A Logic for Approximate First-Order Reasoning

Abstract. In classical approaches to knowledge representation, reasoners are assumed to derive all the logical consequences of their knowledge base. As a result, reasoning in the first-order case is only semi-decidable. Even in the restricted case of finite universes of discourse, reasoning remains inherently intractable, as the reasoner has to deal with two independent sources of complexity: unbounded chaining and unbounded quantification. The purpose of this study is to handle these difficulties in a logic-oriented framework based on the paradigm of approximate reasoning. The logic is semantically founded on the notion of resource, an accuracy measure, which controls at the same time the two barriers of complexity. Moreover, a stepwise technique is included for improving approximations. Finally, both sound approximations and complete ones are covered. Based on the logic, we develop an approximation algorithm with a simple modification of classical instance-based theorem provers. ...

• Type: Conference
• Year: 2001
• Where: CSL
• Authors: Frédéric Koriche
• Keywords: Approximate Reasoning, Automated Reasoning, CSL 2001, Reasoner, Yields Approximate Proofs