冲突信念扩展算法：一种Clausal Beliefs的推理方法
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"An Algorithm for Extension of Clausal Beliefs - GUO Qian, DENG An-sheng - 2015 IEEE 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD'15)"
这篇研究论文"An Algorithm for Extension of Clausal Beliefs"探讨了在处理矛盾信念推理问题时的一种算法方法。作者是GUO Qian和DENG An-sheng，来自大连海事大学的信息科学与技术学院。论文发表于2015年的第12届国际模糊系统和知识发现会议（FSKD'15）上，出版商是IEEE，书号为978-1-4673-7681-5。
在知识表示和推理领域，子句信念（Clausal Beliefs）是一种常见的形式化方法，它用一阶逻辑中的子句来表达复杂的知识结构。当这些信念系统中出现冲突时，需要有一种方法来解决或调整这些矛盾。论文提出了一种新颖的假设扩展（Hypothesis Expansion）策略，该策略选择那些不包含相反信息的结论作为假设扩展的基础。这种方法基于非修订的信念处理方式，即在不彻底改变原有信念体系的前提下进行推理。
论文中定义了基于这种非修订方法的假设扩展，并指出这种扩展具有良好的数学性质，如一致性（Consistency）和接近性（Closeness）。这意味着即使在信念系统发生冲突时，仍能保持系统的内在逻辑连贯性。然而，由于扩展过程可能涉及大量子句信念，这可能会降低算法的工作效率。尽管如此，该算法通过减少信念的数量，增强了对应结论的正确性。
实验结果证明，在一定数量的信念集合下，提出的算法能够有效地处理信念扩展问题，并且提高了推理的准确性。这表明，对于处理复杂信念系统中的冲突，这种算法具有实际应用价值，特别是在需要处理模糊或不确定信息的领域，如人工智能、知识工程和决策支持系统中。
这篇论文提供了一种处理和扩展矛盾子句信念的新方法，对理解和改进模糊和不确定环境下的推理机制有重要的理论和实践意义。
978-1-4673-7681-5 ©2015 IEEE 638
2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD'15)
An Algorithm for Extension of Clausal Beliefs
GUO Qian
Information Science and Technology College. Dalian
Maritime University
Dalian Maritime University, DMU
Dalian, China
DENG An-sheng
Information Science and Technology College. Dalian
Maritime University
Dalian Maritime University, DMU
Dalian, China
Abstract—In order to reason for the conflicting beliefs, this paper
employs the conclusion that does not contain opposite
information as the hypothesis expansion. Furthermore, it
provides the definition of hypothesis extension based on the
method of belief non-revision. The hypothesis expansion has a
series of good mathematical properties, e.g., consistency and
closeness. This paper proposes the algorithm for extension of
clausal beliefs based on the definition and its good nature.
Although the number of clausal beliefs may decrease the working
speed of the algorithm, the correctness of the corresponding
conclusion is enhanced. The experimental results demonstrate
that, for a certain amount of beliefs, the efficiency of proposed
approach still can be guaranteed.
Keywords-hypothesist; non-revision belief; expansion
I. INTRODUCTION
Recently, many efforts have been paid to exploit a variety
of common sense reasoning technologies. However, the
process of reasoning appears the problems of monotonic,
inaccurate and incompatible
[1]
. We called the contradictive
common sense as belief
[2]
. The research for the processing
method of inconsistent beliefs is an important aspect in
artificial intelligence area.
There are many important research results about the field
of the common sense reasoning. McDermott and Doyle
proposed the theory of non-monotonic logic
[3]
and the related
theory based on modal logic
[4]
. Reiter proposed the theory of
default logic
[5]
. A few years later, the equivalence relation
between the default logic and the auto-epistemic logic
[6]
have
proved by Konolige. Until the mid of 1980s, Gardenfors,
Alchourron and Makinsond founded the famous theory of
belief revision
[7]
, it can also be named as AGM
[8]
.
However, under the condition that is lack of heuristic
information, the method of belief revision is more difficult to
reasoning, and it cloud lead to the system loss the important
information or bring unfavorable information. Therefore, we
put forward the theory of the non-revision belief
[9]
.
The set of hypothesis expansion means the set of
conclusion that does not contain opposite information. It does
not make any correct operation to inconsistent beliefs. This
paper provides the definition of hypothesis extension based on
the method of belief non-revision. It proves that each
hypothesis has the only expansion. This paper proposes the
algorithm for extension of clausal beliefs based on the
definition and its good nature. It can reduce the loss of
important information and improve the precision of reasoning
by using the method of non-revision belief. The experimental
results demonstrate the process of reasoning is correct.
II. T
HEORETICAL BASIS
A. The Definitions of the Propositional Logic
In this paper, the hypothesis is limited to the propositional
logic. The hypothesis expansion is defined with the general
resolution principle.
Definition 1 Proposition is a statement that affirms or
denies something and is either true or false.
Proposition can be divided into the atomic proposition and
the complex proposition.
The atomic proposition is consist of some simple
statements, as the following formula shows:
()
,,1
iii
PQR PQRi≥L，，
The logical connection symbols used in this paper are as the
follows:
(
)
,,, ,¬∧∨→↔
.
The complex proposition is consist of some atomic
propositions that connect with some logical connection symbol,
e.g.,
(
)
PQ R∨ →¬
.
Definition 2 Let
A
be a formula. Then
A
must meet one of
the following criteria
：
⑴
‘0’and ‘1’is formula.
⑵ Atomic proposition is formula.
⑶
If PQ， is formula, then
(
)
()()( )( )
,,P Q P Q P Q and P QP¬∧∨→ ↔，
are formulae.
⑷
String produced by the combination of ⑴, ⑵ and ⑶is
also formula.
Definition 3 Clause is the disjunctive form of
finite
characters in the propositional logic. Let
A
be clause, as
the following example 1 shows:
Project Supported by The National Natural Science Foundation of China （permission number：61272171, 61371090.）
The Fundamental Research Funds for the Central Universities of China（NO.3132015044）
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