17 HSL747: Language Computations and Mental Architecture Sem 1, 2024-2025 Semantics Module Ojaswee Bhalla Post Doctoral Fellow, HUSS, IIT-D [email protected], [email protected] Laying the ground: Week 2: Principle of Compositionality Truth Conditions Semantic Rules Lecture Material - based on Fromkin et al. and Language Files readings 10/17/24 2 What lexical ambiguity informed you → Meaning of an expression does depend upon the meaning of the words it contains Ex: The bank is clean. 10/17/24 3 What structural ambiguity informed you → Meaning of an expression also depends upon its underlying syntactic structure Ex: I saw the man with a telescope. Additionally, (1) Harry loves Mary. (2) Mary loves Harry. Same set of words, similar structures, in a world proposition expressed by (1) may be true but (2) false – structure matters! 10/17/24 4 Combining insights from both - Principle of Compositionality - Meaning of a sentence (or any other multi-word expression) is a function of the meaning of the words it contains and the way in which they are syntactically combined. Principle of compositionality is related to design feature of productivity – we can produce and understand an infinite number of sentences 10/17/24 5 Syntactic rules – accounted for generating structures of infinite number of sentences; takes as input words and gives as output grammatically well-formed phrases and sentences Semantic rules – accounted for meaning composition of infinite number of sentences; takes as input meaning of words and gives as output meaningful phrases and sentences Both are part of speaker’s inherent mental grammar along with mental lexicon (where meaning of all words and lexical expressions is stored) 10/17/24 6 Where compositionality fails? Idiomatic meaning Ex: Mary kicked the bucket Literal interpretation: Mary physically kicked a bucket. This interpretation aligns with compositionality, as the meaning is derived from the words and their combination. Idiomatic interpretation: Mary died. This interpretation deviates from compositionality, as the meaning is not derived from the literal meanings of the words. 2 interpretations? Entire phrase is stored in mental lexicon along with its non-compositional meaning completely wrong! fy ojasvee! 10/17/24 7 Previously we have seen that… Proper Names – pick a precise object in the world – its referent Predicates (verbs, adjectives, common nouns) – may seem like they don’t pick a particular thing in the world – however, the best way to define them is in terms of individuals those predicates successfully describe Ex: Meaning of swim – in a way that is reflected in the world – by having it denote the set of individuals (e.g. human beings and animals) that swim This captures the intuition that if we know the meaning of swim, then given a specific situation and enough knowledge about it, one can separate who is a swimmer and who is not, i.e. one can group the swimmers together. 10/17/24 8 Sentence: Jack swims Word Meaning Jack refers to (or means) the individual Jack swims refers to (or means) the set of individuals that swim Phrase structure rules for this sentence: S → NP VP NP → N VP → V 10/17/24 9 PSR tree for this sentence: Syntactic tree indicate that NP and VP combine to form S This composition is mirrored in semantics (and hence the need to understand semantics after some prior knowledge of syntax!) 10/17/24 10 Goal: Combine the meaning of NP Jack (an individual) and the meaning of VP swims (a set of individuals) to obtain the meaning of the sentence Jack swims Semantic Rule I: The meaning of S (where S → NP VP) is the following truth condition: If the meaning of NP (an individual) is a member of the meaning of VP (a set of individuals), then the sentence is true, otherwise it is false. 10/17/24 11 This rule is general and does not refer to any particular sentence, individual or verb. Therefore, What is the meaning of Johnny barks? Meaning of this sentence is the truth condition (i.e. the if-sentence) that states that the sentence is true if the individual denoted by Johnny is among the set of barking individuals. 10/17/24 12 What about…. Sentence: Jack hit Laura 10/17/24 13 Word Meaning Jack refers to (or means) the individual Jack Laura refers to (or means) the individual Laura hit refers to (or means) the set of pairs of individuals X and Y such that X hit Y Phrase structure rules for this sentence: S → NP VP NP → N VP → V NP 10/17/24 14 PSR tree for this sentence: Meaning of transitive verb is still a set but this is a set of pairs of individuals {,} Captures the intuition that if we know the meaning of hit, then given a situation, we know who is the hitter and who is the hittee 10/17/24 15 Meaning of the VP resulting from combination of V with its object i.e. is hit Laura is a set of individuals – all and only those individuals who hit Laura in a given situation Semantic Rule II: The meaning of VP (where VP → V and NP) is the set of individuals X such that X is the first member of any pair in the meaning of V whose second member is the meaning of NP. 10/17/24 16 Sentence meaning is derived by first applying Semantic Rule II (which establishes the meaning of VP – a certain set of individuals who hit Laura) and then applying Semantic Rule I (which checks whether Jack is an individual who is part of the denotation of the VP and if yes, the sentence is true). In other words, the sentence is true if Jack hit Laura and false otherwise. 10/17/24 17  HSL747: Language Computations and Mental Architecture Sem 1, 2024-2025 Semantics Module Ojaswee Bhalla Post Doctoral Fellow, HUSS, IIT-D [email protected], [email protected] Handout based on Saeed (2009): Ch-4 and Ch-10; on Hurford et al. (2007) Units-12-15 1. Logic and Truth: - Tools of logic can help us to represent sentence meaning (Richard Montague 1974) - Beginning of logic – Aristotle (Greek philosopher) – search for valid argument and inference Example: Aristotle’s modus ponens (a type of logical argument) Premise: If Jack is a student, then he is in IIT-D. Jack is a student. Conclusion: Jack is in IIT-D. 2. Rules for logical calculation (logical inferences) are difficult to be stated in terms of ordinary language sentences Ex 3: ‘John and Mary worked diligently’ entails ‘John worked diligently’ Rule: Noun and Noun Verb Adverb entails Noun Verb Adverb X entails Y if and only if when X is true, Y has to be true too BUT: ‘John and Mary worked together’ does not entail ‘John worked together’ à Thus, sentences having similar grammatical forms may have different logical forms. Rules of inferences, to be completely systematic, must work upon representations of logical form of sentences. 3. Logical notation – a specially developed system to represent propositions unambiguously - includes symbols that make up logical formulae and rules for putting the logical formulae together correctly  Þ A system of logic consists of: - A notation (in effect, a definition of all possible proper formulae in the system) - A set of rules (for ‘calculating’ with the formulae in various ways) 4. Logic deals with meaning in language system (i.e. with propositions) – a system for describing logical thinking contains a notation for representing propositions unambiguously and rules of inference defining how propositions go together to make up valid arguments. MODUS PONENS is a rule stating that if a proposition P entails a proposition Q, and P is true, then Q is true. 5. Propositional Logic – - A logical system or a formal language whose units are propositions - Analyze meaning composition of propositions in a logical schemata, specifically the study of truth effects of connectives on propositions - Translation of natural language into propositional variables and propositional logical symbols Simplex (or atomic) formulas – translations of simple sentences in natural language that don’t have any truth-conditional or logical operator in them - represented by small case letters p, q, r etc. in propositional logic Complex formulas – a composite of simplex formulas and one or more operator of propositional logic - translations for complex sentences of natural language - the connectives are not, and, or, if-then, if and only if Connectives - provide a way of joining simple propositions to form complex propositions - a logical analysis must state exactly how joining propositions by means of a connective affects the truth of the complex propositions so formed  English Connective Symbol Example not Negation ¬ (Jack did not sleep) and Conjunction ∧ (Jack slept and Mary worked) or Disjunction ∨ (I will see you today or tomorrow) or Exclusive Or ∨e (You will pay the fine or you will go to jail) If-then Material Implication → (If it rains, then I will go the movies) If and only if (iff). Biconditional ≡ (we will leave iff we are forced to) 6. Formulas of propositional logic get interpreted in terms of their truth value – an atomic formula can be T/F depending on the evaluation of its truth conditions in a world – a complex formula also has a truth value that can be derived using the truth values of its atomic sub-parts and the meaning of the connective used in that specific complex formula – since the connectives of propositional logic generate formulas whose truth value depends only on the truth values of the constituent formulas, these connectives are called Truth Functional Connectives too 7. Truth Tables – represent how the truth value of the atomic formulas can be mapped to the truth value of a complex formula by the semantics of the connective involved Truth Table for Negation: p ¬p T F F T Truth Table for Conjunction: p q p∧q T T T T F F F T F F F F Truth Table for Inclusive Disjunction: p q p∨q T T T T F T F T T F F F Truth Table for Exclusive Disjunction: p q p∨e q T T F T F T F T T F F F Truth Table for Material Implication: p q p→q T T T T F F F T T F F T Truth Table for Biconditional or Equivalence: p q p≡q T T T T F F F T F F F T  What happens when we have complex formulas with more than one connective?? 8. Formal Semantics – a family of denotational theories that use logic in semantic analysis Other names – truth-conditional semantics, model-theoretic semantics, Montague Grammar, logical semantics 9. Denotational approach (understanding meaning of an utterance is matching it to the situation it describes; search for meaning is search for how symbols of language relate to reality) - primary function of language is that we can talk about the world around us - language is used to describe or model facts and situations. 10. Correspondence Theory of truth – matching up of utterance and situation – true and false value – truth conditions 11. Model-Theoretic Semantics: Predicate logic -work of Gottlob Frege, Alfred Tarski, Richard Montague Model- a formal structure representing linguistically relevant aspects of a situation Three stages of semantic analysis: Firstly, a translation from a natural language like English into a logical language whose syntax and semantics are explicitly defined. Secondly, the establishment of a mathematical model of the situations that the language describes. Thirdly, a set of procedures for checking the mapping between the expressions in the logical language and the modelled situations. à Essentially these algorithms check whether the expressions are true or false of the modelled situations. 12. Syntax of predicate logic includes vocabulary of symbols and rules for formation of logical formulae: Symbols of predicate logic: Predicate letters: A, B, C etc. Individual constants: a, b, c etc.  Individual variables: x, y, z etc. Truth-functional connectives: ¬, ∧, ∨, ∨e, →, ≡ Quantifiers: ∀, ∃ Rules for creating logical formulae: a. Individual constants and variables are terms b. If A is an n-place predicate and |t1…tn| are n terms, then A(t1…tn) is a formula. c. If ϕ is a formula, then ¬ ϕ is a formula d. If ϕ and ψ are formulae, then (ϕ ∧ ψ), (ϕ ∨ ψ), (ϕ ∨e ψ), (ϕ → ψ) and (ϕ ≡ ψ) are all formulae. e. If ϕ is a formula and x is a variable, then ∀x ϕ and ∃x ϕ are formulae. 13. Advantage of predicate logic – semantic representation of quantifiers clarifies an ambiguity found in natural language – scope ambiguity (occurs when more than one quantifier in a sentence) Ex 1: Everyone loves someone Interpretation 1: Everyone has someone that they love Interpretation 2: There is some person who is loved by everyone. Formula 1: ∀x ∃y (L (x,y)) Formula 2: ∃y ∀x (L (x,y)) è Scope of one quantifier contained within the scope of another quantifier (wide scope – narrow scope) Negation ‘not’ also has scope over predication; sentence containing a combination of quantifiers and negation can be ambiguous  Ex 2: Everybody didn’t visit Delhi Interpretation 1: For every person x, it is not the case that x visited Delhi Formula 1: ∀x ¬ (V(x,d)) Interpretation 2: It is not the case that every person x visited Delhi Formula 2: ¬ ∀x (V(x,d)) 14. The Semantics of the Logical Metalanguage Recall Steps in Semantic Analysis: Step 1: Translating from natural language into logical metalanguage Step 2: Relate symbols of logic to the situation described / establishing a mathematical model of the situations that the language describes Step 3: Set or procedures to check mapping of expressions in logical language and the modelled situation – checking whether expression is true or false of the modelled situation a. A semantic interpretation for the symbols of the predicate logic; b. A domain: this is a model of a situation which identifies the linguistically relevant entities, properties and relations; and c. A denotation assignment function: this is a procedure, or set of procedures, which match the logical symbols for nouns, verbs, etc. with the items in the model that they denote. This function is also sometimes called a naming function Domain and a Naming Function = a model 15. Semantic Interpretation of Predicate Logic Symbols: a. Sentences b. Individual constant terms c. Predicate constants  SENTENCES: Following denotational theory of reference and correspondence theory of truth, denotatum of a whole sentence is the match or lack of match with the situation it describes. Using square brackets to symbolize the denotatum of an expression, [p]v = 1 A sentence p is true in a situation v [p]v = 0 The sentence p is false in a situation v Individual Constant Terms: denotation of an individual constant term is the individual or the sets of individuals in the situation Predicate Constants: identify sets of individuals for which the predicate holds 1-place predicate ‘be standing’ – picks out set of individuals who are standing in the situation described {x|….} or {x: …} – ‘the set of all x such that…’ {x: x is standing in v} - the set of individuals who are standing in situation v. 2-place predicate: identify set of ordered pairs; two individuals in a given order Predicate ‘punch’ picks out {: x punches y in v} 3-place predicate: identifies a 3-tuple Predicate ‘hand’ picks out {: x hands y to z in v} 16. Domain - representation of the individuals and relationships in a situation v - a set of individuals identified in a situation v : U In a situation of Jack loving Mary, U= {Jack, Mary} 17. Denotation assignment function - This function matches symbols from the logical representation with elements of the domain, according to the semantic nature of the symbols  - Assignment as a function symbolized as F(x) – always returns extension of x in the situation - It matches individual constant terms with individuals in the situation v F(j) = Jack F(m) = Mary - It matches predicate constants with sets of individuals in v F(L) = loves = {} F(S)= be standing = {Jack, Mary} 18. Model – combination of a domain and the assignment function Schematically described as Mn = Where M = the model; U = set of individuals in the situation; F = denotation assignment function Subscript ‘n’ – relativizes the model to one particular situation M1 and M2 would correspond to models in different situation 19. Checking the truth-value of a simple sentence: Model M1 = U1 = {Jack, Harry, Mary} F1(j) = Jack F1(h) = Harry F1(m) = Mary F1(S) = sings = {Jack, Mary} F1(D) = danced = {Harry, Mary} F1(L) = loves= {,,} Sentences in predicate logic can be evaluated for their value in a model D(h) S(h) L(m,j) L(j, m) [D(h)]M1 = 1 iff [h]M1 ∈ [D]M1 The sentence Harry danced is true if and only if the extension of Harry is part of the set defined by danced in the model M1. F1(h) = Harry F1(D) = danced = {Harry, Mary} Since we know Harry ∈ {Harry, Mary}, therefore the sentence is true for our given model i.e. [D(h)]M1 = 1 HSL747: Language Computations and Mental Architecture Sem 1, 2024-2025 Semantics Module Ojaswee Bhalla Post Doctoral Fellow, HUSS, IIT-D [email protected], [email protected] An Introduction to Implications Implication – an inferential relationship between two sentences or sets of sentences; it is a directional relation - where one sentence or a set ‘leads to’ another sentence or a set. Example:- Sentence 1: Jack doesn’t like John anymore. Sentence 2: Jack used to like John at some point prior to the utterance time. →Sentence 1 implies sentence 2 or sentence 2 can be inferred from sentence 1 Can be further classified based on what licenses them (informational content of a sentence or conversational expectations) or their contribution to the ongoing discourse If an implication can be traced to a particular lexical item or as arising because of a particular syntactic construction, then that lexical item or construction is tagged as a ‘trigger’ for that inference. Example: lexical item ‘anymore’ triggers the inference from sentence 1 to sentence 2 above. 11/12/2024 2  INFERENCE ENTAILMENT PRESUPPOSITION IMPLICATURE 11/12/2024 3 Entailment Definition : sentence A entails sentence B if and only if whenever A is true, B has to be true too Example:- A: After Ravi cooked his dinner, his flat-mate cleaned their kitchen. B: Ravi cooked dinner. → In all possible worlds where sentence A is true , sentence B will be true too. Thus, A entails B. Note 1: In semantics, a speaker knows the meaning of a sentence if he knows under what condition that sentence is true or not. He need not know whether a sentence is actually true or not , only the conditions under which it is true or not. Example: I am a human being. To know the meaning of this sentence, one needs to know the conditions under which this sentence will be true. If in a given world those conditions are met, then the sentence is true in that world. Otherwise false. Such conditions are the truth-conditions of a sentence. Note 2: Entailment is a strong implication relation that is judged based on the truth-conditional content of sentence A (conditions under which sentence A is true) 11/12/2024 4 Test to check entailments Defeasibility Test: ‘A and not B’ should be contradictory Applying this test to the previous example: A: After Ravi cooked his dinner, his flat-mate cleaned their kitchen. B: Ravi cooked dinner. Not B: It is not the case that Ravi cooked dinner. ‘A and not B’: # After Ravi cooked his dinner, his flat-mate cleaned their kitchen. It is not the case that Ravi cooked dinner. → In a world where sentence A is true, Ravi did cook dinner and his flat-mate did clean the kitchen. In a world where ‘not B’ is true, Ravi did not cook dinner. These two worlds are contradictory as the same condition is met in one and not in the other. Thus, the sentence (A and not B) is indeed contradictory confirming that whenever A is true, B has to be true too. This proves A entails B in the given example. 11/12/2024 5 Let us try these out: Does (i) entail (ii) ? What about the reverse? (A) (i) Alex swims beautifully. (ii) Alex swims. (B) (i) Alex does not swim beautifully. (ii) Alex does not swim. (C) (i) Mary used to swim a mile daily. (ii) Mary no longer swims a mile daily 11/12/2024 6 Presupposition Definition: sentence A presupposes sentence B if A implies B and also if the truth of B is implied to be taken for granted as background for considering A Example: Sentence A: The class president has green hair. Sentence B: There is a unique class president. →A presupposes B as existence of a unique class president is taken for granted and assertion of sentence A is based over this background. →English definite article ‘the’ triggers this presupposition as definite descriptions license such existence and uniqueness inferences 11/12/2024 7 Lexical items or constructions can ‘trigger’ presuppositions: Definite descriptions Ex: The king of France is bald. >> There is a king of France. Factive predicates Ex: He knows that today is a holiday. >> Today is a holiday. Ex: He regrets that today is a holiday. >> Today is a holiday. 11/12/2024 8  Aspectual/change of state predicates Ex: He has stopped preparing for the major exam. >> He had been preparing for the major exam. Implicative predicates Ex: He managed to pass the major exam. >> He tried to pass the major exam. Iteratives Ex: He returned to hostel after the exam. >> He was in hostel before 11/12/2024 9  Temporal Clauses Ex: After she left IIT, she got a wonderful job. >> She left IIT. Cleft Sentences Ex: It was Ravi who announced an extra class on a Saturday. >> Someone announced an extra class on a Saturday. Pseudo-cleft sentences Ex: What Ravi announced was an extra class on a Saturday. >> Ravi announced something. 11/12/2024 10 Testing for Presuppositions: Projection Test: presuppositions project through a P-family of contexts (affirmative declarative, negative of declarative, interrogative, antecedent of conditional) A presupposes B iff if not only A but also other members of P family imply (and assume as background) B. Affirmative Declarative: The class president has green hair. Negative Declarative: The class president does not have green hair. Interrogative: Does the class president have green hair? Antecedent of Conditional: If the class president has green hair, then she must be expressing a point via them. Underlying presupposition: There is a unique class president. 11/12/2024 11