Open logic （OL） is a noticeable logic theory dealing with the description of knowledge growth and updating, as well as the evolution of hypothesis. Up to now, however, many problems related to the proof theoretical ...Open logic （OL） is a noticeable logic theory dealing with the description of knowledge growth and updating, as well as the evolution of hypothesis. Up to now, however, many problems related to the proof theoretical approach of OL remain to be explored. In this paper, the typical proof theoretical problems for OL are described and the concept of open proof is defined. Two major conclusions are as follows： （i） For the consistent OL systems, the open proof problem is semi-decidable （a decision algorithm is presented）. （ii） For general （normal, not necessarily consistent） OL systems, the open proof problem is not semi-decidable.展开更多
Recently, Li established an open logic system to describe growth and updating of knowledge and evolution of hypothesis. Afterwards, he used it to give a logical framework for knowledge base maintenance. In a knowledge...Recently, Li established an open logic system to describe growth and updating of knowledge and evolution of hypothesis. Afterwards, he used it to give a logical framework for knowledge base maintenance. In a knowledge base, there are some special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
The open logic is defined by model theory which can be viewed as a process-based nonmonotonic logic. Some new notions and results of open logic are introduced. The relation of open logic to circumscription is studied,...The open logic is defined by model theory which can be viewed as a process-based nonmonotonic logic. Some new notions and results of open logic are introduced. The relation of open logic to circumscription is studied, and the relationship between open logic and other nonmonotonic logics is pointed out as well.展开更多
文摘Open logic （OL） is a noticeable logic theory dealing with the description of knowledge growth and updating, as well as the evolution of hypothesis. Up to now, however, many problems related to the proof theoretical approach of OL remain to be explored. In this paper, the typical proof theoretical problems for OL are described and the concept of open proof is defined. Two major conclusions are as follows： （i） For the consistent OL systems, the open proof problem is semi-decidable （a decision algorithm is presented）. （ii） For general （normal, not necessarily consistent） OL systems, the open proof problem is not semi-decidable.
文摘Recently, Li established an open logic system to describe growth and updating of knowledge and evolution of hypothesis. Afterwards, he used it to give a logical framework for knowledge base maintenance. In a knowledge base, there are some special
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.
基金Project partially supported by the National Natural Science Foundation of China (Grant No. 69673045)National High-Tech Project and National Climbing Program of Fundamental Research
文摘The open logic is defined by model theory which can be viewed as a process-based nonmonotonic logic. Some new notions and results of open logic are introduced. The relation of open logic to circumscription is studied, and the relationship between open logic and other nonmonotonic logics is pointed out as well.
