In this paper being a sequel to our [1] the logic with semi-negation is chosen as an example to elucidate some basic notions of the semantics for sentential calculi. E.g., there are shown some links between the Post number and the degree of complexity of a sentential logic, and it is proved that the degree of complexity of the sentential logic with semi-negation is 20. This is the first known example of a logic with such a degree of complexity. The (...) results of the final part of the paper cast a new light on the scope of the Kripke-style semantics in comparison to the matrix semantics. (shrink)