How do you learn to rewrite clauses with double negation or hypernegation? [closed]

Per p 24, A Student's Introduction to English Grammar (2005), by Huddleston & Pullum,

Polarity is the name of the system contrasting positive and negative clauses.

I ask this question in general, and NOT only for English. Negativity still incapicitate my reading comprehension, but one recourse is to rewrite negative clauses into positive clauses. For example, these equivalences helped me to parse the negative clauses:
cannot ... anything = can ... nothing, and not without = only with or only by.

I wish to learn more and be exposed to more such rewrites. So what's this kind of syntactical rewrite or substitution called? Are there any practice books or guides?

Are there any lists or catalogues of such equivalences, for my reference?

• You want to learn how to shift the negation around inside a clause? Negatives have different placement rules depending on whether they're adverbs, adjectives, or nouns. Likewise negative polarity items. – jlawler Jun 17 '15 at 20:13
• @jlawler No; I wish to learn how to minimise and eliminate negations in a clause. I find positives easier to understand than negations. – AYX.CLDR Jun 17 '15 at 20:36
• You can't. If it's there, it's there; it can only appear in a different place. All the examples you gave and their transformed sentences are equally negative. – jlawler Jun 17 '15 at 21:05
• No, it can't be answered in the abstract, because it can't be answered in the concrete. There are no examples of transforms of negative sentences that have no negation in them, yet mean the same thing as the negative. Negation is a logical prime, and we can't do without it. – jlawler Jun 17 '15 at 23:27
• I'm voting to close this question as off-topic because it's about writing style advice. Maybe try Writing. – curiousdannii Jun 18 '15 at 0:38

I don't understand this idea of yours about rewriting negative clauses into positive ones. When a "not" attaches to an indefinite, as when "not"+"any" changes to "no", it doesn't change the clause to positive. It just changes where the negative word turns up.

Positive clause: "Tom gives some candy to some friends."
Negative clause: "Tom doesn't give any candy to any friends."

We know that the whole clause is in the scope of negation, because all the "some"s change to "any"s. Now, when the "not" attaches to the first "any", if the clause became positive, other "any"s would revert to "some"s. But that doesn't happen:

Negative clause: "Tom gives no candy to any friends."

So the clause remains negative.

As with all the areas of English syntax that were well studied in transformational grammar (like this one), you can find an excellent summary of English negation in McCawley's The Syntactic Phenomena of English.

• Thanks. I edited my OP; I meant double negation or hypernegation. Better now? – AYX.CLDR Jun 17 '15 at 20:37
• In general, double or hypernegation isn't avoidable by algorithm; there are too many different ways to combine things, and people are not always clear on what they mean. – jlawler Jun 17 '15 at 23:28