如何比较两个逻辑表达式的相等性？

Question

I have two logical expression (just examples):

!(n >= x || n < -y)

and

n < x && n >= -y

Are there any tools out there to compare expressions like these to see if they are logically equal for all values? Or just to help me find the most compact/simple form?

Answer 1

The "most compact/simple form" answer would depend on your notion of compactness/simplicity. For instance, you can perform a number of simplification steps such as conversion to the conjunctive normal form (elimination of ||) followed by negation elimination (replacing !(n > y) by (n <= y)).

Equivalence of formulas F and G can be checked by taking the conjunction of F and the negation of G and checking for satisfiability of F && !G with, eg, a constraints solver. You should be careful with your domain though since the result depends on your domain (integers, rationals, reals): 2 < n && n < 3 is not satisfiable for the integers, but it is satisfiable for the reals!