On the decidability of open logic

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.