Learning Formal Language Systems ( Sentenal Logic, Predicate Logic, Set Theory; etc)

I was wondering if anybody developed a method for learning and memorizing Formal Language Systems? Memorizing the syntax of the language, the rules/guidelines for transcribing an English sentence into its formal symbolisation, memorizing the semantics of the language; memorizing their derivation systems and their rules? If not, if anybody had advice on how to go about doing so? I have gone through a few logic textbooks in my day, but I hate always haveing to refer to them, particularly, for the transcription guidelines and the derivation rules.

Examples:

So let’s say I have a list of common connectives in English, how to paraphrase them, then how to symbolize them in a formal language:

English:
A and G
A but G
A however G
A although G
A nonetheless G
A nevertheless G
A moreover G

Paraphrase:
A and G

Symbolization:
A ^ B

Examples of Derivation Rules:

Derivation rule:
Disjuction-Out (vO) Rule: If an available line is the form of disjunction (A v B), and another line is the form of the negation of the first disjunt (-A), then you can write down the line of the second disjunct (B); likewise, if an available line is the form of a disjunct (A v B), and another line is the form of the negation of the second disjunct (-B), then you can write down the first disjunct (A).

Example of derivation system rule:
At any point in a derivation, a formula may be written down if it follows from previous available lines by an inference rule. The annotation cites the line numbers, and the inference rule, in that order.

Thank you, in advance, for your responses.

  • Justin