Seminar Künstliche Intelligenz (01954) "Measuring Inconsistency"

Measuring Inconsistency
Prof. Dr. Matthias Thimm


Inconsistency is a ubiquitous phenomenon whenever knowledge is compiled is some formal language. The notion of inconsistency refers (usually) to multiple pieces of information and represents a conflict between those, i. e., they cannot hold at the same time. The two statements "It is sunny outside" and "It is not sunny outside" represent inconsistent information and in order to draw meaningful conclusions from a knowledge base containing these statements, this conflict has to be consolidated somehow. The field of Inconsistency Measurement provides an analytical perspective on the issue of inconsistency. Its aim is to quantitatively assess the severity of inconsistency in order to both guide automatic reasoning mechanisms and to help human modellers in identifying issues and compare different alternative formalisations. Consider the following two knowledge bases K1 and K2 formalised in classical propositional logic modelling some information about the weather: K1 ={sunny,!sunny,hot,!hot} K2 ={!hot,sunny,sunny->hot,humid}. Both K1 and K2 are classically inconsistent, i. e., there is no interpretation satisfying any of them. But looking closer into the structure of the knowledge bases one can identify differences in the severity of the inconsistency. In K1 there are two apparent contradictions, i. e., {sunny, !sunny} and {hot,!hot} are directly conflicting formulas. In K2, the conflict is a bit more hidden. Here, three formulas are necessary to produce a contradiction ({!hot, sunny, sunny->hot}). Moreover, there is one formula in K2 (humid), which is not participating in any conflict and one could still infer meaningful information from this by relying on e. g. paraconsistent reasoning techniques. In conclusion, one should regard K1 as more inconsistent than K2. Inconsistency measures aim at formalising this intuition.

The goal of the seminar is to provide an overview of the field of inconsistency measurement, looking at different approaches to measuring inconsistency as well as different formalisms in which inconsistency measurement is applied. Note that the seminar will be in English, this includes that participants must give their seminar presentation an prepare their seminar paper in English.