Abstract
On the ground of Kant’s reformulation of the principle of con-
tradiction, a non-classical logic KC and its extension KC+ are constructed.
In KC and KC+, \neg(\phi \wedge \neg\phi), \phi \rightarrow (\neg\phi \rightarrow \phi), and \phi \vee \neg\phi are not valid due
to specific changes in the meaning of connectives and quantifiers, although
there is the explosion of derivable consequences from {\phi, ¬\phi} (the deduc-
tion theorem lacking). KC and KC+ are interpreted as fragments of an
S5-based first-order modal logic M. The quantification in M is combined
with a “subject abstraction” device, which excepts predicate letters from the
scope of modal operators. Derivability is defined by an appropriate labelled
tableau system rules. Informally, KC is mainly ontologically motivated (in
contrast, for example, to Jaśkowski’s discussive logic), relativizing state of
affairs with respect to conditions such as time.