| Measuring Inconsistency in Finitary First-order Logic
John Grant
Since the early 2000s, researchers in logic and AI have developed a framework for measuring inconsistency in information. They proposed inconsistency measures as well as desirable properties for them and dealt with related issues. AI researchers are interested in this topic because some intelligent systems need to handle inconsistencies. However, the bulk of the research has been done for propositional knowledge bases, that is, finite sets of formulas in propositional logic. But much of the information that intelligent systems deal with, such as databases, use first-order logic formulas. The purpose of this paper is to extend inconsistency measuring to finite sets of firstorder logic formulas. We propose five different measures and explain the rationale for each. Furthermore, we extend some of the properties proposed for propositional inconsistency measures to first-order logic and introduce several new properties appropriate for first-order logic. We show the satisfaction or violation of each property for each measure.
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