Each logic class implements as many operators that make sense for it as possible. They have standardized names, signatures and semantics, as follows:
__and__ (&): And
__or__ (|): Or
__invert__ (~), __neg__ (-): Not
__pos__ (+): Identity
implies: Implication
iff, xnor: Biconditional
nor: Neither
nand: Sheffer stroke
abjunction: Nonimplication
converse_implies: Converse implication
converse_abjunction: Converse nonimplication
strong_conjunction: Strong conjunction; not (a implies (not b))
strong_disjunction: Strong disjunction; (not a) implies b
diamond: Modal diamond; (not a) implies a
box: Modal box; not diamond(not a)
doubtful: a equivalent to (not a)
gullibility: a if a is equivalent to b, uncertain otherwise
consensus: a if a is equivalent to b; the other input if an input is uncertain, uncertain otherwise