Transactions on Large-Scale Data- and Knowledge-Centered Systems XXXIV

Postulates for inconsistency measures are examined, the set of postulates proposed by Hunter and Konieczny being the starting point. The focus is on two postulates that were questioned by various authors. Studying the first suggests a systematic transformation to guard postulates against a certain kind of counter-examples. The second postulate under investigation here is devoted to independence, for which a general version is proposed that avoids the pitfalls mentioned in the literature. Combining these two additions with some postulates previously introduced by the same author, a set of basic postulates alternative to the core set given by Hunter and Konieczny arises. 1 Inconsistency Measures There are plenty of reasons for belief bases to be inconsistent. Unfortunately, inconsistency is a nuisance on a number of counts (it makes deductive reasoning to collapse, it allows decision-making to simultaneaously enforce two mutually exclusive options, . . . ). In short, inconsistency in belief bases is bad. How bad? This is the question that inconsistency measures have been taking seriously. Informally speaking, an inconsistency measure tells to what extent a belief base is inconsistent. Indeed, there seems to be degrees. Consider e.g. the statement “This item is robust and affordable”. One way to contradict it is by means of the statement “If it’s robust then it is not affordable”. Another way is by means of the statement “It is neither robust nor affordable”. The latter expresses that both claims (i.e., “the item is robust” and “the item is affordable”) in the initial statement are false but the former only objects that either “the item is robust” is false or “the item is affordable” is false. Accordingly, the belief base K1 = { This item is robust and affordable If it’s robust then it is not affordable } can be viewed as less inconsistent than the belief base K2 = { This item is robust and affordable It is neither robust nor affordable }