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Jef Wijsen

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Arnab Bhattacharya

IIT Kanpur

Vasant G Honavar

Pennsylvania State University

Cardiff University

Mohammad Shojafar

University of Surrey

Willeke Wendrich

University of California, Los Angeles

Annajiat Alim Rasel

BRAC University

Carlo Bianchini

University of Pavia

László Lovrics

Corvinus University of Budapest

Jakarta State Islamic University

Dag I K Sjoberg

University of Oslo

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Papers by Jef Wijsen

Temporal Dependencies

Consistent Query Answering for Primary Keys in Logspace

ArXiv, 2019

We study the complexity of consistent query answering on databases that may violate primary key c... more We study the complexity of consistent query answering on databases that may violate primary key constraints. A repair of such a database is any consistent database that can be obtained by deleting a minimal set of tuples. For every Boolean query q, CERTAINTY(q) is the problem that takes a database as input and asks whether q evaluates to true on every repair. In [KW17], the authors show that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either in P or coNP-complete, and it is decidable which of the two cases applies. In this paper, we sharpen this result by showing that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either expressible in symmetric stratified Datalog or coNP-complete. Since symmetric stratified Datalog is in L, we thus obtain a complexity-theoretic dichotomy between L and coNP-complete. Another new finding of practical importance is that CERTAINTY(q) is on the logspace side of the dichotomy for qu...

Connecting Databases and Ontologies: A Data Quality Perspective

Taking a database-theoretic perspective on the problem of mapping relational databases to ontolog... more Taking a database-theoretic perspective on the problem of mapping relational databases to ontologies, we come up with a new mapping language that is inspired by the semijoin algebra. We illustrate the user friendliness of the mapping language by examples, and prove the decidability of some important reasoning problems by embedding our mapping language into the guarded fragment of first-order logic. We argue that these reasoning problems are relevant in data quality explorations.

Logic-Based Ranking of Assertions in Inconsistent ABoxes

This paper concerns the problem of inconsistency in knowledge bases caused by ABox assertions. If... more This paper concerns the problem of inconsistency in knowledge bases caused by ABox assertions. If such inconsistency occurs, users may be asked to rate the truthfulness of one or more ABox assertions. A potential difficulty is that users may not well understand how different ABox assertions interact (and possibly conflict) with one another through the TBox axioms. We therefore introduce a principled framework that uses TBox axioms for inferring positive and negative support for ABox assertions. This leads to a system of linear equations whose solution enhances the user’s truthfulness rating by means of logical information from the TBox.

First-Order Rewritability in Consistent Query Answering with Respect to Multiple Keys

Proceedings of the 39th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, 2020

We study consistent query answering with respect to key dependencies. Given a (possibly inconsist... more We study consistent query answering with respect to key dependencies. Given a (possibly inconsistent) database instance and a set of key dependencies, a repair is an inclusion-maximal subinstance that satisfies all key dependencies. Consistent query answering for a Boolean query is the following problem: given a database instance as input, is the query true in every repair? In [Koutris and Wijsen, ICDT 2019], it was shown that for every self-join-free Boolean conjunctive query and set of key dependencies containing exactly one key dependency per relation name (also called the primary key), this problem is in FO, L-complete, or coNP-complete, and it is decidable which of the three cases applies. In this paper, we consider the more general case where a relation name can be associated with more than one key dependency. It is shown that in this more general setting, it remains decidable whether or not the above problem is in FO, for self-join-free Boolean conjunctive queries. Moreover, it is possible to effectively construct a first-order query that solves the problem whenever such a query exists. CCS CONCEPTS • Information systems → Relational database query languages; • Theory of computation → Incomplete, inconsistent, and uncertain databases; Logic and databases.

Consistent Query Answering for Primary Keys and Conjunctive Queries with Negated Atoms

Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, 2018

This paper studies query answering on databases that may be inconsistent with respect to primary ... more This paper studies query answering on databases that may be inconsistent with respect to primary key constraints. A repair is any consistent database that is obtained by deleting a minimal set of tuples. Given a Boolean query q, the problem CERTAINTY(q) takes a database as input and asks whether q is true in every repair of the database. A significant complexity classification task is to determine, given q, whether CERTAINTY(q) is first-order definable (and thus solvable by a single SQL query). This problem has been extensively studied for self-join-free conjunctive queries. An important extension of this class of queries is to allow negated atoms. It turns out that if negated atoms are allowed, CERTAINTY(q) can express some classical matching problems. This paper studies the existence and construction of first-order definitions for CERTAINTY(q) for q in the class of self-join-free conjunctive queries with negated atoms. CCS CONCEPTS • Information systems → Relational database query languages; • Theory of computation → Logic and databases; Incomplete, inconsistent, and uncertain databases;

Consistent Query Answering for Primary Keys in Datalog

Theory of Computing Systems, 2020

We study the complexity of consistent query answering on databases that may violate primary key c... more We study the complexity of consistent query answering on databases that may violate primary key constraints. A repair of such a database is any consistent database that can be obtained by deleting a minimal set of tuples. For every Boolean query q, CERTAINTY(q) is the problem that takes a database as input and asks whether q evaluates to true on every repair. In Koutris and Wijsen (ACM Trans. Database Syst. 42(2), 9:1-9:45, 2017), the authors show that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either in P or coNP-complete, and it is decidable which of the two cases applies. In this article, we sharpen this result by showing that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either expressible in symmetric stratified Datalog (with some aggregation operator) or coNP-complete. Since symmetric stratified Datalog is in L, we thus obtain a complexity-theoretic dichotomy between L and coNPcomplete. Another new finding of practical importance is that CERTAINTY(q) is on the logspace side of the dichotomy for queries q where all join conditions express foreign-to-primary key matches, which is undoubtedly the most common type of join condition.

Consistent Query Answering for Primary Keys

ACM SIGMOD Record, 2016

We study the complexity of consistent query answering with respect to primary key violations, for... more We study the complexity of consistent query answering with respect to primary key violations, for self-join-free conjunctive queries. A repair of a possibly inconsistent database is obtained by selecting a maximal number of tuples without selecting two distinct tuples with the same primary key value. For any Boolean query q, CERTAINTY(q) is the problem that takes a database as input, and asks whether q is true in every repair of the database. The complexity of this problem has been extensively studied for q ranging over the class of self-join-free Boolean conjunctive queries. A research challenge is to determine, given q, whether CERTAINTY(q) belongs to complexity classes FO, P, or coNP-complete. We show that for any self-join-free Boolean conjunctive query q, it can be decided whether or not CERTAINTY(q) is in FO. Further, CERTAINTY(q) is either in P or coNP-complete, and the complexity dichotomy is effective. This settles a research question of practical relevance that has been op...

First-Order Under-Approximations of Consistent Query Answers

Lecture Notes in Computer Science, 2015

On Condensing Database Repairs Obtained by Tuple Deletions

16th International Workshop on Database and Expert Systems Applications (DEXA'05)

Counting database repairs that satisfy conjunctive queries with self-joins

An uncertain database is defined as a relational database in which primary keys need not be satis... more An uncertain database is defined as a relational database in which primary keys need not be satisfied. A block is a maximal subset of tuples of the same relation that agree on the primary key. A repair (or possible world) of an uncertain database is obtained by selecting exactly one tuple from each block. From a probabilistic database perspective, an uncertain database is a restricted kind of block-independent disjoint (BID) probabilistic database, where the restriction is that the probabilities of tuples in a block are equal and ...

The Data Complexity of Consistent Query Answering for Self-Join-Free Conjunctive Queries Under Primary Key Constraints

Proceedings of the 34th ACM Symposium on Principles of Database Systems - PODS '15, 2015

A relational database is said to be uncertain if primary key constraints can possibly be violated... more A relational database is said to be uncertain if primary key constraints can possibly be violated. A repair (or possible world) of an uncertain database is obtained by selecting a maximal number of tuples without ever selecting two distinct tuples with the same primary key value. For any Boolean query q, CERTAINTY(q) is the problem that takes an uncertain database db as input, and asks whether q is true in every repair of db. The complexity of this problem has been particularly studied for q ranging over the class of self-join-free Boolean conjunctive queries. A research challenge is to determine, given q, whether CERTAINTY(q) belongs to complexity classes FO, P, or coNP-complete. In this paper, we combine existing techniques for studying the above complexity classification task. We show that for any self-join-free Boolean conjunctive query q, it can be decided whether or not CERTAINTY(q) is in FO. Further, for any self-join-free Boolean conjunctive query q, CERTAINTY(q) is either in P or coNP-complete, and the complexity dichotomy is effective. This settles a research question that has been open for ten years.

A Survey of the Data Complexity of Consistent Query Answering under Key Constraints

Lecture Notes in Computer Science, 2014

This paper adopts a very elementary representation of uncertainty. A relational database is calle... more This paper adopts a very elementary representation of uncertainty. A relational database is called uncertain if it can violate primary key constraints. A repair of an uncertain database is obtained by selecting a maximal number of tuples without selecting two distinct tuples of the same relation that agree on their primary key. For any Boolean queryi¾?q, CERTAINTYq is the problem that takes an uncertain database db on input, and asks whether q is true in every repair of db. The complexity of these problems has been particularly studied for q ranging over the class of Boolean conjunctive queries. A research challenge is to solve the following complexity classification task: given q, determine whether CERTAINTYq belongs to complexity classes FO, P, or coNP-complete. The counting variant of CERTAINTYq, denoted $\sharp$ CERTAINTYq, asks to determine the exact number of repairs that satisfy q. This problem is related to query answering in probabilistic databases. This paper motivates the problems CERTAINTYq and $\sharp$ CERTAINTYq, surveys the progress made in the study of their complexity, and lists open problems. We also show a new result comparing complexity boundaries of both problems with one another.

Project-Join-Repair: An Approach to Consistent Query Answering Under Functional Dependencies

Lecture Notes in Computer Science, 2006

Consistent query answering is the term commonly used for the problem of answering queries on data... more Consistent query answering is the term commonly used for the problem of answering queries on databases that violate certain integrity constraints. We address this problem for universal relations that are inconsistent with respect to a set of functional dependencies. In order to obtain more meaningful repairs, we apply a project-join dependency prior to repairing by tuple deletion. A positive result is that the additional project-join can yield tractability of consistent query answering. This article extends [21] by providing theorem proofs.

Towards a Foundation of Data Currency

2011 Eighteenth International Symposium on Temporal Representation and Reasoning, 2011

Relation I equipped with a currency order ≺ such that: distinct tuples that agree on the primary ... more

On counting database repairs

Proceedings of the 4th International Workshop on Logic in Databases - LID '11, 2011

An uncertain database is defined as a relational database in which primary keys need not be satis... more An uncertain database is defined as a relational database in which primary keys need not be satisfied. A block is a maximal subset of tuples of the same relation that agree on the primary key. A repair (or possible world) of an uncertain database is obtained by selecting exactly one tuple from each block. From a probabilistic database perspective, an uncertain database is a restricted kind of block-independent disjoint (BID) probabilistic database, where the restriction is that the probabilities of tuples in a block are equal and sum up to one. For every fixed Boolean query q, the counting problem ♮CERTAINTY(q) takes as input an uncertain database db and asks to determine the number of repairs that satisfy q. A Boolean conjunctive query is self-join-free if no relation name occurs more than once in it. In previous work, it was proved that for every self-join-free Boolean conjunctive query q, the problem ♮CERTAINTY(q) is either in FP or ♮P-complete, and it is decidable which of the two cases applies. This complexity dichotomy has its analogue in BID probabilistic databases. The current paper investigates the complexity of the problem ♮CERTAINTY(q) for Boolean conjunctive queries with self-joins. Our most appealing result is that for every Boolean conjunctive query q (possibly with self-joins) in which all primary keys consist of a single attribute, ♮CERTAINTY(q) is either in FP or ♮P-complete, and it is decidable which of the two cases applies. Significantly, no analogous dichotomy for conjunctive queries with self-joins is known for BID probabilistic databases.

On First-Order Query Rewriting for Incomplete Database Histories

2009 16th International Symposium on Temporal Representation and Reasoning, 2009

Multiwords are defined as words in which single symbols can be replaced by nonempty sets of symbo... more Multiwords are defined as words in which single symbols can be replaced by nonempty sets of symbols. Such a set of symbols captures uncertainty about the exact symbol. Words are obtained from multiwords by selecting a single symbol from every set. A pattern is certain in a multiword W if it occurs in every word that can be obtained from W. For a given pattern, we are interested in finding a logic formula that recognizes the multiwords in which that pattern is certain. This problem can be seen as a special case of consistent query answering (CQA). We show how our results can be applied in CQA on database histories under primary key constraints. * A previous version of this article has been presented at the Workshop on Logic in Databases (LID 2008, http://conferenze.dei.polimi.it/lid2008/). This workshop had informal proceedings that were distributed only to the participants. cessive time points t 0 , t 1 , t 2 , t 3. The primary key Name is violated at times t 1 and t 2. t 0 Name Company Ed IBM t

On Monotone Data Mining Languages

Lecture Notes in Computer Science, 2002

We present a simple Data Mining Logic (DML) that can express common data mining tasks, like "Find... more We present a simple Data Mining Logic (DML) that can express common data mining tasks, like "Find Boolean association rules" or "Find inclusion dependencies." At the center of the paper is the problem of characterizing DML queries that are amenable to the levelwise search strategy used in the a-priori algorithm. We relate the problem to that of characterizing monotone first-order properties for finite models.

Discovering roll-up dependencies

Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '99, 1999

We introduce the problem of discovering functional determinacies that result from "rolling up" da... more We introduce the problem of discovering functional determinacies that result from "rolling up" data to a higher abstraction level. Such a determinacy is called a Roll-Up Dependency (RUD). An example RUD is: The probability that two files in the same directory have the same file extension, is greater than a specific number. We show the applicability of RUDs for OLAP and data mining. We consider the problem of mining RUDs that satisfy specified support and confidence thresholds. This problem is NP-hard in the number of attributes. We give an algorithm for this problem. Experimental results show that the algorithm uses linear time in the number of tuples of the input database.

Temporal Dependencies Generalized for Spatial and Other Dimensions

Lecture Notes in Computer Science, 1999

Recently, there has been a lot of interest in temporal granularity, and its applications in tempo... more Recently, there has been a lot of interest in temporal granularity, and its applications in temporal dependency theory and data mining. Generalization hierarchies used in multi-dimensional databases and OLAP serve a role similar to that of time granularity in temporal databases, but they also apply to non-temporal dimensions, like space. In this paper, we rst generalize temporal functional dependencies for non-temporal dimensions, which leads to the notion of roll-up dependency (RUD). We show the applicability of RUDs in conceptual modeling and data mining. We then indicate that the notion of time granularity used in temporal databases is generally more expressive than the generalization hierarchies in multi-dimensional databases, and show how this surplus expressiveness can be introduced in non-temporal dimensions, which leads to the formalism of RUD with negation (RUD :). A complete axiomatization for reasoning about RUD : is given.

Temporal Dependencies

Consistent Query Answering for Primary Keys in Logspace

ArXiv, 2019

We study the complexity of consistent query answering on databases that may violate primary key c... more We study the complexity of consistent query answering on databases that may violate primary key constraints. A repair of such a database is any consistent database that can be obtained by deleting a minimal set of tuples. For every Boolean query q, CERTAINTY(q) is the problem that takes a database as input and asks whether q evaluates to true on every repair. In [KW17], the authors show that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either in P or coNP-complete, and it is decidable which of the two cases applies. In this paper, we sharpen this result by showing that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either expressible in symmetric stratified Datalog or coNP-complete. Since symmetric stratified Datalog is in L, we thus obtain a complexity-theoretic dichotomy between L and coNP-complete. Another new finding of practical importance is that CERTAINTY(q) is on the logspace side of the dichotomy for qu...

Connecting Databases and Ontologies: A Data Quality Perspective

Taking a database-theoretic perspective on the problem of mapping relational databases to ontolog... more Taking a database-theoretic perspective on the problem of mapping relational databases to ontologies, we come up with a new mapping language that is inspired by the semijoin algebra. We illustrate the user friendliness of the mapping language by examples, and prove the decidability of some important reasoning problems by embedding our mapping language into the guarded fragment of first-order logic. We argue that these reasoning problems are relevant in data quality explorations.

Logic-Based Ranking of Assertions in Inconsistent ABoxes

This paper concerns the problem of inconsistency in knowledge bases caused by ABox assertions. If... more This paper concerns the problem of inconsistency in knowledge bases caused by ABox assertions. If such inconsistency occurs, users may be asked to rate the truthfulness of one or more ABox assertions. A potential difficulty is that users may not well understand how different ABox assertions interact (and possibly conflict) with one another through the TBox axioms. We therefore introduce a principled framework that uses TBox axioms for inferring positive and negative support for ABox assertions. This leads to a system of linear equations whose solution enhances the user’s truthfulness rating by means of logical information from the TBox.

First-Order Rewritability in Consistent Query Answering with Respect to Multiple Keys

Proceedings of the 39th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, 2020

We study consistent query answering with respect to key dependencies. Given a (possibly inconsist... more We study consistent query answering with respect to key dependencies. Given a (possibly inconsistent) database instance and a set of key dependencies, a repair is an inclusion-maximal subinstance that satisfies all key dependencies. Consistent query answering for a Boolean query is the following problem: given a database instance as input, is the query true in every repair? In [Koutris and Wijsen, ICDT 2019], it was shown that for every self-join-free Boolean conjunctive query and set of key dependencies containing exactly one key dependency per relation name (also called the primary key), this problem is in FO, L-complete, or coNP-complete, and it is decidable which of the three cases applies. In this paper, we consider the more general case where a relation name can be associated with more than one key dependency. It is shown that in this more general setting, it remains decidable whether or not the above problem is in FO, for self-join-free Boolean conjunctive queries. Moreover, it is possible to effectively construct a first-order query that solves the problem whenever such a query exists. CCS CONCEPTS • Information systems → Relational database query languages; • Theory of computation → Incomplete, inconsistent, and uncertain databases; Logic and databases.

Consistent Query Answering for Primary Keys and Conjunctive Queries with Negated Atoms

Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, 2018

This paper studies query answering on databases that may be inconsistent with respect to primary ... more This paper studies query answering on databases that may be inconsistent with respect to primary key constraints. A repair is any consistent database that is obtained by deleting a minimal set of tuples. Given a Boolean query q, the problem CERTAINTY(q) takes a database as input and asks whether q is true in every repair of the database. A significant complexity classification task is to determine, given q, whether CERTAINTY(q) is first-order definable (and thus solvable by a single SQL query). This problem has been extensively studied for self-join-free conjunctive queries. An important extension of this class of queries is to allow negated atoms. It turns out that if negated atoms are allowed, CERTAINTY(q) can express some classical matching problems. This paper studies the existence and construction of first-order definitions for CERTAINTY(q) for q in the class of self-join-free conjunctive queries with negated atoms. CCS CONCEPTS • Information systems → Relational database query languages; • Theory of computation → Logic and databases; Incomplete, inconsistent, and uncertain databases;

Consistent Query Answering for Primary Keys in Datalog

Theory of Computing Systems, 2020

We study the complexity of consistent query answering on databases that may violate primary key c... more We study the complexity of consistent query answering on databases that may violate primary key constraints. A repair of such a database is any consistent database that can be obtained by deleting a minimal set of tuples. For every Boolean query q, CERTAINTY(q) is the problem that takes a database as input and asks whether q evaluates to true on every repair. In Koutris and Wijsen (ACM Trans. Database Syst. 42(2), 9:1-9:45, 2017), the authors show that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either in P or coNP-complete, and it is decidable which of the two cases applies. In this article, we sharpen this result by showing that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either expressible in symmetric stratified Datalog (with some aggregation operator) or coNP-complete. Since symmetric stratified Datalog is in L, we thus obtain a complexity-theoretic dichotomy between L and coNPcomplete. Another new finding of practical importance is that CERTAINTY(q) is on the logspace side of the dichotomy for queries q where all join conditions express foreign-to-primary key matches, which is undoubtedly the most common type of join condition.

Consistent Query Answering for Primary Keys

ACM SIGMOD Record, 2016

We study the complexity of consistent query answering with respect to primary key violations, for... more We study the complexity of consistent query answering with respect to primary key violations, for self-join-free conjunctive queries. A repair of a possibly inconsistent database is obtained by selecting a maximal number of tuples without selecting two distinct tuples with the same primary key value. For any Boolean query q, CERTAINTY(q) is the problem that takes a database as input, and asks whether q is true in every repair of the database. The complexity of this problem has been extensively studied for q ranging over the class of self-join-free Boolean conjunctive queries. A research challenge is to determine, given q, whether CERTAINTY(q) belongs to complexity classes FO, P, or coNP-complete. We show that for any self-join-free Boolean conjunctive query q, it can be decided whether or not CERTAINTY(q) is in FO. Further, CERTAINTY(q) is either in P or coNP-complete, and the complexity dichotomy is effective. This settles a research question of practical relevance that has been op...

First-Order Under-Approximations of Consistent Query Answers

Lecture Notes in Computer Science, 2015

On Condensing Database Repairs Obtained by Tuple Deletions

16th International Workshop on Database and Expert Systems Applications (DEXA'05)

Counting database repairs that satisfy conjunctive queries with self-joins

An uncertain database is defined as a relational database in which primary keys need not be satis... more An uncertain database is defined as a relational database in which primary keys need not be satisfied. A block is a maximal subset of tuples of the same relation that agree on the primary key. A repair (or possible world) of an uncertain database is obtained by selecting exactly one tuple from each block. From a probabilistic database perspective, an uncertain database is a restricted kind of block-independent disjoint (BID) probabilistic database, where the restriction is that the probabilities of tuples in a block are equal and ...

The Data Complexity of Consistent Query Answering for Self-Join-Free Conjunctive Queries Under Primary Key Constraints

Proceedings of the 34th ACM Symposium on Principles of Database Systems - PODS '15, 2015

A relational database is said to be uncertain if primary key constraints can possibly be violated... more A relational database is said to be uncertain if primary key constraints can possibly be violated. A repair (or possible world) of an uncertain database is obtained by selecting a maximal number of tuples without ever selecting two distinct tuples with the same primary key value. For any Boolean query q, CERTAINTY(q) is the problem that takes an uncertain database db as input, and asks whether q is true in every repair of db. The complexity of this problem has been particularly studied for q ranging over the class of self-join-free Boolean conjunctive queries. A research challenge is to determine, given q, whether CERTAINTY(q) belongs to complexity classes FO, P, or coNP-complete. In this paper, we combine existing techniques for studying the above complexity classification task. We show that for any self-join-free Boolean conjunctive query q, it can be decided whether or not CERTAINTY(q) is in FO. Further, for any self-join-free Boolean conjunctive query q, CERTAINTY(q) is either in P or coNP-complete, and the complexity dichotomy is effective. This settles a research question that has been open for ten years.

A Survey of the Data Complexity of Consistent Query Answering under Key Constraints

Lecture Notes in Computer Science, 2014

This paper adopts a very elementary representation of uncertainty. A relational database is calle... more This paper adopts a very elementary representation of uncertainty. A relational database is called uncertain if it can violate primary key constraints. A repair of an uncertain database is obtained by selecting a maximal number of tuples without selecting two distinct tuples of the same relation that agree on their primary key. For any Boolean queryi¾?q, CERTAINTYq is the problem that takes an uncertain database db on input, and asks whether q is true in every repair of db. The complexity of these problems has been particularly studied for q ranging over the class of Boolean conjunctive queries. A research challenge is to solve the following complexity classification task: given q, determine whether CERTAINTYq belongs to complexity classes FO, P, or coNP-complete. The counting variant of CERTAINTYq, denoted $\sharp$ CERTAINTYq, asks to determine the exact number of repairs that satisfy q. This problem is related to query answering in probabilistic databases. This paper motivates the problems CERTAINTYq and $\sharp$ CERTAINTYq, surveys the progress made in the study of their complexity, and lists open problems. We also show a new result comparing complexity boundaries of both problems with one another.

Project-Join-Repair: An Approach to Consistent Query Answering Under Functional Dependencies

Lecture Notes in Computer Science, 2006

Consistent query answering is the term commonly used for the problem of answering queries on data... more Consistent query answering is the term commonly used for the problem of answering queries on databases that violate certain integrity constraints. We address this problem for universal relations that are inconsistent with respect to a set of functional dependencies. In order to obtain more meaningful repairs, we apply a project-join dependency prior to repairing by tuple deletion. A positive result is that the additional project-join can yield tractability of consistent query answering. This article extends [21] by providing theorem proofs.

Towards a Foundation of Data Currency

2011 Eighteenth International Symposium on Temporal Representation and Reasoning, 2011

Relation I equipped with a currency order ≺ such that: distinct tuples that agree on the primary ... more

On counting database repairs

Proceedings of the 4th International Workshop on Logic in Databases - LID '11, 2011

An uncertain database is defined as a relational database in which primary keys need not be satis... more An uncertain database is defined as a relational database in which primary keys need not be satisfied. A block is a maximal subset of tuples of the same relation that agree on the primary key. A repair (or possible world) of an uncertain database is obtained by selecting exactly one tuple from each block. From a probabilistic database perspective, an uncertain database is a restricted kind of block-independent disjoint (BID) probabilistic database, where the restriction is that the probabilities of tuples in a block are equal and sum up to one. For every fixed Boolean query q, the counting problem ♮CERTAINTY(q) takes as input an uncertain database db and asks to determine the number of repairs that satisfy q. A Boolean conjunctive query is self-join-free if no relation name occurs more than once in it. In previous work, it was proved that for every self-join-free Boolean conjunctive query q, the problem ♮CERTAINTY(q) is either in FP or ♮P-complete, and it is decidable which of the two cases applies. This complexity dichotomy has its analogue in BID probabilistic databases. The current paper investigates the complexity of the problem ♮CERTAINTY(q) for Boolean conjunctive queries with self-joins. Our most appealing result is that for every Boolean conjunctive query q (possibly with self-joins) in which all primary keys consist of a single attribute, ♮CERTAINTY(q) is either in FP or ♮P-complete, and it is decidable which of the two cases applies. Significantly, no analogous dichotomy for conjunctive queries with self-joins is known for BID probabilistic databases.

On First-Order Query Rewriting for Incomplete Database Histories

2009 16th International Symposium on Temporal Representation and Reasoning, 2009

Multiwords are defined as words in which single symbols can be replaced by nonempty sets of symbo... more Multiwords are defined as words in which single symbols can be replaced by nonempty sets of symbols. Such a set of symbols captures uncertainty about the exact symbol. Words are obtained from multiwords by selecting a single symbol from every set. A pattern is certain in a multiword W if it occurs in every word that can be obtained from W. For a given pattern, we are interested in finding a logic formula that recognizes the multiwords in which that pattern is certain. This problem can be seen as a special case of consistent query answering (CQA). We show how our results can be applied in CQA on database histories under primary key constraints. * A previous version of this article has been presented at the Workshop on Logic in Databases (LID 2008, http://conferenze.dei.polimi.it/lid2008/). This workshop had informal proceedings that were distributed only to the participants. cessive time points t 0 , t 1 , t 2 , t 3. The primary key Name is violated at times t 1 and t 2. t 0 Name Company Ed IBM t

On Monotone Data Mining Languages

Lecture Notes in Computer Science, 2002

We present a simple Data Mining Logic (DML) that can express common data mining tasks, like "Find... more We present a simple Data Mining Logic (DML) that can express common data mining tasks, like "Find Boolean association rules" or "Find inclusion dependencies." At the center of the paper is the problem of characterizing DML queries that are amenable to the levelwise search strategy used in the a-priori algorithm. We relate the problem to that of characterizing monotone first-order properties for finite models.

Discovering roll-up dependencies

Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '99, 1999

We introduce the problem of discovering functional determinacies that result from "rolling up" da... more We introduce the problem of discovering functional determinacies that result from "rolling up" data to a higher abstraction level. Such a determinacy is called a Roll-Up Dependency (RUD). An example RUD is: The probability that two files in the same directory have the same file extension, is greater than a specific number. We show the applicability of RUDs for OLAP and data mining. We consider the problem of mining RUDs that satisfy specified support and confidence thresholds. This problem is NP-hard in the number of attributes. We give an algorithm for this problem. Experimental results show that the algorithm uses linear time in the number of tuples of the input database.

Temporal Dependencies Generalized for Spatial and Other Dimensions

Lecture Notes in Computer Science, 1999

Recently, there has been a lot of interest in temporal granularity, and its applications in tempo... more Recently, there has been a lot of interest in temporal granularity, and its applications in temporal dependency theory and data mining. Generalization hierarchies used in multi-dimensional databases and OLAP serve a role similar to that of time granularity in temporal databases, but they also apply to non-temporal dimensions, like space. In this paper, we rst generalize temporal functional dependencies for non-temporal dimensions, which leads to the notion of roll-up dependency (RUD). We show the applicability of RUDs in conceptual modeling and data mining. We then indicate that the notion of time granularity used in temporal databases is generally more expressive than the generalization hierarchies in multi-dimensional databases, and show how this surplus expressiveness can be introduced in non-temporal dimensions, which leads to the formalism of RUD with negation (RUD :). A complete axiomatization for reasoning about RUD : is given.