John Cainoy

Topic 03 – Compositional Semantics and Predicate Logic

1. Coverage

Reporters are expected to cover the following subtopics in detail:

  • Principle of compositionality: how sentence meaning derives from the meaning of parts and their syntactic arrangement.
  • Predicate logic: predicates, arguments, variables, constants, quantifiers, connectives.
  • Scope ambiguity and its resolution in natural language.
  • Lambda calculus basics for representing functions and argument structures.
  • Event semantics (Davidsonian approach) for representing events, thematic roles, and modifiers.
  • Applications in formal and applied contexts (e.g., law, computing, AI reasoning).
  • Research potential: How formal semantics frameworks can frame empirical studies of sentence meaning and ambiguity.
2. Topic Overview
  • Define compositional semantics and explain its role in connecting words to sentence meaning.
  • Show how predicate logic serves as a formal language for modeling natural language meaning.
  • Introduce how ambiguity in quantification and scope challenges the idea of compositionality.
  • Highlight the importance of event semantics in representing complex sentences.
3. Core Readings & References
4. Key Concepts & Terms
  • Compositionality
  • Predicate, Argument, Variable, Constant
  • Quantifier (∀, ∃)
  • Scope Ambiguity
  • Logical Connectives (¬, ∧, ∨, →)
  • Lambda Calculus
  • Event Semantics, Davidsonian Events
5. Analytical Frameworks & Methods
  • Predicate logic notation for simple and complex sentences.
  • Logical Form (LF) representation of quantifier scope.
  • Lambda abstraction and functional application.
  • Davidsonian event representation with thematic roles (Agent, Theme, Instrument, Location).
6. Applied Examples
  • Quantifier Scope Ambiguity:
    “Every student read a book.”
    (∀x)(∃y)[Student(x) ∧ Book(y) ∧ Read(x,y)] vs. (∃y)(∀x)[Book(y) ∧ Student(x) ∧ Read(x,y)].
  • Event Semantics:
    “John kissed Mary in the park.”
    ∃e[Kiss(e) ∧ Agent(e, John) ∧ Theme(e, Mary) ∧ Location(e, Park)].
  • Lambda Calculus:
    “runs” → λx_Run(x).   “John runs” → Run(John).
7. Discussion Questions
  • Does compositionality hold for idioms and figurative language?
  • How does predicate logic capture (or fail to capture) natural language meaning?
  • In what ways do scope ambiguities reflect deeper cognitive or cultural preferences?
8. Research Link
  • Comparative analysis of quantifier scope preferences across languages.
  • Application of event semantics to legal contracts or AI-generated text.
  • Lambda calculus as a tool for modeling natural language inference in computational linguistics.