*de dicto*modalities, provided modalities apply simultaneously, conclusion being always in the weakest modality present in premises:

[-C+B]+[-B+A]=[-C+A][-C+B]+[+A-B]=[-C+A][+B-C]+[-B+A]=[-C+A][+B-C]+[+A-B]=[-C+A][+A-B]+[+B-C]=[+A-C][+A-B]+[-C+B]=[+A-C][-B+A]+[+B-C]=[+A-C][-B+A]+[-C+B]=[+A-C] | [-C+B]+[-B-A]=[-C-A][-C+B]+[-A-B]=[-C-A][+B-C]+[-B-A]=[-C-A][+B-C]+[-A-B]=[-C-A][-A-B]+[+B-C]=[-A-C][-A-B]+[-C+B]=[-A-C][-B-A]+[+B-C]=[-A-C][-B-A]+[-C+B]=[-A-C] |

[+C+B]+[-B+A]=[+C+A][+C+B]+[+A-B]=[+C+A][+B+C]+[-B+A]=[+C+A][+B+C]+[+A-B]=[+C+A][+A-B]+[+B+C]=[+A+C][+A-B]+[+C+B]=[+A+C][-B+A]+[+B+C]=[+A+C][-B+A]+[+C+B]=[+A+C] | [+C+B]+[-B-A]=[+C-A][+C+B]+[-A-B]=[+C-A][+B+C]+[-B-A]=[+C-A][+B+C]+[-A-B]=[+C-A][-A-B]+[+B+C]=[-A+C][-A-B]+[+C+B]=[-A+C][-B-A]+[+B+C]=[-A+C][-B-A]+[+C+B]=[-A+C] |

Some examples of syllogisms in different modalities:

[[-C+B]+[-B+A]]=[[-C+A]][[-C+B]+[+A-B]]=[[-C+A]][[+B-C]+[-B+A]]=[[-C+A]][[+B-C]+[+A-B]]=[[-C+A]][[+A-B]+[+B-C]]=[[+A-C]][[+A-B]+[-C+B]]=[[+A-C]][[-B+A]+[+B-C]]=[[+A-C]][[-B+A]+[-C+B]]=[[+A-C]] | ([-C+B]+[-B-A])=([-C-A])([-C+B]+[-A-B])=([-C-A])([+B-C]+[-B-A])=([-C-A])([+B-C]+[-A-B])=([-C-A])([-A-B]+[+B-C])=([-A-C])([-A-B]+[-C+B])=([-A-C])([-B-A]+[+B-C])=([-A-C])([-B-A]+[-C+B])=([-A-C]) |

[+C+B]+[[-B+A]]=[+C+A][+C+B]+[[+A-B]]=[+C+A][+B+C]+[[-B+A]]=[+C+A][+B+C]+[[+A-B]]=[+C+A][[+A-B]]+[+B+C]=[+A+C][[+A-B]]+[+C+B]=[+A+C][[-B+A]]+[+B+C]=[+A+C][[-B+A]]+[+C+B]=[+A+C] | ([+C+B])+[[-B-A]]=([+C-A])([+C+B])+[[-A-B]]=([+C-A])([+B+C])+[[-B-A]]=([+C-A])([+B+C])+[[-A-B]]=([+C-A])[[-A-B]]+([+B+C])=([-A+C])[[-A-B]]+([+C+B])=([-A+C])[[-B-A]]+([+B+C])=([-A+C])[[-B-A]]+([+C+B])=([-A+C]) |

Problematic modalities are funny, because, as said, they don't have to be coherent. Thus diagram 6 is valid because both premises are taken to be possibly true simultaneously. Were they taken to be possibly true separately (diagram 9; I use different shades of red to stress separated possibilities), then the conclusion does not follow necessarily, even if it remains a possibility. I mean: if it is possible that all C is B, and it is possible that no B is A, then it does not necessarily follow, that it is possible, that no C is A, but as it is not definitly impossible, we may count it as a possibility. But then the structure of deduction has changed from "what does necessarily follow" to "what is not necessarily excluded". If one possibility is in the range of the other (i.e. given one possibility, the other would be possible also; so called accessibilty-relation), then the deduction is valid necessarily.