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Measuring Inconsistency through Minimal Inconsistent Sets
"... 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 defin ..."
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Cited by 24 (3 self)
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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.
Measuring inconsistency for description logics based on paraconsistent semantics. Khaled Mellouli, editor
- Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, (ECSQARU 2007), Hammamet, Tunisia, October 31 - November 2, 2007
, 2007
"... Abstract. In this paper, we present an approach for measuring inconsistency in a knowledge base. We first define the degree of inconsistency using a four-valued semantics for the description logicALC. Then an ordering over knowledge bases is given by considering their inconsistency degrees. Our meas ..."
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Cited by 14 (11 self)
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Abstract. In this paper, we present an approach for measuring inconsistency in a knowledge base. We first define the degree of inconsistency using a four-valued semantics for the description logicALC. Then an ordering over knowledge bases is given by considering their inconsistency degrees. Our measure of inconsistency can provide important information for inconsistency handling. 1
Computing inconsistency measure based on paraconsistent semantics
- J. Log. Comput
, 2011
"... Abstract. Measuring inconsistency in knowledge bases has been recog-nized as an important problem in several research areas. Many methods have been proposed to solve this problem and a main class of them is based on some kind of paraconsistent semantics. However, existing meth-ods suffer from two li ..."
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Cited by 7 (3 self)
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Abstract. Measuring inconsistency in knowledge bases has been recog-nized as an important problem in several research areas. Many methods have been proposed to solve this problem and a main class of them is based on some kind of paraconsistent semantics. However, existing meth-ods suffer from two limitations: 1) They are mostly restricted to propo-sitional knowledge bases; 2) Very few of them discuss computational aspects of computing inconsistency measures. In this paper, we try to solve these two limitations by exploring algorithms for computing an inconsistency measure of first-order knowledge bases. After introducing a four-valued semantics for first-order logic, we define an inconsistency measure of a first-order knowledge base, which is a sequence of incon-sistency degrees. We then propose a precise algorithm to compute our inconsistency measure. We show that this algorithm reduces the com-putation of the inconsistency measure to classical satisfiability checking. This is done by introducing a new semantics, named S[n]-4 semantics, which can be calculated by invoking a classical SAT solver. Moreover, we show that this auxiliary semantics also gives a direct way to compute upper and lower bounds of inconsistency degrees. That is, it can be easily revised to compute approximating inconsistency measures. The approx-imating inconsistency measures converge to the precise values if enough resources are available. Finally, by some nice properties of the S[n]-4 se-mantics, we show that some upper and lower bounds can be computed in P-time, which says that the problem of computing these approximating inconsistency measures is tractable. 1
Inconsistency Management Policies
- PROCEEDINGS, ELEVENTH INTERNATIONAL CONFERENCE ON PRINCIPLES OF KNOWLEDGE REPRESENTATION AND REASONING
, 2008
"... Though there is much work on how inconsistency in databases should be managed, there is good reason to believe that end users will want to bring their domain expertise and needs to bear in how to deal with inconsistencies. In this paper, we propose the concept of inconsistency management policies (I ..."
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Cited by 5 (2 self)
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Though there is much work on how inconsistency in databases should be managed, there is good reason to believe that end users will want to bring their domain expertise and needs to bear in how to deal with inconsistencies. In this paper, we propose the concept of inconsistency management policies (IMPs). We show that IMPs are rich enough to specify many types of inconsistency management methods proposed previously, but provide end users with tools that allow them to use the policies that they want. Our policies are also capable of allowing inconsistency to persist in the database or of eliminating more than a minimal subset of tuples involved in the inconsistency. We present a formal axiomatic definition of IMPs and present appropriate complexity results, together with results linking different IMPs together. We extend the relational algebra (RA) to incorporate IMPs and present theoretical results showing how IMPs and classical RA operators interact.
Measure-Based Inconsistency-Tolerant Maintenance of Database Integrity
- Proc. 5th SDKB
"... This is a revised version of a paper with the same title, published in a collection of revised papers that were selected from the 5th International Workshop on ..."
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Cited by 4 (4 self)
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This is a revised version of a paper with the same title, published in a collection of revised papers that were selected from the 5th International Workshop on
An Anytime Algorithm for Computing Inconsistency Measurement ⋆
, 2009
"... Abstract. Measuring inconsistency degrees of inconsistent knowledge bases is an important problem as it provides context information for facilitating inconsistency handling. Many methods have been proposed to solve this problem and a main class of them is based on some kind of paraconsistent semanti ..."
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Cited by 3 (3 self)
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Abstract. Measuring inconsistency degrees of inconsistent knowledge bases is an important problem as it provides context information for facilitating inconsistency handling. Many methods have been proposed to solve this problem and a main class of them is based on some kind of paraconsistent semantics. In this paper, we consider the computational aspects of inconsistency degrees of propositional knowledge bases under 4-valued semantics. We first analyze its computational complexity. As it turns out that computing the exact inconsistency degree is intractable, we then propose an anytime algorithm that provides tractable approximation of the inconsistency degree from above and below. We show that our algorithm satisfies some desirable properties and give experimental results of our implementation of the algorithm. 1
On the measure of instability in normal residuated logic programs
- In Proceedings of FUZZ-IEEE’10
, 2010
"... Abstract. Inconsistency in the framework of general residuated logic programs can be, somehow, decomposed in two notions: incoherence and instability. In this work, we focus on the measure of instability of normal residuated programs. Some measures are provided and initial results are obtained in te ..."
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Cited by 2 (0 self)
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Abstract. Inconsistency in the framework of general residuated logic programs can be, somehow, decomposed in two notions: incoherence and instability. In this work, we focus on the measure of instability of normal residuated programs. Some measures are provided and initial results are obtained in terms of the amount of information that have to be discarded in order to recover stability. 1
Computing inconsistency measurements under multi-valued semantics by partial maxSAT solvers
- in Proc. of KR’10
, 2010
"... Measuring the inconsistency degree of a knowledge base can help us to deal with inconsistencies. Several inconsistency measures have been given under different multi-valued se-mantics, including 4-valued semantics, 3-valued semantics, LPm and Quasi Classical semantics. In this paper, we first carefu ..."
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Cited by 2 (2 self)
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Measuring the inconsistency degree of a knowledge base can help us to deal with inconsistencies. Several inconsistency measures have been given under different multi-valued se-mantics, including 4-valued semantics, 3-valued semantics, LPm and Quasi Classical semantics. In this paper, we first carefully analyze the relationship between these inconsis-tency measures by showing that the inconsistency degrees under 4-valued semantics, 3-value semantics, LPm are the same, but different from the one based on Quasi Classical se-mantics. We then consider the computation of these inconsis-tency measures and show that computing inconsistency mea-surement under multi-valued semantics is usually intractable. To tackle this problem, we propose two novel algorithms that respectively encode the problems of computing inconsistency degrees under 4-valued semantics (3-valued semantics, LPm) and under Quasi Classical semantics into the partial Max-SAT problems. We implement these algorithms and do ex-periments on some benchmark data sets. The preliminary but encouraging experimental results show that our approach is efficient to handle large knowledge bases. 1.
Computational complexity and anytime algorithm for inconsistency measurement
- IJSI
, 2010
"... Abstract Measuring inconsistency degrees of inconsistent knowledge bases is an important problem as it provides context information for facilitating inconsistency handling. Many methods have been pro-posed to solve this problem and a main class of them is based on some kind of paraconsistent semanti ..."
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Cited by 2 (2 self)
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Abstract Measuring inconsistency degrees of inconsistent knowledge bases is an important problem as it provides context information for facilitating inconsistency handling. Many methods have been pro-posed to solve this problem and a main class of them is based on some kind of paraconsistent semantics. In this paper, we consider the computational aspects of inconsistency degrees of propositional knowl-edge bases under 4-valued semantics. We first give a complete analysis of the computational complexity of computing inconsistency degrees. As it turns out that computing the exact inconsistency degree is intractable, we then propose an anytime algorithm that provides tractable approximations of the incon-sistency degree from above and below. We show that our algorithm satisfies some desirable properties and give experimental results of our implementation of the algorithm. Key words: knowledge representation; inconsistency measurement; multi-valued logic; computa-tional complexity; algorithm
Some representation and computational issues in social choice
- In Proceedings of ECSQARU-2005
, 2005
"... Abstract. This paper briefly considers several research issues, some of which are on-going and some others are for further research. The starting point is that many AI topics, especially those related to the EC-SQARU and KR conferences, can bring a lot to the representation and the resolution of soc ..."
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Cited by 2 (1 self)
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Abstract. This paper briefly considers several research issues, some of which are on-going and some others are for further research. The starting point is that many AI topics, especially those related to the EC-SQARU and KR conferences, can bring a lot to the representation and the resolution of social choice problems. I surely do not claim to make an exhaustive list of problems, but I rather list some problems that I find important, give some relevant references and point out some potential research issues 1. 1
