Apparently someone had the following thought. "Everyone when faced with the dilemma of having either an unsound or incomplete formal system chooses incompleten

Apparently someone had the following thought. "Everyone when faced with the dilemma of having either an unsound or incomplete formal system chooses incompleteness. What happens when we allow for unsoundness and treat this notion as first class?" There has been a slow burn on paraconsistent logics going back to the 80s or so now. https://en.wikipedia.org/wiki/Paraconsistent_logic https://en.wikipedia.org/wiki/Paraconsistent_logic I seem to recall at least one where one of the states was something analogous to a maybe/don't know.