Combined Paraconsistent Logics and their (Co)Exponentials

Combined logics of sentences and events consist of two parts: the external logic depending on epistemological assumptions and the internal logic depending on ontological ones. They were introduced by V.A. Smirnov following some G. Frege's and N. Vasiliev's ideas. An analysis of the structure of combined logics shows that, in fact, they employs the links between two logical systems postulating in the role of ontological part algebras which serve as the models of respective logics. It prompts us to consider systems which describe the direct interplay of two logics on syntactic level where we have an access to these logics without mediation of their models. In the role of those systems might be used the so-called coexponential and exponential ones which were introduced in [15]. In the paper the case of two paraconsistent combined logics (having paraconsistent algebras as their ontological part) is considered.

combined lopgics, Jaskowski's discursive logic, da Costa paraconsistent logics, translation, (un)constrained possible translating