16 - Semantics 2

Semantics and Compositionality

Compositional Semantics

  • Compositional semantics studies how meanings of linguistic expressions combine.

  • Example: "brown cow" translates to "the brown cows are kissing," illustrating linguistic combination beyond mere word meanings.

Combining Meanings

  • Question: How do we combine meanings of different linguistic expressions?

  • Example given: "brown cow" leads to conclusions about actions involving the subject.

Principle of Compositionality

  • The meaning of a linguistic expression is derived systematically from:

    • Lexical Semantics: Meanings of individual components.

    • Syntactic Organization: How components are structured.

  • This principle enables understanding of new utterances.

Examples of Compositionality

  • Sentence: "All ice cream is delicious"

    • Meaning derived as:

      • all: every instance

      • ice cream: frozen sweetened cream (usually dairy)

      • delicious: gustatorily pleasing

      • Final interpretation: "Every instance of a frozen sweetened cream product is gustatorily pleasing."

Importance of Syntax

  • Example: "the dog bit the cow" vs. "the cow bit the dog" demonstrates that syntax influences meaning and agent identification.

Non-compositionality

  • Some expressions do not follow compositional rules:

    • Example: "It's raining cats and dogs" means a heavy downpour, not a literal interpretation.

    • Requires memorization of non-compositional meanings (holistic understanding).

Understanding Compositionality

  • Fundamental question to explore: How does compositionality operate in language?

Mathematical Tool: Sets

  • Set: An orderless collection of entities, clearly defined without ambiguity.

  • Theoretical constructs that do not require practical enumeration of all entities.

Set Examples

  • The set of all even numbers: {2, 4, 6, ...}

  • Proper nouns can refer to unique or multiple entities, e.g., Barack Obama may refer to various individuals with that name.

Lexical Semantics

Reference of Individual Words

  • Common Nouns: Refer to sets with shared properties (e.g., cow refers to all bovines).

  • Verbs: Represent actions or occurrences (e.g., to freeze represents all instances of liquid becoming solid).

Compositionality in Practice

Case Studies:

  • Noun Phrase (NP) + Verb Phrase (VP): Asserts propositions.

  • Adjustments of meaning through combinations illustrate compositionality.

Propositions

  • Declarative sentences make assertions about the world:

    • Example: "This is the best group of Introduction to Linguistics students ever!"

    • Noun phrases refer to entities; sentences assert characteristics of these entities.

Adjectives and Noun Phrases (ADJ NP)

Modification

  • Adjectives specify subsets of entities referenced by nouns.

  • Example: "brown cows" refers to cows with a specific color.

Intersection

  • Some adjectives combine with NPs to narrow down the referent set.

    • Example: "married felon" combines properties of being married with being a felon.

Relative Intersection

  • Certain adjectives specify a set that is dependent on the noun's context:

    • Example: "big" is relative and depends on the context of comparison.

Non-Intersection and Anti-Intersection

  • Non-intersective adjectives do not establish clear sets of referents (e.g., "possible thief").

  • Anti-intersective adjectives refer to individuals outside the set denoted by the NP (e.g., "fake gun" is not a true gun).