For our course, we are going to work with the Words & Rules proposal. This is a theory—a proposal for causal relations that describe, explain or predict behavior.
Words are arbitrary pairing between forms (signed/spoken/written) and meanings. These pairings are largely arbitrary (although see the supplemental reading). They work because we all buy in to the conventions, which need to be memorized. We store these memorized words in our mental lexicon. There are several proposals for the how the mental lexicon is represented (e.g., graph, hierarchy, ordered list). Importantly, we do not have the same mental lexicons. Thankfully, our mental lexicons are mutually intelligible.
Words depend on each other to express complex meanings. These dependencies can be described by rules that govern how words combine. A grammar is simply a set of these rules. There is no “correct grammar”" or “one grammar to rule them all”. Grammars are descriptive representations for convenience. There are several ways we can write down a grammar and this is studied in formal language theory. In this course, we are only going to work with phrase-structure rules, which are often used for illustration.
Let’s consider three rules that will allow us to construct one sentence structure:
The first rule says that a Sentence (S) consists of a Noun Phrase (NP) and a Verb Phrase (VP). The second rule says that a VP consists of a Verb (V) and a NP. The third rule says that a NP consists of a determiner (det) and a Noun (N).
The symbols in the rules are abstract categories. A particular grammar is free to use any of these categories they wish; however, by convention we tend to use the same Part of Speech symbols over and over.
While these rules only allow us to generate one sentence structure, they do allow us to generate multiple sentences. For example, the twins built a rocket; the twins threw a party; and the twins circumnavigated the world. By using abstract symbols instead of individual words, the rules are productive.
For human languages, the rules are often recursive—i.e., a rule can be applied within itself. For example, let’s add the rule: VP –> V S
We can now construct infinitely long sentences. Here’s a finite example of recursion.
| Rule | ||||
|---|---|---|---|---|
| Start with S | S | — | — | — |
| S –> NP VP | NP | VP | — | — |
| VP –> V S | NP | V | S | — |
| S –> NP VP | NP | V | NP | VP |
We start off using the S –> NP VP rule. We then use it again inside the VP we created using the rule the first time. This structure would correspond to a sentence like: The Lorelai said the Rory loves the bookstore.
Notice this sentence sounds weird. We treat Lorelia and Rory as nouns but might be better off using a different Part of Speech, e.g., Proper Noun (PN). We could then add a rule like NP –> PN which would allow us to say the more natural sentence: Lorelai said Rory loves the bookstore.
You will get plenty of experience working with this formalism in the tutorial so I’ll keep it brief here.
Words & Rules embodies two important first principles for cognitive systems: productivity and reuse.
Productivity is the computation of a structure by the application of rules in a given framework.
Reuse is the storage and retrieval of past computations or the output of past computations.
Importantly, productivity and reuse generalizes beyond words and phrases/sentences. Consider math. Assuming you had excessive drilling of multiplication tables, do you think you have just stored the answer or productively compute the answer? I can tell you 25x25 off the top of my head but I need to think through 26x26. I’m probably just weird though.