Logical Functions

~ Monadic
APL: not
Q: use not
Note that not in Q can work on numeric values other than 0 and 1.
e.g. you can say:
q) not 42
0b

~ dyadic (not strictly a logical function)
APL: without
Q:

∨ dyadic
APL: or
Q: use or

^ dyadic
APL: and
Q: use and

⍱ dyadic
APL: nor
Q: use not or

⍲ dyadic
APL: nand
Q: use not and