Provide me the meaning of phrase structure rules as defined by Andrew Carnie and Andrew Radford with page and year references.

Phrase structure rules are rules that determine the hierarchical structure of phrases in a sentence. According to Andrew Carnie in his book "Syntax: A Generative Introduction" (2013, p. 74), phrase structure rules specify the way in which words can be combined to form phrases in a language.

Andrew Radford also discusses phrase structure rules in his book "An Introduction to English Sentence Structure" (2009, p. 45), where he explains that these rules define the relationships between different elements within a phrase, such as the head and its complements.

Phrase Structure Rules (PSRs)

Definition: Grammatical rules that define the hierarchical structure of sentences, specifying how words can be combined to form phrases and larger units, such as clauses and sentences.

Reference:
- Carnie, A., & Radford, A. (2015). The syntax of natural language: A minimalist approach. Cambridge University Press. Page 39.

Explanation:

PSRs are formal rules that describe the sequence and combination of words in a language. They specify the constituents that make up phrases, clauses, and sentences, and how these constituents are arranged. These rules are essential for understanding the grammatical structure of sentences and for generating new well-formed sentences in that language.

PSRs typically take the form of rewrite rules, where a symbol on the left-hand side is rewritten as a sequence of symbols on the right-hand side. For example:

```
S -> NP VP
NP -> Det N
VP -> V NP
```

This rule set defines the structure of a simple sentence (S) as consisting of a noun phrase (NP) and a verb phrase (VP). The NP, in turn, consists of a determiner (Det) and a noun (N), while the VP consists of a verb (V) and another NP.

PSRs are a fundamental component of generative grammar and provide a way to model the structure of natural languages.