Reasoning with Assertions and Examples

M. Kerber, E. Melis, and J. H. Siekmann

The hallmark of traditional Artificial Intelligence (AI) research is tile symbolic representation and processing of knowledge. This is in sharp contrast to many forms of human reasoning, which to an extraordinary extent, rely on cases and (typical) examples. Although these examples could themselves encoded into logic, this raises the problem of restricting the corresponding model classes to include only the intended models. There are, however, more compelling reasons to argue for a hybrid representation based on assertions as well as examples. The problems of adequacy, availability of information, compactness of representation, processing complexity, and last but not least, results from the psychology of human reasoning, all point to the same conclusion: Common sense reasoning requires different knowledge sources and hybrid reasoning principles that combine symbolic as well as semantic-based inference. In this paper we address the problem of integrating semantic representations of examples into automated deduction systems. The main contribution is a formal framework for combining sentential with direct representations. The framework consists of a hybrid knowledge base, made up of logical formulae on the one hand and direct representations of examples on the other, and of a hybrid reasoning method based on the resolution calculus. The resulting hybrid resolution calculus is shown to be sound and complete.

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