Operator Grammar - Reduction

Reduction

The reduction constraint acts on high likelihood combinations of operators and arguments and makes more compact forms. Certain reductions allow words to be omitted completely from an utterance. For example, I expect John to come is reducible to I expect John, because to come is highly likely under expect. The sentence John wears boots and John wears hats can be reduced to John wears boots and hats because repetition of the first argument John under the operator and is highly likely. John reads things can be reduced to John reads, because the argument things has high likelihood of occurring under any operator.

Certain reductions reduce words to shorter forms, creating pronouns, suffixes and prefixes (morphology). John wears boots and John wears hats can be reduced to John wears boots and he wears hats, where the pronoun he is a reduced form of John. Suffixes and prefixes can be obtained by appending other freely occurring words, or variants of these. John is able to be liked can be reduced to John is likeable. John is thoughtful is reduced from John is full of thought, and John is anti-war from John is against war.

Modifiers are the result of several of these kinds of reductions, which give rise to adjectives, adverbs, prepositional phrases, subordinate clauses, etc.

1. John wears boots; the boots are of leather (two sentences joined by semicolon operator) →
2. John wears boots which are of leather (reduction of repeated noun to relative pronoun) →
3. John wears boots of leather (omission of high likelihood phrase which are) →
4. John wears leather boots (omission of high likelihood operator of, transposition of short modifier to left of noun)

Each language has a unique set of reductions. For example, some languages have morphology and some don’t; some transpose short modifiers and some do not. Each word in a language participates only in certain kinds of reductions. However, in each case, the reduced material can be reconstructed from knowledge of what is likely in the given operator/argument combination. The reductions in which each word participates are observable and therefore learnable, just as one learns a word’s dependency and likelihood properties.