Major themes of the course
Table of Contents
1. Themes
In class, we talked about some major themes, and how they will become manifest in the different parts of the course, in the way we approach the topics we study. These themes were the following:
- Compositionality
- A principle of interpretation often attributed to Gottlob Frege. ``The meaning of an expression should be a function of the meanings of its parts and the way in which they are combined.''
- Richard Montague (at least implicitly) viewed compositionality as arising from a property of the semantic interpretation function, viz., that it is a homomorphism from an algebra of syntactic expressions to an algebra of semantic formulae (or model-theoretic objects). (See, e.g., Montague, Richard (1970).)
- Modularity
- In a way, this is like compositionality, but at the level of entire models or theories of the semantic phenomena we study. We should be able to state accounts of different phenomena separately from each other, and to have a systematic recipe for combining the accounts in a way that preserves certain important aspects of their structure. (In practice, we we will sometimes do this by looking the at homomorphisms between monads which arise when using monad transformers (Liang, Shen and Hudak, Paul and Jones, Mark, 1995).
- Abstraction
- We should be able to zero in on the properties of meanings (and also, the properties of theories of meaning) that we care about, and not worry about the sometimes irrelevant details of how they are implemented. IMO, finding the right level of abstraction at which to study some linguistic phenomenon makes it easier to connect different theories together, since it can facilitate finding a common interface. This idea will show up repeatedly in this course.
2. Organization of the course
I tried to organize the course into three parts (indicated below). The themes above show up in each part in the following… guises?
| Compositionality/Modularity | Abstraction | Topics | |
|---|---|---|---|
| Part 1: truth-conditional semantics | Frege's principle (e.g., functional application) | λ-calculus | verbs, arguments, etc. |
| Part 2: dynamic semantics | Modularity and composition of entire theories (as well as the above) | λ-calculus and functors | indefiniteness, anaphora resolution, quantification, etc. |
| Part 3: Bayesian modeling | All of the above | λ-calculus and functors | The semantic theory module, the response behavior module |
3. References
Liang, Shen and Hudak, Paul and Jones, Mark (1995). Monad transformers and modular interpreters.
Montague, Richard (1970). Universal grammar, Theoria.