The preferential semantics of a multi-modal nonmonotonic logic

2005 ◽  
pp. 326-331 ◽  
Author(s):  
Hua Shu
Keyword(s):  
Nonmonotonic Logic ◽  
Preferential Semantics

scholarly journals More on Modal Aspects of Default Logic1

1992 ◽  
Vol 17 (1-2) ◽  
pp. 99-116
Author(s):  
V. Wiktor Marek ◽  
Miroslaw Truszczynski
Keyword(s):  
Modal Logic ◽  
Default Logic ◽  
Nonmonotonic Logic ◽  
Default Reasoning ◽  
Default Theory ◽  
Autoepistemic Logic ◽  
The Relationship ◽  
Natural Classes ◽  
Weak Extension

Investigations of default logic have been so far mostly concerned with the notion of an extension of a default theory. It turns out, however, that default logic is much richer. Namely, there are other natural classes of objects that might be associated with default reasoning. We study two such classes of objects with emphasis on their relations with modal nonmonotonic formalisms. First, we introduce the concept of a weak extension and study its properties. It has long been suspected that there are close connections between default and autoepistemic logics. The notion of weak extension allows us to precisely describe the relationship between these two formalisms. In particular, we show that default logic with weak extensions is essentially equivalent to autoepistemic logic, that is, nonmonotonic logic KD45. In the paper we also study the notion of a set of formulas closed under a default theory. These objects are shown to correspond to stable theories and to modal logic S5. In particular, we show that skeptical reasoning with sets closed under default theories is closely related with provability in S5. As an application of our results we determine the complexity of reasoning with weak extensions and sets closed under default theories.

Query answering in nondeterministic, nonmonotonic logic databases

1998 ◽  
pp. 175-187 ◽  
Author(s):  
Fosca Giannotti ◽  
Giuseppe Manco ◽  
Mirco Nanni ◽  
Dino Pedreschi
Keyword(s):  
Nonmonotonic Logic ◽  
Query Answering

Research developments in multiple inheritance with exceptions

1994 ◽  
Vol 9 (1) ◽  
pp. 21-55
Author(s):  
Peter W. Eklund
Keyword(s):  
Proof Theory ◽  
Nonmonotonic Logic ◽  
Problem Structure ◽  
Multiple Inheritance ◽  
Model Based ◽  
Inheritance Hierarchy ◽  
The Individual ◽  
Inheritance Network ◽  
Intuitive Interpretation

AbstractThe inheritance problem can be simply stated: for any instantiation of an inheritance network, say a specific hierarchy Γ, find a conclusion set for Γ. In other words, find out what is logically entailed by Γ. This can be done in two ways: either by defining a deductive or proof theoretic definition to determine what paths are entailed by a network; or by translating the individual links in the network to a more general nonmonotonic logic and using its model and proof theory to generate entailments that correspond to what one would expect from “viewing” the inheritance hierarchy. Two approaches to a solution to the inheritance problem structure this paper. The first is widely known as the “path-based” or “proof theoretic”, and the second, the “Model-based” or “model theoretic”. The two approaches result in both a different interpretation of default links as well as a variation in the entailment strategy for a solution to teh inheritance problem. In either case, the entailments produced need some intuitive interpretation, which can be either credulous or skeptical. The semantics of both skeptical and credulous inheritance reasoners are examined.

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