# 缺省邏輯

## 缺省邏輯的語法

${\displaystyle {\frac {Prerequisite:Justification_{1},...,Justification_{n}}{Conclusion}}}$

${\displaystyle W}$ 中邏輯公式和在缺省中的所有公被初始的假定為一階邏輯公式，但是它們潛在的可以是任意形式邏輯的公式。公式都是命題邏輯的情況是研究最多的。

### 例子

${\displaystyle D=\left\{{\frac {Bird(X):Flies(X)}{Flies(X)}}\right\}}$

W = { Bird（禿鷲）, Bird（企鵝）, ¬ Flies（企鵝）, Flies（鷹）}。

${\displaystyle {\frac {:{\neg }F}{{\neg }F}}}$

## 缺省邏輯的語義

${\displaystyle \left\langle \left\{{\frac {Republican(X):\neg Pacifist(X)}{\neg Pacifist(X)}},{\frac {Quaker(X):Pacifist(X)}{Pacifist(X)}}\right\},\left\{Republican(Nixon),Quaker(Nixon)\right\}\right\rangle }$

T=W           /* 当前理论*/
A=0           /* 迄今应用的缺省的集合*/

/* 应用一序列的缺省*/
while有个不在A中的缺省d对于T是可应用的
增加d的结论到T
增加d到A

/* 最终的一致性检查*/
if
for所有缺省d in A
T一致于d的所有论据
then
输出T


${\displaystyle \left\langle \left\{{\frac {:A(b)}{\neg A(b)}}\right\},\emptyset \right\rangle }$

• 積累缺省邏輯
• 委託假定缺省邏輯
• 准缺省邏輯

## 轉換

• 經典命題邏輯；
• 自動認識邏輯；
• 限定於被正規理論的命題缺省邏輯；
• 缺省邏輯的可作為替代的語義；
• 界限。

## 引用

• G. Antoniou (1999). A tutorial on default logics. ACM Computing Surveys, 31 (4):337-359.
• M. Cadoli, F. M. Donini, P. Liberatore, and M. Schaerf (2000). Space efficiency of propositional knowledge representation formalisms. Journal of Artificial Intelligence Research, 13:1-31.
• P. Cholewinski, V. Marek, and M. Truszczynski (1996). Default reasoning system DeReS. In Proceedings of the Fifth International Conference on the Principles of Knowledge Representation and Reasoning（KR'96）, pages 518-528.
• J. Delgrande and T. Schaub (2003). On the relation between Reiter's default logic and its (major) variants. In Seventh European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2003), pages 452-463.
• J. P. Delgrande, T. Schaub, and W. K. Jackson (1994). Alternative approaches to default logic. Artificial Intelligence, 70:167-237.
• G. Gottlob (1992). Complexity results for nonmonotonic logics. Journal of Logic and Computation, 2:397-425.
• G. Gottlob (1995). Translating default logic into standard autoepistemic logic. Journal of the ACM, 42:711-740.
• T. Imielinski (1987). Results on translating defaults to circumscription. Artificial Intelligence, 32:131-146.
• T. Janhunen (1998). On the intertranslatability of autoepistemic, default and priority logics, and parallel circumscription. In Proceedings of the Sixth European Workshop on Logics in Artificial Intelligence（JELIA'98）, pages 216-232.
• T. Janhunen (2003). Evaluating the effect of semi-normality on the expressiveness of defaults. Artificial Intelligence, 144:233-250.
• P. Liberatore and M. Schaerf (1998). The complexity of model checking for propositional default logics. In Proceedings of the Thirteenth European Conference on Artificial Intelligence（ECAI'98）, pages 18-22.
• W. Lukaszewicz (1988). Considerations on default logic: an alternative approach. Computational Intelligence, 4 (1):1-16.
• W. Marek and M. Truszczynski (1993). Nonmonotonic Logics: Context-Dependent Reasoning. Springer.
• A. Mikitiuk and M. Truszczynski (1995). Constrained and rational default logics. In Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence（IJCAI'95）, pages 1509-1517.
• R. Reiter (1980). A logic for default reasoning. Artificial Intelligence, 13:81-132.
• T. Schaub, S. Brüning, and P. Nicolas (1996). XRay: A prolog technology theorem prover for default reasoning: A system description. In Proceedings of the Thirteenth International Conference on Automated Deduction（CADE'96）, pages 293-297.

## 外部連結

• Ramsay, Allan (1999). Default Logic. Retrieved August 10th. 2004.