Pawlak had proposed the notion of rough truth in 1987 [16]. The
article takes a fresh look at this "soft" truth, and presents a formal system
L
_R
, that is shown to be sound and complete with respect to
a semantics determined by this notion. L
_R
is based on the
modal logic S5. Notable is the rough consequence relation defining
L
_R
(a first version introduced in [9]), and rough
consistency (also introduced in [9]), used to prove the completeness result.
The former is defined in order to be able to derive roughly true propositions
from roughly true premisses in an information system. The motivation for the
latter stems from the observation that a proposition and its negation may well
be roughly true together. A characterization of
L
_R
-consequence shows that the paraconsistent discussive
logic J of Jaśkowski is equivalent to L
_R
. So,
L
_R
, developed from a totally independent angle, viz. that
of rough set theory, gives an alternative formulation to this well-studied
logic. It is further observed that pre-rough logic [3] and 3-valued
Łukasiewicz logic are embeddable into L
_R
.
