Information Technology Reference
In-Depth Information
2.3
Nonmonotonic Logic
Driven by the development of the intelligence science, various non-classical
logics were preposed and studied since the eighties of the last century.
Nonmonotonic is one of these logics (McDermott,1980).
The human understanding of the world is a dialectical developing process
which obeys the negation-of-negation law. During the cognitive process, man's
understanding of the objective world is always uncertain and incomplete; it will
be negatived or completed as while as some new knowledge is acquired. As
pointed by Karl Popper, the process of scientific discovery is a process of
falsification. Under certain condition and environment, every theory always has
its historical limitations. Along with the increase of human understands of the
world and along with the development of scientific research, old theories will not
meet the new needs and will be overthrew by the new discovery; upon that, old
theories are negated and new theories are born. In this sense, the growth of
human knowledge is in fact a nonmonotonic development process.
Classical logics such as the formal logic and the deductive logic are all
monotonic in their dealing with the human cognitive process. With these logics,
new knowledge acquired according to rigorous logic inference must be consistent
with the old knowledge. In another word, if there is a knowledge base A and it is
known that A implies the knowledge B, i.e. A
B, then the knowledge B can be
inferenced by these logics. However, as stated above, human cognitive process is
in fact nonmonotonic and is not consistent with such a process at all.
Nonmonotonic reasoning is characterized by the fact that the theorem set of
an inference system is not monotonic increased along with the progress of
inference. Formally, let F be the set of knowledge holded by humans at some
stage of the cognitive process, and let F(t) be the corresponding function on time
t. Then the set F(t) is not monotonic increased along with the progress of time. In
another word, F(t
1
)⊆ F(t
2
) is not always holds for any t
1
<t
2
. At the same time,
human understanding of the world is in fact enhanced. A basic reason for such a
phenomenon is the incomplete knowledge base used in the reasoning process.
Nonmonotonic logic is a family of tools for the processing of incomplete
knowledge.
Inference rules used in monotonic logics are monotonic. Let Γ be the set of
inference rules of a monotonic logic, then the language Th(Γ) = {A | Γ→ A}
determined by these rules holds the following monotonicity:
(1) Γ ∈ Th(Γ)
