Incremental Knowledge Acquisition is an alternative approach to the ”established” knowledge engineering paradigm for constructing rule bases from experts. The particular method studied in this research is the Ripple Down Rule framework. In this framework, knowledge is incrementally constructed in the context in which it arises rather than transferred through expert interviews. Ripple Down Rules have proved successful in a wide range of research and commercial applications. However, its theoretical foundation has not been adequately studied. My research aims to present an analysis of the incremental knowledge acquisition, and in particular of the Ripple Down Rule framework. Firstly, a learning model which characterizes the key features of the method is formalized. We present the process of building a correct knowledge base as a scenario involving a user, an expert, and a system. The user provides data for classification. The expert helps the system to build its knowledge base incrementally, using the output of the latter in response to the last datum provided by the user. In case the system's output is not satisfactory, the expert guides the system to improve its future performance while not affecting its ability to properly classify past data. The conditions under which the sequence of knowledge bases constructed by the system eventually converges to a knowledge base that faithfully represents the target classification function are then examined. The results are in accordance with the observed behaviour of real-life systems. Secondly, we examine the rate at which experts construct their knowledge bases working with data cases. Evaluation of knowledge acquisition is always difficult because of the cost of expertise. We characterize an expert with two parameters: overgeneralization and overspecialization. It can be argued they are the most abstract characterization of errors that an expert makes. With these assumptions, we propose a generic simulation framework that allows autonomous evaluation of most of incremental knowledge acquisition methods. We demonstrate this on a number of variants of RDR and obtain fundamental insights to the methods which suggest various hints for improvement. The simulation framework is further applied to investigate two fundamental aspects of incremental KA: the importance of acquiring domain ontological structures and the usage of cornerstone cases. Thirdly, we propose a generalization of the RDR approach to building knowledge based systems that is based on tightly controlling the order of evaluation of the system's knowledge components. There are two relations in the order of evaluation: sequence and correction. These correspond to the types of changes that an expert may do to a knowledge based system.