The aim of this paper is to extend the system of belief revision developed by Alchourron, Gardenfors and Makinson (AGM) to a more general framework.This extension enables a treatment of revision not only by single sen...The aim of this paper is to extend the system of belief revision developed by Alchourron, Gardenfors and Makinson (AGM) to a more general framework.This extension enables a treatment of revision not only by single sentences but also by any sets of sentences, especially by infinite sets. The extended revision and contraction operators will be called general ones, respectively. A group of postulates for each operator is provided in such a way that it coincides with AGM's in the limit case. A notion of the nice-ordering partition is introduced to characterize the general contraction operation. A comp ut ation- orient ed ap-proach is provided for belief revision operations.展开更多
As an important variant of Relier's default logic, Poole (1988) developed a nonmonotonic reasoning framework in the classical first-order language. Brewka and Nebel extended Poole's approach in order to enabl...As an important variant of Relier's default logic, Poole (1988) developed a nonmonotonic reasoning framework in the classical first-order language. Brewka and Nebel extended Poole's approach in order to enable a representation of priorities between defaults. In this paper a general framework for default reasoning is presented, which can be viewed as a generalization of the three approaches above. It is proved that the syntax-independent default reasoning in this framework is identical to the general belief revision operation introduced by Zhang et al. (1997). This result provides a solution to the problem whether there is a correspondence between belief revision and default logic for the infinite case. As a by-product, an answer to the question, raised by Mankinson and Gardenfors (1991), is also given about whether there is a counterpart contraction in nonmonotonic logic.展开更多
The problem of uniqueness of reconstruction in open logic is dealt with by introducing the concept of total ordered partitions, an ordering structure for modeling belief degrees of knowledge, and redefining the recons...The problem of uniqueness of reconstruction in open logic is dealt with by introducing the concept of total ordered partitions, an ordering structure for modeling belief degrees of knowledge, and redefining the reconstruction operation. Based on the resulting definition, a nontrivial condition for the convergency of cognitive processes is given. It is shown that if new knowledge is not always accepted with an extremely skeptical attitude and the changes of belief degrees follow the criterion of minimal changes, the cognitive process will converge. The results provide an approach to unifying two kinds of theories for knowledge base maintenance: belief revision and open logic.展开更多
文摘The aim of this paper is to extend the system of belief revision developed by Alchourron, Gardenfors and Makinson (AGM) to a more general framework.This extension enables a treatment of revision not only by single sentences but also by any sets of sentences, especially by infinite sets. The extended revision and contraction operators will be called general ones, respectively. A group of postulates for each operator is provided in such a way that it coincides with AGM's in the limit case. A notion of the nice-ordering partition is introduced to characterize the general contraction operation. A comp ut ation- orient ed ap-proach is provided for belief revision operations.
基金This work was supported by the National Natural Science Foundation of China (No.69785004) and the Science and Technology Fundin
文摘As an important variant of Relier's default logic, Poole (1988) developed a nonmonotonic reasoning framework in the classical first-order language. Brewka and Nebel extended Poole's approach in order to enable a representation of priorities between defaults. In this paper a general framework for default reasoning is presented, which can be viewed as a generalization of the three approaches above. It is proved that the syntax-independent default reasoning in this framework is identical to the general belief revision operation introduced by Zhang et al. (1997). This result provides a solution to the problem whether there is a correspondence between belief revision and default logic for the infinite case. As a by-product, an answer to the question, raised by Mankinson and Gardenfors (1991), is also given about whether there is a counterpart contraction in nonmonotonic logic.
文摘The problem of uniqueness of reconstruction in open logic is dealt with by introducing the concept of total ordered partitions, an ordering structure for modeling belief degrees of knowledge, and redefining the reconstruction operation. Based on the resulting definition, a nontrivial condition for the convergency of cognitive processes is given. It is shown that if new knowledge is not always accepted with an extremely skeptical attitude and the changes of belief degrees follow the criterion of minimal changes, the cognitive process will converge. The results provide an approach to unifying two kinds of theories for knowledge base maintenance: belief revision and open logic.
