Infectious semantics and analytic calculi for even more inclusion logics

We show that non-determinism can be used to give simple and effective many-valued semantics, by the mere addition of a suitably infectious value, to a range of companions of a given many-valued logic that result from filtering its inferences by requiring that variables, as well as certain other prescribed subformulas, of the premises and conclusion of an inference respect an inclusion requirement. Further, we show how to obtain analytic calculi for the resulting logics in a systematic way.