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
A comparative study between the theories of default reasoning and open logic is given.Some concepts of open logic,such as new premises,rejections by facts,reconstructions,epistemic processes, and its limit are introdu...A comparative study between the theories of default reasoning and open logic is given.Some concepts of open logic,such as new premises,rejections by facts,reconstructions,epistemic processes, and its limit are introduced to describe the evolution of hypotheses.An improved version of the limit the- orem is given and proved.A model-theoretic interpretation of the closed normal defaults is given using the above concepts and the corresponding completeness is proved.Any extension of a closed normal default theory is proved to be the limit of a δ-partial increasing epistemic process of that theory,and vice versa.It Ls proved that there exist two distinct extensions of a closed normal default theory iff there is an δ-non-monotonic epistemic process of that theory.The completeness of Reiter's proof is also given and proved,in terms of the epistemic processes.Finally,the work is compared with G(?)rdenfors's theory of knowledge in flux.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A comparative study between the theories of default reasoning and open logic is given.Some concepts of open logic,such as new premises,rejections by facts,reconstructions,epistemic processes, and its limit are introduced to describe the evolution of hypotheses.An improved version of the limit the- orem is given and proved.A model-theoretic interpretation of the closed normal defaults is given using the above concepts and the corresponding completeness is proved.Any extension of a closed normal default theory is proved to be the limit of a δ-partial increasing epistemic process of that theory,and vice versa.It Ls proved that there exist two distinct extensions of a closed normal default theory iff there is an δ-non-monotonic epistemic process of that theory.The completeness of Reiter's proof is also given and proved,in terms of the epistemic processes.Finally,the work is compared with G(?)rdenfors's theory of knowledge in flux.
