Negative logic and low-level signal
If by negative logic you are referring to a 0 in a digital circuit, then it is kind of a tautology. A 0 indicates no-presence of voltage, while a 1 indicates the presence of a voltage.

You could easily flip this notation and everything would still work out. In an and gate you have the inputs A,B and the output C. AB = C works very nicely using a 1 as positive logic since then the truth table simply looks like 1-bit multiplication. However, if you came along and decided that a 0 meant TRUE and a 1 meant FALSE, you would just change the truth table around and everything would still work out.  The truth table would then look like 0 was the multiplicative identity element. For an or gate, the reverse would hold. Currently a 0 is the additive identity element, but if you flipped them then 1 would be the additive identity element.