The following expressions use positive lookaheads for saying “it must match” and negative lookaheads for saying “it must not match” (logical “NOT”). By using lookaheads with .* at the start, it means that it can be found anywhere on the line (or file) in any order. But it also doesn’t consume anything, so alone, these expressions are “zero width”.

If ☐ . matches newline is not checked (☐), or if (?-s) is enabled in your regex, then those expressions will mean “a single line matches the logic expression chosen”. if ☑ . matches newline is checked (☑) (or (?s) is enabled in your regex), then those expressions will mean “the whole file matches the logic expression chosen”.

All these expresions require Search Mode = ☑ Regular Expression to work.

In case it’s not obvious, aaa and bbb and nnn are meant as placeholders for the terms or regex sub-expressions that you’re actually trying to combine.

If you actually want to select the whole line, you cannot just use the zero-width forms above. Instead, you would use (?-s)(?:×××)^.*$ (where the ××× is the two-term or n-term expression): the (?-s) will force it to contain the match on a single-line (by making the . wildcard not match newlines), the (?:×××) will add the logic expression that you derived from the table, and the ^.*$ will cause it to actually match the whole line, rather than the zero-width sequence at the start of the line.

Similarly, if you want to Find in Files to figure out which files match the logic expression, you can use (?s)\A^(×××)., where (?s) will make . match newlines, so the .* in each of the logic terms can match anywhere in the file; then the \A will match only at the start of the file, the (×××) will do the logic on the whole file; and the . will mean that it actually marks/matches the first character in each of the files it finds (which will make it actually report something in the Find Results after running Find in Files).

Examples

With the (?-s)(?:×××)^.*$ given above, if you chose the “two-term expression” and had the literal aaa and bbb as your search terms, the following “truth table” will show a T on the conditions that would match:

text          | OR | AND | XOR | NOR | NOR | NAND
--------------|----+-----+-----+-----+-----+------
aaa other aaa | T  |     | T   |     |     | T
aaa other bbb | T  | T   |     |     |     |
aaa other ccc | T  |     | T   |     |     | T
bbb other aaa | T  | T   |     |     |     | 
bbb other bbb | T  |     | T   |     |     | T
bbb other ccc | T  |     | T   |     |     | T
ccc other aaa | T  |     | T   |     |     | T
ccc other bbb | T  |     | T   |     |     | T
ccc other ccc |    |     |     | T   | T   | T

In other words, the text aaa other aaa will be matched by the OR expression (?=.*aaa|.*bbb), or by the XOR expression (?=.*aaa)(?!.*bbb)|(?!.*aaa)(?=.*bbb), or by the NAND expression (?!(?=.*aaa)(?=.*bbb)). (Similar interpretation for the other rows in the truth table.)

For a more concrete example,

I baked a cake.
The Brits call some cookies "biscuits".
I ate a cookie.
The fridge contains one cake and one cookie.

With the expression (?-s)(?:(?=.*cake|.*cookie)(?!.*biscuit))^.*$, says “(cake OR cookie) AND NOT biscuit”, which was my first example of what you might want to implement. In this text, the first, third, and fourth lines would match, but the second line would not match (because it contains biscuit). This also give an example of how to combine multiple of the logic conditions together in one expression

And @Alan-Kilborn came up with the following example:
Say you want to match some particular combination of Bob and Ted on a line – here’s examples on how to do that:

References

Originally developed in developing generic regex sequences and subsequent discussion

For other generic expressions, see FAQ Desk: Generic Regular Expression (regex) Formulas