A Logic for Approximate Reasoning

We investigate the problem of reasoning with imprecise quantitative information. We give formal semantics to a notion of approximate observations, and deene two types of entail-ment for a knowledge base with imprecise information: a cautious notion, which allows only completely justiied conclusions, and a bold one, which allows jumping to conclusions. Both versions of the entailment relation are shown to be decidable. We investigate the behavior of the two alternatives on various examples, and show that the answers obtained are intuitively desirable. The behavior of these two entailment relations is completely characterized for a certain sublan-guage, in terms of the logic of true equality. We demonstrate various properties of the full logic, and show how it applies to many situations of interest.