adequate

a. proportionate (to the requirements); sufficient, satisfactory; barely sufficient; hence adequacy..

Linguists evaluate their theories by criteria of adequacy. A theory can be adequate at different levels: for instance, it might describe all possible sentences that a language includes (and no other sentences) but not give any insight into how a brain produces these sentences. If you want to produce a description of the sentences of a language, this must be an adequate theory: if you intended to throw light onto human linguistic processes, then the theory is inadequate.

Linguists constrain their theories by requiring them to be "barely sufficient". At a grand level, it is alleged that a roomful of chimpanzees typing into word processors would eventually produce the complete works of Shakespeare, simply by the coincidence of their having hit the right keys in the right order, but without understanding what they are typing. (Cynics (who are perhaps realists) may claim that the fictitious Buddhist monks working on the large-scale Tower of Hanoi problem are more likely to finish their task before the chimps finish theirs.) An account of play-writing that stated that Shakespeare managed to complete his canon by the good luck of randomly writing words in some order that other people thought good is clearly a rotten theory: it explains nothing. What we want is a theory that is sufficiently constrained as to fit into what we know about the resources available. Shakespeare had only one lifetime of fifty-two years available to him. A theory to describe Shakespeare's ability would have to be constrained at least by time.

The idea of constraints or resources can be turned around. We know little about what the human brain does. We can make intelligent guesses at its capabilities by what it produces. Suppose we have three grammars that have differing mathematical power and different amounts of [computer] processing requirements:

1. Strongest: accounts for all of syntax - maximum resource requirements.
2. Median: accounts for all of syntax - middling resource requirements.
3. Weakest: doesn't account for all of syntax - minimal resource requirements.

Mathematical adequacy is concerned with whether the formal objects characterized by the notation, under the intended semantics, have the properties manifested in the real-world objects that the notation and its interpretation is intended to model.

Notational adequacy is to do with how elegantly the notation describes the real-world objects that the notation and its interpretation is intended to model.

These definitions may seem daunting, but we'll look at how we use them to evaluate Finite State Automata as models of English syntax and then their meaning will become clear.

• the cat
• the large cat
• the very large cat
• the very very large cat
• the very very very large cat
• etc.

Instead of labelling the arcs with pre-terminals, such as det, adj and noun, we'll use strings of letters to illustrate our examples. We could draw a FSTN that could recognise and generate the following strings:

• cde
• ccde
• cdee
• ccdee
• cccccccdeee
• cdeeeeeeeeeeee

This is a very unrestricted language: we can have any number of c and any number of e. However, suppose that we want to model a recogniser that will accept any of the following:

• cde
• ccdee
• cccdeeee
• etc

• ccde
• cdee
• cccdee
• cccccccdeee
• cdeeeeeeeeeeee

It may seem that strings of arbitrary letters have nothing to do with English. However, we can soon demonstrate that English includes sentences which are similar in structure. Consider a sentence such as:

The girl whose mother told me that she'd been painted by Van Gogh at the party shouted.

• The girl
  • whose mother told me
    • that she'd been painted by Van Gogh
  • at the party
• shouted.

We could go on extending this sentence infinitely by simply embedding more and more phrases in the centre of this sentence. (This type of structure is known as centre-embedded.) From this we can conclude that it is impossible to model the entirety of English syntax with a FSTN, or indeed any Finite State Automata.

To put it more briefly: Finite State Automata are mathematically inadequate as a model of English because they can't model centre-embedding.

It is easy to see that this network contains repetitions. For instance, the sequence det noun appears three times and the sequence prep det noun appears twice. If we were writing programs (that is writing a description of how to solve a computing problem), then we would procedurize. It is a mark of a poor program that code is repeated instead of being gathered into procedures. Procedurazation in programs is a mark of an elegant program: a program that is devoid of repetitions and avoids long-windedness.

The same kind of subjective criterion can be brought to bear on grammars. This FSTN is inelegant because it is repetitious and long than necessary. If we have an insight into the structure of words that proceed nouns (for instance, that it's also possible to have det adj noun sequences such as the tabby cat), this insight would have to be added to the network wherever there is a noun. If we had been able to procedurize our knowledge, we would only have to make that change once.