Model-theoretic semantics provides a mathematical framework for analyzing linguistic meaning. It focuses on truth conditions and compositionality, using formal models with domains, interpretation functions, and assignment functions to represent meaning systematically.

This approach allows precise semantic analysis and study of logical relations between sentences. While it excels at capturing truth-conditional aspects, it may struggle with context-dependent meanings and non-truth-conditional elements of language.

Foundations of Model-Theoretic Semantics

Principles of model-theoretic semantics

• Formal approach to analyzing meaning of natural language expressions provides rigorous mathematical framework for representing meaning allows precise and unambiguous interpretation
• Meaning determined by truth conditions the conditions under which a sentence is true or false define its meaning
• Compositionality principle meaning of complex expression determined by meanings of its parts and rules used to combine them
• Enables systematic representation of meaning of linguistic expressions formulation of precise semantic rules and principles and study of entailment presupposition and other semantic relations

Components of semantic models

• Domain of discourse (D) set of entities or objects language assumed to be talking about can include individuals (people) events (weddings) times (yesterday) and other relevant entities
• Interpretation function (I) maps non-logical constants (names like John predicates like tall) to elements in domain of discourse assigns meanings to basic expressions of language
• Assignment function (g) maps variables to elements in domain of discourse allows interpretation of expressions containing variables (someone)

Applying Model-Theoretic Semantics

Truth conditions in natural language

• Specify circumstances under which a sentence is true or false
• To determine truth conditions using model-theoretic semantics:

1. Identify relevant components of model (domain interpretation function assignment function)
2. Break down sentence into constituent parts (subject predicate quantifiers)
3. Apply interpretation function to non-logical constants
4. Evaluate truth value based on model and semantic rules

• "Every student passed the exam." interpreted as $\forall x (Student(x) \rightarrow PassedExam(x))$ true if and only if for every individual $x$ in domain if $x$ is a student then $x$ passed exam

Strengths vs limitations of model-theoretic semantics

• Strengths:
  • Precise and formal framework for representing meaning
  • Enables formulation of clear semantic rules and principles
  • Facilitates study of logical relations between sentences (entailment contradiction)
• Limitations:
  • Focuses primarily on truth-conditional aspects of meaning may not fully capture non-truth-conditional aspects (presuppositions implicatures)
  • Assumes fixed domain of discourse and interpretation may not account for context-dependent meanings or dynamic aspects of language use
  • Relies on idealized models of world may not capture full complexity and richness of natural language meaning
• Despite limitations remains powerful tool for formal semantic analysis provides solid foundation for understanding core aspects of linguistic meaning can be extended and refined to address more complex phenomena