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and4L

And4L is a term used in logic and computer science to denote the conjunction operator in four-valued logics. It extends classical logical conjunction to tolerate incomplete and inconsistent information by introducing four truth values: true, false, both true and false (inconsistent), and neither true nor false (undetermined). The four-valued approach supports reasoning in environments where data from multiple sources may conflict or be incomplete, such as data integration, knowledge bases, and robust rule systems.

Origin and semantics: The general idea builds on Belnap’s four-valued logic from the early 1980s and related

Applications and properties: and4L is designed to preserve monotonicity with respect to information, and is typically

See also: Belnap logic, four-valued logic, paraconsistent logic, bilattice.

paraconsistent
frameworks.
The
label
and4L
indicates
an
adaptation
of
the
standard
AND
operator
to
a
four-valued
setting.
The
exact
semantics
of
and4L
depend
on
the
chosen
bilattice
or
truth-table
scheme;
common
designs
interpret
conjunction
as
the
meet
with
respect
to
an
information
order,
yielding
results
that
reflect
both
sources
and
certainty
levels.
Some
variants
use
distinct
truth
and
information
orders,
producing
tables
where
true
and
true
yields
true,
true
and
false
yields
false,
and
the
results
for
other
combinations
encode
various
levels
of
inconsistency
or
lack
of
knowledge.
idempotent
and
commutative.
It
is
used
in
knowledge
representation,
databases
with
conflicting
entries,
and
logic
programming
to
enable
reasoning
in
the
presence
of
conflicting
or
incomplete
data.