Compositional semantics explores how complex expressions derive meaning from their parts and combination rules. This principle, attributed to Gottlob Frege, explains our ability to understand novel sentences and create infinite meaningful expressions from finite vocabulary.

The field delves into semantic composition rules, types, and the process of combining meanings. While it offers insights into how grammatical categories contribute semantically, compositional semantics has limitations in handling non-literal language, context-dependent meanings, and pragmatic aspects of communication.

Principles of Compositional Semantics

Principle of compositionality in language

• Meaning of complex expressions determined by parts and combination rules explains novel sentence understanding
• Gottlob Frege attributed this systematic approach to analyzing linguistic meaning
• Facilitates language acquisition and processing through lexical semantics and syntactic structure
• Enables infinite meaningful expressions from finite vocabulary and rules (productivity)

Rules of compositional semantics

• Semantic composition rules combine meanings:
  1. Function application joins predicates with arguments
  2. Predicate modification alters nouns with adjectives
  3. Lambda abstraction forms complex predicates
• Semantic types: entities (e), truth values (t), functions (e.g., $<e,t>$ for predicates)
• Composition process:
  1. Identify constituent semantic types
  2. Apply appropriate rule based on types
  3. Combine meanings step-by-step following syntax
• Tree diagrams represent structure, annotate nodes with semantic types and expressions

Semantic Analysis and Limitations

Semantic contributions of grammatical categories

• Nouns refer to entities/concepts (common: $<e,t>$ predicates, proper: e entities)
• Verbs express actions/states/relations (intransitive: $<e,t>$, transitive: $<e,<e,t>>$)
• Adjectives modify nouns (intersective: predicate modification, non-intersective: complex analysis)
• Determiners specify reference/quantity (quantifiers relate entity sets, articles affect uniqueness/familiarity)
• Adverbs modify verbs/adjectives/sentences (manner: action performance, sentential: proposition comments)

Limitations of compositional semantics

• Non-compositional expressions challenge literal interpretation (idioms, metaphors)
• Context-dependent meaning requires situational understanding (deixis, presuppositions)
• Pragmatic aspects extend beyond literal content (implicatures, speech acts)
• Ambiguity and vagueness complicate interpretation (lexical, structural)
• World knowledge and common sense reasoning necessary for full comprehension
• Emotional and connotative meanings not derivable from literal interpretations