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But in fact, respect to some predicate, consistency of the augmented theory
can not be guaranteed still. For example, let KB={P(A)∨Q, P(B)∨¬Q}, and let P
be the particular predicate; then we have KBasm ={¬P(A), ¬P(B)}. Since
KB|=P(A)∨P(B), the augmented theory CWA'(KB) with respect to the predicate
P is inconsistent.
2.5 Default Logic
Default reasoning is a family of plausible reasoning. The intuition of various
forms of default reasoning is to derive conclusions based upon patterns of
inference of the following form:
In the ordinary situation A holds,
In the typical situation A holds,
Then it is a default assumption that A holds.
A typical example of default reasoning is about the statement “birds fly”. As
we know, the statement “birds fly” is different from the statement “All birds will
fly”, since there are many exceptions suth as the penguins, ostriches and Maltese
falson. Given a particular bird we will conclude that it flies according to the
following plausible proposition:
In the ordinary situation birds can fly, or
In the typical situation birds can fly, or
If x is a bird, then it is a default assumption that x can flies.
However, if we know that this bird is an ostrich according to the subsequent
discovery, we will revise our conclusion with a new result that this bird can not
fly. Therefore, it is obvious that what reflected in this example is a process of
plausible reasoning instead of deductive reasoning.
Based on the study of reasoning about incompletely specified worlds, a logic
system named default logic was proposed by Reiter in 1980 (Reiter, 1980).
“By default” is an ordinary technology used in computer program designing.
For example, let P be a program, let Q be a procedure specified in P, and let x be
a variable that occurs in both P and Q. Then, the type of x which occurring in P
will by default be the type of x which occurring in Q, unless the type of x is
redeclared in Q. In another word, with the “by default” technology, operations of
the system will be carried out according to predetermined rules, unless other
requirements are explicitly specified by the programmer.
The idea of “by default” is introduced into logic by Reiter and forms the
so-called default logic. In classical logics, new facts about a world are deduced
