On case-based learnability of languages

Case-based reasoning is deemed an important technology to alleviate the bottleneck of knowledge acquisition in Artificial Intelligence (AI). In case-based reasoning, knowledge is represented in the form of particular cases with an appropriate similarity measure rather than any form of rules. The case-based reasoning paradigm adopts the view that an Al system is dynamically changing during its life-cycle which immediately leads to learning considerations. Within the present paper, we investigate the problem of case-based learning of indexable classes of formal languages. Prior to learning considerations, we study the problem of case-based representability and show that every indexable class is case-based representable with respect to a fixed similarity measure. Next, we investigate several models of case-based learning and systematically analyze their strengths as well as their limitations. Finally, the general approach to case-based learnability of indexable classes of formal languages is prototypically applied to so-called containmet decision lists, since they seem particularly tailored to case-based knowledge processing.