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19
Logic and databases: a deductive approach
 ACM Computing Surveys
, 1984
"... The purpose of this paper is to show that logic provides a convenient formalism for studying classical database problems. There are two main parts to the paper, devoted respectively to conventional databases and deductive databases. In the first part, we focus on query languages, integrity modeling ..."
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Cited by 143 (2 self)
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The purpose of this paper is to show that logic provides a convenient formalism for studying classical database problems. There are two main parts to the paper, devoted respectively to conventional databases and deductive databases. In the first part, we focus on query languages, integrity modeling and maintenance, query optimization, and data
A Normal Form for XML Documents
"... This paper takes a rst step towards the design and normalization theory for XML documents. We show that, like relational databases, XML documents may contain redundant information, and may be prone to update anomalies. Furthermore, such problems are caused by certain functional dependencies among p ..."
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Cited by 121 (9 self)
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This paper takes a rst step towards the design and normalization theory for XML documents. We show that, like relational databases, XML documents may contain redundant information, and may be prone to update anomalies. Furthermore, such problems are caused by certain functional dependencies among paths in the document. Our goal is to nd a way of converting an arbitrary DTD into a welldesigned one, that avoids these problems. We rst introduce the concept of a functional dependency for XML, and de ne its semantics via a relational representation of XML. We then de ne an XML normal form, XNF, that avoids update anomalies and redundancies. We study its properties and show that it generalizes BCNF and a normal form for nested relations when those are appropriately coded as XML documents. Finally, we present a lossless algorithm for converting any DTD into one in XNF.
Horn clauses and database dependencies
 Journal of the ACM
, 1982
"... Abstract. Certain firstorder sentences, called "dependencies, " about relations in a database are defined and studied. These dependencies seem to include all prewously defined dependencies as special cases A new concept is mtroduced, called "faithfulness (with respect to direct produ ..."
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Cited by 60 (6 self)
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Abstract. Certain firstorder sentences, called "dependencies, " about relations in a database are defined and studied. These dependencies seem to include all prewously defined dependencies as special cases A new concept is mtroduced, called "faithfulness (with respect to direct product), " which enables powerful results to be proved about the existence of "Armstrong relations " in the presence of these new dependencies. (An Armstrong relaUon is a relation that obeys precisely those dependencies that are the logical consequences of a given set of dependencies.) Results are also obtained about characterizing the class of projections of those relations that obey a given set of dependencies.
On the structure of Armstrong relations for functional dependencies
 Journal of the ACM
, 1984
"... Abstract. An Armstrong relation for a set of functional dependencies (FDs) is a relation that satisfies each FD implied by the set but no FD that is not implied by it. The structure and size (number of tuples) of Armstrong relatsons are investigated. Upper and lower bounds on the size of minimalsiz ..."
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Cited by 42 (3 self)
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Abstract. An Armstrong relation for a set of functional dependencies (FDs) is a relation that satisfies each FD implied by the set but no FD that is not implied by it. The structure and size (number of tuples) of Armstrong relatsons are investigated. Upper and lower bounds on the size of minimalsized Armstrong relations are derived, and upper and lower bounds on the number of distinct entries that must appear m an Armstrong relation are given. It is shown that the time complexity of finding an Armstrong relation, gwen a set of functional dependencies, is precisely exponential in the number of attributes. Also shown,s the falsity of a natural conjecture which says that almost all relations obeying a given set of FDs are Armstrong relations for that set of FDs. Finally, Armstrong relations are used to generahze a result, obtained by Demetrovics using quite complicated methods, about the possible sets of keys for a relauon.
A Normal Form for Relational Databases that is Based on Domains and Keys
 ACM Transactions on Database Systems
, 1981
"... A new normal form for relational databases, called domainkey normal form (DK/NF), is defined. Also, formal definitions of insertion anomaly and deletion anomaly are presented. It is shown that a schema is in DK/NF if and only if it has no insertion or deletion anomalies. Unlike previously defined n ..."
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Cited by 39 (2 self)
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A new normal form for relational databases, called domainkey normal form (DK/NF), is defined. Also, formal definitions of insertion anomaly and deletion anomaly are presented. It is shown that a schema is in DK/NF if and only if it has no insertion or deletion anomalies. Unlike previously defined normal forms, DK/NF is not defined in terms of traditional dependencies (functional, multivalued, or join). Instead, it is defined in terms of the more primitive concepts of domain and key, along with the general concept of a “constraint. ” We also consider how the definitions of traditional normal forms might be modified by taking into consideration, for the first time, the combinatorial consequences of bounded domain sizes. It is shown that after this modification, these traditional normal forms are all implied by DK/NF. In particular, if all domains are infinite, then these traditional normal forms are all implied by DK/NF.
Reasoning with Examples: Propositional Formulae and Database Dependencies
"... For humans, looking at how concrete examples behave is an intuitive way of deriving conclusions. The drawback with this method is that it does not necessarily give the correct results. However, under certain conditions examplebased deduction can be used to obtain a correct and complete inference pr ..."
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Cited by 14 (4 self)
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For humans, looking at how concrete examples behave is an intuitive way of deriving conclusions. The drawback with this method is that it does not necessarily give the correct results. However, under certain conditions examplebased deduction can be used to obtain a correct and complete inference procedure. This is the case for Boolean formulae (reasoning with models) and for certain types of database integrity constraints (the use of Armstrong relations). We show that these approaches are closely related, and use the relationship to prove new results about the existence and sizes of Armstrong relations for Boolean dependencies. Furthermore, we exhibit close relations between the questions of finding keys in relational databases and that of finding abductive explanations. Further applications of the correspondence between these two approaches are also discussed. 1 Introduction One of the major tasks in database systems as well as artificial intelligence systems is to express some know...
Efficient Global Probabilistic Deduction from Taxonomic and Probabilistic KnowledgeBases over Conjunctive Events
 In Proceedings CIKM97
, 1997
"... We present a new, efficient linear programming approach to probabilistic deduction from probabilistic knowledgebases over conjunctive events. We show that this approach enables us to solve the classical problem of probabilistic deduction along a chain of basic events in polynomial time in the lengt ..."
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Cited by 11 (6 self)
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We present a new, efficient linear programming approach to probabilistic deduction from probabilistic knowledgebases over conjunctive events. We show that this approach enables us to solve the classical problem of probabilistic deduction along a chain of basic events in polynomial time in the length of the chain. We then elaborate how taxonomic knowledge can be exploited in our new approach for an increased efficiency. We also present important new results for the classical linear programming approach to probabilistic deduction under taxonomic knowledge. 1 Introduction There are many approaches to nonBayesian probabilistic deduction in the literature. They can be classified in global techniques based on linear programming and in local methods founded on the iterative application of inference rules. NonBayesian probabilistic deduction by solving linear programs is discussed e.g. in [23], [13], [24], [17], [14], [2], [15], and [22]. It can be performed within rich probabilistic lang...
Magic Inference Rules for Probabilistic Deduction under Taxonomic Knowledge
 In Proc. of the 14th Conference on Uncertainty in Artificial Intelligence
, 1998
"... We present locally complete inference rules for probabilistic deduction from taxonomic and probabilistic knowledgebases over conjunctive events. Crucially, in contrast to similar inference rules in the literature, our inference rules are locally complete for conjunctive events and under additional ..."
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Cited by 8 (4 self)
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We present locally complete inference rules for probabilistic deduction from taxonomic and probabilistic knowledgebases over conjunctive events. Crucially, in contrast to similar inference rules in the literature, our inference rules are locally complete for conjunctive events and under additional taxonomic knowledge. We discover that our inference rules are extremely complex and that it is at first glance not clear at all where the deduced tightest bounds come from. Moreover, analyzing the global completeness of our inference rules, we find examples of globally very incomplete probabilistic deductions. More generally, we even show that all systems of inference rules for taxonomic and probabilistic knowledgebases over conjunctive events are globally incomplete. We conclude that probabilistic deduction by the iterative application of inference rules on interval restrictions for conditional probabilities, even though considered very promising in the literature so far, seems very limite...
Differential Constraints
, 2005
"... Differential constraints are a class of finite difference equations specified over functions from the powerset of a finite set into the reals. We characterize the implication problem for such constraints in terms of lattice decompositions, and give a sound and complete set of inference rules. We rel ..."
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Cited by 7 (3 self)
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Differential constraints are a class of finite difference equations specified over functions from the powerset of a finite set into the reals. We characterize the implication problem for such constraints in terms of lattice decompositions, and give a sound and complete set of inference rules. We relate differential constraints to a subclass of propositional logic formulas, allowing us to show that the implication problem is coNPcomplete. Furthermore, we apply the theory of differential constraints to the problem of concise representations in the frequent itemset problem by linking differential constraints to disjunctive rules. We also establish a connection to relational databases by associating differential constraints to positive boolean dependencies.
Uncertain Reasoning in Concept Lattices
 In Proc. of the 3 rd European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, volume 946 of LNCS/LNAI
, 1995
"... . This paper presents concept lattices as a natural representation of class hierarchies in objectoriented databases and frame based knowledge representations. We show how to extend concept lattices by uncertainty in the form of conditional probabilities. We illustrate that uncertain reasoning withi ..."
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Cited by 5 (4 self)
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. This paper presents concept lattices as a natural representation of class hierarchies in objectoriented databases and frame based knowledge representations. We show how to extend concept lattices by uncertainty in the form of conditional probabilities. We illustrate that uncertain reasoning within the hierarchical structure of concept lattices can be performed efficiently and makes uncertain conclusions more precise. 1 Introduction The aim of this paper is to integrate uncertainty into class hierarchies of objectoriented databases and frame based knowledge representations. Extensional subclass relationships and disjointness statements are characteristic of class hierarchies. They can naturally be represented by concept lattices (see e.g. [14]). A concept is a pair consisting of a set of objects and a set of properties that all these objects share. The concept order is based on a coupled extensional and intensional order. For our purpose it is sufficient to concentrate just on the...