One syntactical alternative I could think of is:
A &&& B # defined-and
A ||| B # defined-or
A >>> B # safe arrow
This would be a systematic approach reminiscent of the role of undef in ternary logic -- triple sign, third kind of truth value involved.
I am not sure whether a whole lot of other similar symbols like ^^^ would make as much sense, though, which means we then had to explain why only those mentioned above were there.
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