---
layout: linguistics
title: linguistics/semantics
---

# notes on semantics

Semantics is the study of **meaning**.

How do we know what sentences are true and which are false?<br>
What does it *mean* for a sentence to be true?<br>
What conditions must hold for a sentence to be true?

Formal semantics attempts to answer those questions by providing a *framework* for determining what *conditions* must hold for a sentence to be true.

This framework is [first-order/predicate logic](../mathematics/logic) and the [simply-typed lambda calculus](../plt/lambda-calculus). On top of this, we often build set theory, relying on *characteristic functions* of the lambda calculus as denotations of *set membership*.


## Basic Principles

### Compositionality


### Predicate Logic & The Lambda Calculus

Formal semantics begets a formal system for such semantics, and *first-order logic* and *the lambda calculus* are a natural fit. Semantics is the study of meaning - and what is logic but a system for expressing meaning? As discussed above, language functions by composition - and what are functions but their property of composition?

[*An Invitation to Formal Semantics*](https://eecoppock.info/bootcamp/semantics-boot-camp.pdf) covers basic logic and the lambda calculus well in its first six chapters. Otherwise, for a worse introduction, see [logic](../mathematics/logic), and [the lambda calculus](../plt/lambda-calculus).

## Denotational Semantics

With basic logic and the lambda calculus under our belt, we may simply get straight to assigning *meaning* to language. We consider two *basic types* to start: the type of entities, $e$, and the type of truth values, $t$. Our function types we denote by ordered pairs: that is, a function from $e$ to $t$ is of type $⟨e,t⟩$. This is perhaps clunkier notation than the type-theoretic $e→t$, but it is what it is. (And does avoid issues of precedence.)

### Entities and Functions

> I am Alice.
> Alice is bad.
> The blue pigeon flew away.

### Quantification

### Reference

### Numbers and Plurality

### Event Semantics

### Tense and Aspect

## Beyond Truth

### Necessity and Possibility

### Command, Request, Obligation

> Alice, run!<br>
> Alice, please run.<br>
> Alice should run.

### Questions
## Resources
- ✨ [Invitation to Formal Semantics](https://eecoppock.info/bootcamp/semantics-boot-camp.pdf)