We may speak about syntax. From this point of view
any logic can be considered as as the set of axioms and rules. Here we
are interested in formal proofs and deduction systems. Second, we can
also think about semantics, namely, about some models in which it is
possible to de ne the notions of truth and falsity.
As for the logical calculi, we are working with propositional logics.
Thus, we are not so much interested in quanti ers. Our logics are
non-classical. Of course, there are many kinds of non-classical logic
and many reasons for which certain system can be considered as nonclassical.
In our case, there are two main ways which are notoriously
combined. On the one hand, we are interested in intuitionistic, superintuitionistic
and subintuitionistic systems. This means that we narrow
down the set of axioms and rules of classical logic. On the other hand,
we use modal operators to de ne and analyse the ideas of necessity
and possibility. As a result, we often obtain classical and intuitionistic
Our semantic models are mostly neighborhood, topological and relational.
These three approaches are also combined. For this reason, we
may speak about bi-relational and relational-neighborhood structures.
Moreover, we go beyond the standard notion of topology in order to
study its various generalizations.
Finally, our aim is to investigate several non-classical calculi using
all the tools mentioned above. We are interested in the issues of completeness
(axiomatization), nite model property, bisimulation and decidability.
Moreover, we analyse some purely topological properties of
the structures in question. The philosophical aspect is also important.