Measuring inconsistency in knowledgebases

It is well-known that knowledgebases may contain inconsistencies. We provide a measure to quantify the inconsistency of a knowledgebase, thereby allowing for the comparison of the inconsistency of various knowledgebases, represented as first-order logic formulas. We use quasi-classical (QC) logic for this purpose. QC logic is a formalism for reasoning and analysing inconsistent information. It has been used as the basis of a framework for measuring inconsistency in propositional theories. Here we extend this framework, by using a first-order logic version of QC logic for measuring inconsistency in first-order theories. We motivate the QC logic approach by considering some formulae as database or knowledgebase integrity constraints. We then define a measure of extrinsic inconsistency that can be used to compare the inconsistency of different knowledgebases. This measure takes into account both the language used and the underlying domain. We show why this definition also captures the intrinsic inconsistency of a knowledgebase. We also provide a formalization of paraconsistent equality, called quasi-equality, and we use this in an extended example of an application for measuring inconsistency between heterogeneous sources of information and integrity constraints prior to merging.     

A general framework for measuring inconsistency through minimal inconsistent sets

Hunter and Konieczny explored the relationships between measures of inconsistency for a belief base and the minimal inconsistent subsets of that belief base in several of their papers. In particular, an inconsistency value termed MIV _C , defined from minimal inconsistent subsets, can be considered as a Shapley Inconsistency Value. Moreover, it can be axiomatized completely in terms of five simple axioms. MinInc, one of the five axioms, states that each minimal inconsistent set has the same amount of conflict. However, it conflicts with the intuition illustrated by the lottery paradox, which states that as the size of a minimal inconsistent belief base increases, the degree of inconsistency of that belief base becomes smaller. To address this, we present two kinds of revised inconsistency measures for a belief base from its minimal inconsistent subsets. Each of these measures considers the size of each minimal inconsistent subset as well as the number of minimal inconsistent subsets of a belief base. More specifically, we first present a vectorial measure to capture the inconsistency for a belief base, which is more discriminative than MIV _C . Then we present a family of weighted inconsistency measures based on the vectorial inconsistency measure, which allow us to capture the inconsistency for a belief base in terms of a single numerical value as usual. We also show that each of the two kinds of revised inconsistency measures can be considered as a particular Shapley Inconsistency Value, and can be axiomatically characterized by the corresponding revised axioms presented in this paper.     

Resource-Bounded Paraconsistent Inference

In this paper, a new framework for reasoning from inconsistent propositional belief bases is presented. A family of resource-bounded paraconsistent inference relations is introduced. Such inference relations are based on S-3 entailment, an inference relation logically weaker than the classical one and parametrized by a set S of propositional variables. The computational complexity of our relations is identified, and their logical properties are analyzed. Among the strong features of our framework is the fact that tractability is ensured each time |S| is bounded and a limited amount of knowledge is taken into account within the belief base. Furthermore, binary connectives , behave in a classical manner. Finally, our framework is general enough to encompass several paraconsistent multi-valued logics (including S-3, J ₃ and its restrictions), the standard coherence-based approach to inconsistency handling (based on the selection of consistent subbases) and some signed systems for paraconsistent reasoning as specific cases.     

Coherence measures and their relation to fuzzy similarity and inconsistency in knowledge bases

Intuitively it seems that the coherence of information received from heterogeneous sources should be one factor in determining the reliability or truthfulness of the information, yet the concept of coherence is extremely difficult to define. This paper draws on recent work on probabilistic measures of coherence by investigating two measures with contrasting properties and then explores how this work relates to similarity of fuzzy sets and comparison of knowledge bases in cases where inconsistency is present. In each area contrasting measures are proposed analogous to the probabilistic case. In particular, concepts of fuzzy and logical independence are proposed and in each area it is found that sensitivity to the relevant concept of independence is a distinguishing feature between the contrasting measures. In the case of inconsistent knowledge bases, it is argued that it is important to take agreeing information and not just conflicting and total information into account when comparing two knowledge bases. One of the measures proposed achieves this and is shown to have a number of properties which enable it to overcome some problems encountered by other approaches.     

基于优先级的超协调本体推理研究

随着语义Web研究的逐步深入，本体推理问题业已受到众多相关人员的重视。而超协调本体的推理问题，作为本体维护以及本体集成的研究基础，更是迫切地有待解决。本文对本体知识库作出了一定的扩充，定义了基于优先级的本体知识库的一系列相关概念，并且在此基础上，给出了两种在超协调的本体中寻求一致性推理的途径，希望能为相关的研究带来一定的参考与借鉴。     

Logical Comparison of Inconsistent Perspectives using Scoring Functions

The language for describing inconsistency is underdeveloped. If a database (a set of formulae) is inconsistent, there is usually no qualification of that inconsistency. Yet, it would seem useful to be able to say how inconsistent a database is, or to say whether one database is more inconsistent than another database. In this paper, we provide a more general characterization of inconsistency in terms of a scoring function for each database . A scoring function S is from the power set of into the natural numbers defined so that S() gives the number of minimally inconsistent subsets of that would be eliminated if the subset was removed from . This characterization offers an expressive and succinct means for articulating, in general terms, the nature of inconsistency in a set of formulae. We then compare databases using their scoring functions. This gives an intuitive ordering relation over databases that we can describe as more inconsistent than. These techniques are potentially useful in a wide range of problems including monitoring progress in negotiations between a number of participants, and in comparing heterogeneous sources of information.     

The Method of Assigning Incidences

Incidence calculus is a probabilistic logic in which incidences, standing for the situations in which formulae may be true, are assigned to some formulae, and probabilities are assigned to incidences. However, numerical values may be assigned to formulae directly without specifying the incidences. In this paper, we propose a method of discovering incidences under these circumstances which produces a unique output comparing with the large number of outputs from other approaches. Some theoretical aspects of this method are thoroughly studied and the completeness of the result generated from it is proved. The result can be used to calculate mass functions from belief functions in the Dempster-Shafer theory of evidence (DS theory) and define probability spaces from inner measures (or lower bounds) of probabilities on the relevant propositional language set.     

Repairing and reasoning with inconsistent and uncertain ontologies

With the development of semantic web, the quality and correctness of ontologies play more and more important roles in semantic representation and knowledge sharing. However, ontologies are often inconsistent and uncertain in real situations. Because of the difficulty in ensuring the quality of ontologies, there is an increasing need for dealing with the inconsistency and uncertainty in real-world applications of ontological reasoning and management. This paper adopts two methods to handle the inconsistent and uncertain ontologies: the first one is to repair the inconsistency, algorithms RIO and RIUO are proposed to compute the candidate repair set, the consistency of ontology could be recovered through deleting or modifying the axioms in candidate repair set; the second one is to develop a non-standard reasoning method to obtain meaningful answers, algorithms RMU and RMIU are proposed to perform query-specific reasoning methods for inconsistent and uncertain ontologies without changing the original ontologies. Finally the prototype system is constructed and the experiment results validate the usability and effectiveness of our approaches.