A logic of topic inconsistency

A significant philosophical justification for the development of paraconsistent logics is the observation that there are theories (and, more generally, datasets) which are informative in their respective domains and yet allow for the derivation of contradictions, either on their own or when combined with other theories. A system of logic can represent deductive reasoning within such theories while avoiding triviality, i.e. it can be designed in such a way that the presence of a contradiction is not sufficient for deriving everything whatsoever. The underlying idea is that inconsistent theories typically contain consistent sub-theories which are legitimate for studying their own domains and should not be affected by contradictions involving propositions that are out of their scope. The framework employed here is a proposal to formally capture this intuition in a precise way, thanks to the possibility of comparing the scope of theories both in the syntax and in the semantics.