Compositional and Formal Semantics
Formal semantics gives a precise, truth-conditional account of meaning in which the meaning of a complex expression is built compositionally from the meanings of its parts.
Definition
Compositional and formal semantics is the study of linguistic meaning using formal logic and model theory, centred on the compositional, truth-conditional interpretation of expressions.
Scope
This area covers the formal, model-theoretic study of natural-language meaning. It includes the principle of compositionality, the use of logical and set-theoretic tools to assign denotations to expressions, Montague's program of treating natural language with the rigour of formal logic, the analysis of quantification and scope, and the semantics of tense, aspect, and modality. The guiding idea is that to know the meaning of a sentence is to know its truth conditions, and that these are computed systematically from the meanings and mode of combination of its constituents.
Sub-topics
Core questions
- How is the meaning of a complex expression determined by the meanings of its parts and their syntactic combination?
- How can the meanings of natural-language expressions be represented in a formal, model-theoretic system?
- How are quantifiers, scope, and binding to be analysed?
- How should context-dependent and intensional phenomena (tense, modality) be modelled?
Key concepts
- principle of compositionality
- truth conditions
- denotation and semantic type
- lambda calculus
- model and interpretation function
- intension and extension
- functional application
Key theories
- Truth-conditional, model-theoretic semantics
- The meaning of a declarative sentence is identified with its truth conditions, computed relative to a model that interprets the basic expressions, following the Fregean and Tarskian tradition.
- Montague grammar
- Natural language can be treated as a formal language: a syntax paired with a model-theoretic semantics via a homomorphism, using typed lambda calculus and intensional logic to interpret expressions compositionally.
- Type-driven compositional interpretation
- Expressions are assigned semantic types and combined by general rules such as functional application, so that interpretation is driven by the types of constituents, as systematized in the Heim and Kratzer framework.
History
Formal semantics descends from Frege's work on sense and reference and Tarski's definition of truth for formal languages. The decisive step was Montague's claim in the early 1970s that there is no fundamental difference between natural and formal languages, and that English could be given a model-theoretic semantics. Barbara Partee played a central role in transmitting Montague's program to linguistics, and the Heim and Kratzer textbook later made type-driven compositional semantics standard in generative grammar.
Debates
- Direct vs. indirect (representational) interpretation
- Whether natural language should be interpreted directly in a model, as in Montague's program, or via translation into a level of logical form / mental representation.
Key figures
- Richard Montague
- Barbara Partee
- Irene Heim
- Angelika Kratzer
- Gottlob Frege
- Alfred Tarski
Related topics
Seminal works
- montague1974
- heimkratzer1998
- partee1990
Frequently asked questions
- What does it mean to say semantics is truth-conditional?
- It means that to specify the meaning of a declarative sentence is to specify the conditions under which it would be true; knowing the meaning is knowing what the world would have to be like for the sentence to hold.