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Logics of Formal Inconsistency
 Handbook of Philosophical Logic
"... 1.1 Contradictoriness and inconsistency, consistency and noncontradictoriness In traditional logic, contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory ..."
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Cited by 69 (24 self)
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1.1 Contradictoriness and inconsistency, consistency and noncontradictoriness In traditional logic, contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory
Formal Inconsistency and Evolutionary Databases
 LOGIC AND LOGICAL PHILOSOPHY
, 2000
"... This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct soun ..."
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Cited by 38 (15 self)
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This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their firstorder extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics of Formal Inconsistency (LFI) and form part of a much larger family of similar logics. We also show that there are translations from classical and paraconsistent firstorder logics into LFI1* and LFI2*, and back. Hence, despite their status as subsystems of classical logic, LFI1* and LFI2* can codify any classical or paraconsistent reasoning.
Coherent Integration of Databases by Abductive Logic Programming
 Journal of Artificial Intelligence Research
, 2004
"... We introduce an abductive method for a coherent integration of independent datasources. ..."
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Cited by 17 (5 self)
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We introduce an abductive method for a coherent integration of independent datasources.
Database repair by signed formulae
 In Seipel, D., & TurellTorres, J. (Eds.), Proc. 3rd Int. Symp. on Foundations of Information and Knowledge Systems (FoIKS’04), No. 2942 in LNCS
, 2004
"... Abstract. We introduce a simple and practically efficient method for repairing inconsistent databases. The idea is to properly represent the underlying problem, and then use offtheshelf applications for efficiently computing the corresponding solutions. Given a possibly inconsistent database, we r ..."
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Cited by 16 (5 self)
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Abstract. We introduce a simple and practically efficient method for repairing inconsistent databases. The idea is to properly represent the underlying problem, and then use offtheshelf applications for efficiently computing the corresponding solutions. Given a possibly inconsistent database, we represent the possible ways to restore its consistency in terms of signed formulae. Then we show how the ‘signed theory ’ that is obtained can be used by a variety of computational models for processing quantified Boolean formulae, or by constraint logic program solvers, in order to rapidly and efficiently compute desired solutions, i.e., consistent repairs of the database. 1
Distance semantics for database repair
 Annals of Mathematics and Artificial Intelligence
"... Abstract. In many scenarios, a database instance violates a given set of integrity constraints. In such cases, it is often required to repair the database, that is, to restore its consistency. A primary motif behind the repairing approaches is the principle of minimal change, which is the aspiration ..."
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Cited by 9 (3 self)
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Abstract. In many scenarios, a database instance violates a given set of integrity constraints. In such cases, it is often required to repair the database, that is, to restore its consistency. A primary motif behind the repairing approaches is the principle of minimal change, which is the aspiration to keep the recovered data as faithful as possible to the original (inconsistent) database. In this paper, we represent this qualitative principle quantitatively, in terms of distance functions and some underlying metrics, and so introduce a general framework for repairing inconsistent databases by distancebased considerations. The uniform way of representing repairs and their semantics clarifies the essence behind several approaches to consistency restoration in database systems, helps to compare the underlying formalisms, and relates them to existing methods of defining belief revision operators, merging data sets, and integrating information systems. 1
Computational methods for database repair by signed formulae
 Ann. Math. Artif. Intell
"... Abstract. We introduce a simple and practical method for repairing inconsistent databases. Given a possibly inconsistent database, the idea is to properly represent the underlying problem, i.e., to describe the possible ways of restoring its consistency. We do so by what we call signed formulae, and ..."
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Cited by 8 (4 self)
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Abstract. We introduce a simple and practical method for repairing inconsistent databases. Given a possibly inconsistent database, the idea is to properly represent the underlying problem, i.e., to describe the possible ways of restoring its consistency. We do so by what we call signed formulae, and show how the ‘signed theory ’ that is obtained can be used by a variety of offtheshelf computational models in order to compute the corresponding solutions, i.e., consistent repairs of the database. 1.
Simplification of integrity constraints for data integration
 Third International Symposium on Foundations of Information and Knowledge Systems (FoIKS), February 17–20, 2004
, 2004
"... Abstract. When two or more databases are combined into a global one, integrity may be violated even when each database is consistent with its own local integrity constraints. Efficient methods for checking global integrity in data integration systems are called for: answers to queries can then be tr ..."
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Cited by 7 (6 self)
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Abstract. When two or more databases are combined into a global one, integrity may be violated even when each database is consistent with its own local integrity constraints. Efficient methods for checking global integrity in data integration systems are called for: answers to queries can then be trusted, because either the global database is known to be consistent or suitable actions have been taken to provide consistent views. The present work generalizes simplification techniques for integrity checking in traditional databases to the combined case. Knowledge of local consistency is employed, perhaps together with given a priori constraints on the combination, so that only a minimal number of tuples needs to be considered. Combination from scratch, integration of a new source, and absorption of local updates are dealt with for both the localasview and globalasview approaches to data integration. 1
INTERVAL NEUTROSOPHIC SETS AND LOGIC: THEORY AND APPLICATIONS IN COMPUTING
, 2006
"... A neutrosophic set is a part of neutrosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. The neutrosophic set is a powerful general formal framework that has been recently proposed. However, the neutrosophic set needs to ..."
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Cited by 6 (2 self)
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A neutrosophic set is a part of neutrosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. The neutrosophic set is a powerful general formal framework that has been recently proposed. However, the neutrosophic set needs to be specified from a technical point of view. Here, we define the settheoretic operators on an instance of a neutrosophic set, and call it an Interval Neutrosophic Set (INS). We prove various properties of INS, which are connected to operations and relations over INS. We also introduce a new logic system based on interval neutrosophic sets. We study the interval neutrosophic propositional calculus and interval neutrosophic predicate calculus. We also create a neutrosophic logic inference system based on interval neutrosophic logic. Under the framework of the interval neutrosophic set, we propose a data model based on the special case of the interval neutrosophic sets called Neutrosophic Data Model. This data model is the extension of fuzzy data model and paraconsistent data model. We generalize the settheoretic operators and relationtheoretic operators of fuzzy relations and paraconsistent relationsto neutrosophic relations. We propose the generalized SQL query constructs and tuplerelational calculus for Neutrosophic Data Model.
Repairing Inconsistent Databases: A ModelTheoretic Approach
 In Proc. ICLP’02 Workshop on Paraconsistent Computational Logic (PCL’02), Federated Logic Conference (FLOC’02
, 2002
"... Abstract. In this paper we consider two points of views to the problem of coherent integration of distributed data. First we give a pure modeltheoretic analysis of the possible ways to `repair ' a database. We do so by characterizing the possibilities to `recover ' consistent data from an ..."
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Abstract. In this paper we consider two points of views to the problem of coherent integration of distributed data. First we give a pure modeltheoretic analysis of the possible ways to `repair ' a database. We do so by characterizing the possibilities to `recover ' consistent data from an inconsistent database in terms of those models of the database that exhibit as minimal inconsistent information as reasonably possible. Then we introduce an abductive application to restore the consistency of a given database. This application is based on an abductive solver (Asystem) that implements an SLDNFAresolution procedure, and computes a list of datafacts that should be inserted to the database or retracted from it in order to keep the database consistent. The two approaches for coherent data integration are related by soundness and completeness results. 1 Introduction Integration of data coming from different databases is a very common, nevertheless nontrivial, task. There are number of different phases involved in this process, the most important of which are the following: 1. Resolving the different ontologies and/or database scheme, setting a
A Paraconsistent Logic Programming Approach for Querying Inconsistent Knowledge Bases
"... When integrating data coming from multiple different sources we are faced with the possibility of inconsistency in databases. A paraconsistent approach for knowledge base integration allows keeping inconsistent information and reasoning in its presence. In this paper, we use a paraconsistent logic ( ..."
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When integrating data coming from multiple different sources we are faced with the possibility of inconsistency in databases. A paraconsistent approach for knowledge base integration allows keeping inconsistent information and reasoning in its presence. In this paper, we use a paraconsistent logic (LFI1) as the underlying logic for the specification of PDatalog, a deductive query language for databases containing inconsistent information. We present a declarative semantics which captures the desired meaning of a recursive query executed over a database containing inconsistent facts and whose rules allow infering information from inconsistent premises. We also present a bottomup evaluation method for PDatalog programs based on an alternating fixpoint operator.