Measuring Inconsistency through Minimal Inconsistent Sets
نویسندگان
چکیده
In this paper, we explore the links between measures of inconsistency for a belief base and the minimal inconsistent subsets of that belief base. The minimal inconsistent subsets can be considered as the relevant part of the base to take into account to evaluate the amount of inconsistency. We define a very natural inconsistency value from these minimal inconsistent sets. Then we show that the inconsistency value we obtain is a particular Shapley Inconsistency Value, and we provide a complete axiomatization of this value in terms of five simple and intuitive axioms. Defining this Shapley Inconsistency Value using the notion of minimal inconsistent subsets allows us to look forward to a viable implementation of this value using SAT solvers.
منابع مشابه
Computational approaches to finding and measuring inconsistency in arbitrary knowledge bases
a r t i c l e i n f o a b s t r a c t Keywords: Inconsistency measures Minimal inconsistent subsets Minimal unsatisfiable subformulae SAT Random SAT There is extensive theoretical work on measures of inconsistency for arbitrary formulae in knowledge bases. Many of these are defined in terms of the set of minimal inconsistent subsets (MISes) of the base. However, few have been implemented or exp...
متن کاملLocalising iceberg inconsistencies
In artificial intelligence, it is important to handle and analyse inconsistency in knowledge bases. Inconsistent pieces of information suggest questions like “where is the inconsistency?” and “how severe is it?”. Inconsistency measures have been proposed to tackle the latter issue, but the former seems underdeveloped and is the focus of this paper. Minimal inconsistent sets have been the main t...
متن کاملOn Structure-Based Inconsistency Measures and Their Computations via Closed Set Packing
Measuring conflicts is important for understanding the contradictory status of a knowledge base (KB). In this work, we propose a new framework called closed set packing, an interesting extension of the well-known set packing problem, by which we define a family of fine-grained inconsistency measures exploiting the structure of minimal inconsistent sets of a KB. We show that closed set packing a...
متن کاملStrong Inconsistency in Nonmonotonic Reasoning
Minimal inconsistent subsets of knowledge bases play an important role in classical logics, most notably for repair and inconsistency measurement. It turns out that for nonmonotonic reasoning a stronger notion is needed. In this paper we develop such a notion, called strong inconsistency. We show that—in an arbitrary logic, monotonic or not—minimal strongly inconsistent subsets play the same ro...
متن کاملFinding and measuring inconsistency in arbitrary knowledge bases
There is extensive theoretical work on measures of inconsistency for arbitrary formulae in knowledge bases. Many of these are de ned in terms of the set of minimal inconsistent subsets (MISes) of the base. However, few have been implemented or experimentally evaluated to support their viability, since computing all MISes is intractable in the worst case. Fortunately, recent work on a related pr...
متن کامل