Abstract

We investigate the problem of reasoning with imprecise quantitative information. We give formal semantics to a notion of approximate observations, and define two types of entailment for a knowledge base with imprecise information: a cautious notion, which allows only completely justified 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 sublanguage, 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.

Citations