This paper discusses how to define logics as deductive
limits of sequences of other logics. The case of da Costa's hierarchy of
increasingly weaker paraconsistent calculi, known as
1 n , is carefully studied.
, in particular, constitutes no more
than a lower deductive bound to this hierarchy and differs considerably
from its companions. A long standing problem in the literature (open
for more than 35 years) is to define the deductive limit to this
hierarchy, that is, its greatest lower deductive bound. The calculus
min, stronger than
, is first
presented as a step toward this limit. As an alternative to the
bivaluation semantics of
min presented thereupon,
possible-translations semantics are then introduced and suggested as
the standard technique both to give this calculus a more reasonable
semantics and to derive some interesting properties about it.
Possible-translations semantics are then used to provide both a
semantics and a decision procedure for
Lim, the real deductive limit of da Costa's
hierarchy. Possible-translations semantics also make it possible to
characterize a precise sense of duality: as an example,
min is proposed as the dual to
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