Compositional semantics explores how complex expressions derive meaning from their parts and combination rules. This principle, developed by Gottlob Frege, explains how we understand new sentences and create unlimited meanings with limited vocabulary.

Semantic rules like function application and predicate modification are applied to analyze sentence meaning. The process involves identifying syntactic structure, assigning semantic types, and applying rules bottom-up, using formal notations like lambda calculus.

Principles of Compositional Semantics

Principle of compositionality in meaning

• Meaning of complex expressions determined by constituent parts and combination rules
• Gottlob Frege developed this concept fundamental to modern semantics
• Enables comprehension of new sentences never encountered before
• Explains how limited vocabulary creates unlimited meanings
• Provides methodical approach to analyze sentence semantics
• Involves lexical semantics (word meanings), syntactic structure (word combination rules), and semantic rules (meaning derivation principles)

Application of semantic rules

• Function application combines predicates with arguments (loves(John, Mary))
• Predicate modification adds descriptive information (red ball)
• Lambda abstraction creates functions from expressions ($λx.loves(x, Mary)$)
• Process: 1) Identify syntactic structure 2) Assign semantic types 3) Apply rules bottom-up
• Noun phrases combine adjectives and nouns (big dog)
• Verb phrases integrate verbs with objects (eat pizza)
• Sentences join subjects with predicates (John runs)
• Formal notation uses lambda calculus ($λx.λy.loves(x,y)$) and type theory (e : entity, t : truth value)

Syntactic Structure and Ambiguity in Semantics

Syntactic structure and sentence meaning

• Syntax-semantics interface shows how structure limits possible interpretations
• Links grammatical roles (subject, object) to semantic roles (agent, patient)
• Structural ambiguity occurs when different structures yield different meanings ("I saw the man with binoculars")
• Meaning builds up from smaller to larger units (words to phrases to sentences)
• Thematic roles assigned by verbs to arguments (agent, patient, theme, experiencer)

Resolving ambiguity through semantics

• Lexical ambiguity involves multiple word meanings (bank: financial institution or river edge)
• Structural ambiguity arises from multiple syntactic structures ("The chicken is ready to eat")
• Scope ambiguity occurs with different quantifier interpretations ("Every child ate a cookie")
• Resolution techniques: contextual clues, pragmatic principles (Grice's maxims), formal semantic analysis
• Quantifier scope interactions affect meaning ("A teacher praised every student")
• Anaphora resolution determines pronoun referents ("John told Bill he was smart")
• Truth-conditional semantics uses conditions to disambiguate ("The king of France is bald")