# A logical Approach to Case-Based Reasoning Using Fuzzy Similarity Relations

This article approaches the formalization of inference in Case-based Reasoning (CBR) systems. CBR systems infer solutions of new problems on the basis of a precedent case that is, to some extent, similar to the current problem. Using the logics developed for similarity-based inference we characterize CBR systems defining what we call the Precedent-based Plausible Reasoning (PPR) model. This model is based on the graded consequence relations named approximation entailment and proximity entailment. A modal interpretation is provided for the precedent-based inference where the plausibility is given by the graded possibility operator $\displaystyle \Diamond_\alpha$ . The PPR model shows that both knowledge-intensive CBR systems and nearest neighbor algorithms share a common core formalism and that their difference is on whether (respectively) they use a general theory in addition to the precedent cases or they do not.