In the first decades of AI the logical point was dominating in many ways. O
n the other hand, it was clear that questions connected with common sense h
ave been difficult to grasp by logic and hence alternative techniques (like
soft computing) have been developed. In some sense, truth was no longer ac
hieved but approximated. Here we propose to work on rigorous, systematic an
d uniform mathematical foundations for the various approaches which have be
en or are currently being developed in this area.