We develop an explanation of how this works in stages. Let's first restrict our attention to the following connectors: S, O, A, D. (Imagine the dictionary with all of the other connectors removed.) The S is used to connect a noun to its verb. The O connector is used to connect a verb to its object. The A connector is used to connect an adjective to its noun. The D is for connecting a determiner to its noun. Notice that this connector is omitted from proper nouns, is optional on plural nouns, and is mandatory on singular nouns. Also notice that the subscripts allow the to act as the determiner for both plural and singular nouns, but a can only work with the singular nouns. Similarly, the S connector is subscripted to ensure verb-noun agreement.
The ordering of the terms in these expressions is often important. For example, the fact that on nouns, the A- occurs to the left of the D- means that the adjective must be closer to the noun than the determiner.
Here are some judgements that can be rendered by what we have described so far:
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*a dog chase a cat
*
*black the dog died
*
*a/*the Mary chased the cat
*
*a dogs died
*
*dog died