Compositional Semantics: The Meaning of Sentences

Syntactic Constituents

• A good friend of mine planned to drive to San Diego to go to the theatre.

  • Use the cleft test to show that a good friend is not a constituent in this sentence.

  • Use the question-answer test to show that to San Diego to go to the theatre is a constituent.

• Is a good friend of mine a constituent or not? Give evidence from all three tests

• The cat was sleeping on the desk

  • Answers to questions: Where was the cat sleeping? On the desk.

  • Clefting: It was on the desk that the cat was sleeping.

  • Pro-Form (pronouns, do (so), be, have, there, then, such)

  • Substitution: The cat was sleeping there

Compositional Semantics

• From knowing what words mean to knowing what sentences mean

• Bag of Words (= collection of words in no order)

• We defined the meaning of words as either referring to specific things in the world (proper nouns) or sets of things in the world (nouns).

• What about sentences?

  • Example: India is the most populous country in the world.

• → The sentence doesn't refer to India, or to the set of countries. The claim that is expressed by a sentence is called a proposition

• Propositions have a truth value, i.e., they can be true or false.

  • Is it true that India is the most populous country in the world. (proposition)

  • Is it true that Luxembourg is the most populous country in the world. (proposition)

  • Is it true that India/Is it true that cat (not proposition)

• The claim that is expressed by a sentence is called a proposition

• Propositions have a truth value, i.e., they can be true or false.

  • Is it true that India is the most populous country in the world.

  • Is it true that Luxembourg is the most populous country in the world.

• Truth values represent the relationship between the sense expressed by a sentence (a proposition) and the world. Thus, we consider truth values to be the reference of sentences.

• Truth conditions: Understanding the conditions that would have to hold in the world for the proposition to be true.

• → Understanding the meaning of a sentence is understanding its truth conditions

• Example: The King of England is sleeping.

  • On [current date] at exactly [current time] the individual the King of England would 

    have to be asleep.

• → We don't necessarily know whether it's true but we know the conditions that would make it true

Relationships Between Propositions

• Entailment: If the proposition expressed by sentence (a) is true, proposition (b) also has to be 

• True.

  • (a)All dogs bark.

    • No dogs bark.

  • (b) Sally's dog barks

    • Sally's dog doesn't bark

• Mutual entailment

  • (c) All dogs bark.

  • (d)Sally's dog barks

• Contradiction: It is impossible to imagine a world in which they could both be true.

  • (e) All dogs bark.

  • (f) No dogs bark

• Neutral: One being true doesn't necessarily make the other true.

  • (g) All dogs bark.

  • (h) My dog's name is Peggy

• Natural Language Inference

Entailment, Contradiction, Neutral

• 1. (a) Hermione studied potions late at night.

  • (b) Hermione studied at night.

    • Entailment 

• 2. (a) Hermione cast a spell to fix Harry's glasses.

  • (b) Hermione refused to use magic on Harry’s glasses.

    • contradiction

• 3. (a) Professor Snape entered the dungeon carrying a large book.

  • (b) Snape was preparing for a lesson.

    • neutral

• 4. (a) The dog was licking its paws in the living room.

  • (b) The dog injured its paw earlier during a walk.

    • neutral

• 5. (a) The golden retriever fetched the stick.

  • (b) The dog fetched something.

    • entailment

• 6. (a) The dog ignored every command given to it.

  • (b) The dog was well-trained and obedient

    • contradiction

• a entails / contradicts / is neutral to b

The Principle of Compositionality

• There is more to complex meaning than just words or propositions.

• Sally loves Polly vs. Polly loves Sally (same words, nonambiguous, different meaning)

• Where does this distinction come from?

• Principle of Compositionality: The meaning of a sentence (or any other multi-word expression) is a function of the meanings of the words it contains and the way in which these 

  words are syntactically combined

• Compositional meaning deriving adjective + noun

  • Example: green sweater

    • Intersective Adjectives

  • Example: big whale / big mouse

    • Subjective Adjectives

  • Example: alleged thief

  • An alleged thief is not in the set of thieves. What is the set of alleged things?

    • Non-intersective Adjectives

Types of Adjectives

• Intersective, Subsective, Non-intersective

• 1. brown dog

  • intersective

• 2. smart puppy

  • subsective

• 3. round glasses

  • intersective

• 4. magical creature

  • Intersective

• 5. former headmaster

  • non-intersective

• 6. young wizard

  • subsective

• 7. fake flowers

  • non-intersective