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Current Approaches to Handling Imperfect Information in Data and Knowledge Bases
, 1996
"... This paper surveys methods for representing and reasoning with imperfect information. It opens with an attempt to classify the different types of imperfection that may pervade data, and a discussion of the sources of such imperfections. The classification is then used as a framework for considering ..."
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Cited by 68 (1 self)
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This paper surveys methods for representing and reasoning with imperfect information. It opens with an attempt to classify the different types of imperfection that may pervade data, and a discussion of the sources of such imperfections. The classification is then used as a framework for considering work that explicitly concerns the representation of imperfect information, and related work on how imperfect information may be used as a basis for reasoning. The work that is surveyed is drawn from both the field of databases and the field of artificial intelligence. Both of these areas have long been concerned with the problems caused by imperfect information, and this paper stresses the relationships between the approaches developed in each.
2004): Completeness in the relational model: A comprehensive framework
 In Proceedings of the Ninth International Conference on Information Quality (ICIQ04
"... Abstract: Completeness is a well known data quality dimension in the area of databases. Intuitively, a database is complete if it represents every fact of the real world coherent with the database semantics, i.e. its intension. In the paper, we provide a comprehensive framework for characterizing co ..."
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Cited by 16 (0 self)
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Abstract: Completeness is a well known data quality dimension in the area of databases. Intuitively, a database is complete if it represents every fact of the real world coherent with the database semantics, i.e. its intension. In the paper, we provide a comprehensive framework for characterizing completeness in the relational model, investigating several different paradigms typical of database models, such as closed world and open world assumptions, and presence or absence of null values. Furthermore, we introduce an algebra for completeness, in order to address the problem of calculating composition of quality dimensions in queries that include relational operators such as union, difference and cartesian product. Under different assumptions and for the different types of completeness, we provide properties and shortcuts for such an algebra.
Stable theories in autoepistemic logic
 Fundamenta Informaticae
, 1989
"... We investigate the operator producing a stable theory out of its objective part (A stable theory is a set of beliefs of a rational agent). We characterize the objective parts of stable theories. Finally, we discuss the predicate calculus case. Recent developments in the artificial intelligence and, ..."
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Cited by 13 (4 self)
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We investigate the operator producing a stable theory out of its objective part (A stable theory is a set of beliefs of a rational agent). We characterize the objective parts of stable theories. Finally, we discuss the predicate calculus case. Recent developments in the artificial intelligence and, in particular, strong interest in the formalizations of the common sense reasonings and nonmonotonic logics ([MC], [Re2], [Li], [MDD]) and reasoning about knowledge leads to new interesting developments in the areas of logic previously left almost exclusively to philosophers. These subjects now get attention of computer scientists and mathematicians,
Contributions to the Complexity Analysis of NonMonotonic Reasoning
, 2000
"... . Part One of this report is a presentation of known results in the areas of logic and complexity theory written in an intuitive style and presents a number of examples. Among other things several nonmonotonic formalisms which can be used for knowledge representation in artificial intelligence a ..."
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. Part One of this report is a presentation of known results in the areas of logic and complexity theory written in an intuitive style and presents a number of examples. Among other things several nonmonotonic formalisms which can be used for knowledge representation in artificial intelligence and their relationship to each other are discussed. The ample second part consists of a large variety of complexity results for model checking of nonmonotonic formalisms and for determining a belief pair of a threevalued semantics of autoepistemic logic. Model Checking is the question whether a given interpretation satisfies a theory (in this case a nonmonotonic theory) and is a viable alternative to reasoning. A number of open complexity problems for model checking with default logic and with default logic with weak extensions is solved; for instance it is shown that model checking with normal default theories is P 2 complete, however in the case of weak extensions P 2 c...
Reasoning with Modularly Pointwise Preferential Relations
"... We introduce a family of preferential consequence relations, defined by a simple and natural manyvalued semantics. These relations share many desirable properties for commonsense reasoning, such as paraconsistency (daCosta, [8]), plausibility (Lehmann, [12]), adaptivity (Batens, [4, 5]), and ..."
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We introduce a family of preferential consequence relations, defined by a simple and natural manyvalued semantics. These relations share many desirable properties for commonsense reasoning, such as paraconsistency (daCosta, [8]), plausibility (Lehmann, [12]), adaptivity (Batens, [4, 5]), and rationality (Lehmann and Magidor, [13]). 1
Bag Relational Algebra with Grouping and Aggregation over CTables with Linear Conditions
"... Abstract—We introduce bag relational algebra with grouping and aggregation over a particular representation of incomplete information called ctables, which was first introduced by Grahne in 1984. In order for this algebra to be closed and “welldefined”, we adopt the closed world assumption as desc ..."
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Abstract—We introduce bag relational algebra with grouping and aggregation over a particular representation of incomplete information called ctables, which was first introduced by Grahne in 1984. In order for this algebra to be closed and “welldefined”, we adopt the closed world assumption as described by Reiter in 1978 and extend the tuple and table conditions to linear ones. We explore the problem of rewriting and simplifying this novel type of ctables, show how to perform equivalence test for ctables, and argue why it is difficult to create a canonical form for ctables. We present certain answer semantics for a fullblown relational algebra with grouping and aggregation and accordingly present algorithms for executing the different relational algebra operators over our representation of incomplete information. The algorithms run in polynomial time relative to the size of the precise information, which makes them a candidate for implementation as part of a DBMS engine that supports storage and retrieval of incomplete information. Keywordsincomplete information; ctables; relational model; null values; bag semantics I.
Local nulls in summarised mobile and distributed databases
"... The concept and semantics of null values in relational databases has been discussed widely since the introduction of the relational data model in the late 1960s. With the introduction of highly mobile, distributed databases, in order to preserve the accepted soundness and completeness criteria, the ..."
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The concept and semantics of null values in relational databases has been discussed widely since the introduction of the relational data model in the late 1960s. With the introduction of highly mobile, distributed databases, in order to preserve the accepted soundness and completeness criteria, the semantics of the null value needs to expand to reflect a localised lack of information that may not be apparent for the global database. This paper discusses an extension to the notion of nulls to include the semantics of ‘local ’ nulls. The paper introduces local nulls in terms of amendments to the relational algebra and examines its impact on query languages. 1 Previous research and motivation Much of the research on the semantics of null values in relational databases dates back to the 1970s and 1980s [1–7]. The two definitions of nulls as given by Codd are missing and applicable, and missing and inapplicable [1] and Zaniolo [4] later proposed a third definition as, essentially, a lack of knowledge about the attribute’s applicability, or no information. To handle null values, various logical approaches have been developed. For example, the commonlyused three value logic includes true, false (often by virtue of a value’s absence q.v. the closedworld assumption [8]), and a maybe value which indicates that the results may be true [9, 10]. A four value logic has also been proposed which includes an additional truth value, which represents the outcome of evaluating expressions which have inapplicable values [11, 12]. Approaches to accommodating null values in practical systems include the work of Motro [13] who uses the ideas of conceptual closeness fill the vacancies represented by a null value and Roth et al. who aim to include nulls in NF2 databases [5]. Null values have also been studied in relation to schema evolution and integration [14, 15].