Case-Based Reasoning (CBR) is the process of solving new problems based on the solution of similar past problems. In the present paper we introduce an absorbing Markov chain on the main steps of the CBR process. In this way we succeed in obtaining the probabilities for the above process to be in a certain step at a certain phase of the solution of the corresponding problem, and a measure for the efficiency of a CBR system. Examples are also given to illustrate our results. Introduction Case-Based Reasoning (CBR) is a recent theory for problem-solving and learning in computers and people.

Broadly construed Case-Based Reasoning (CBR) is the process of solving new problems based on the solution of past problems. The CBR systems' expertise is embodied in a collection (library) of past cases rather, than being encoded in classical rules. Each case typically contains a description of the problem plus a solution and/or the outcomes. When a problem is successfully solved, the experience is retained in order to solve similar problems in future. When an attempt to solve a problem fails, the reason for the failure is identified and remembered in order to avoid the same mistake in future. Thus CBR is a cyclic and integrated process of solving a problem, learning from this experience, solving a new problem, etc.