  Based on ideas of quantum theory of open systems and psychological dual
system theory we propose two novel versions of Non-Boolean logic. The first
version can be interpreted in our opinion as simplified description of
primitive (mythological) thinking and the second one as the toy model of
everyday human reasoning in which aside from logical deduction, heuristic
elements and beliefs also play the considerable role. Several arguments in
favor of the interpretations proposed are adduced and discussed in the paper as
well.
