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Papers by magdalena ortiz

Answer Set Programming: Advances in Theory and Implementation ASP’05, Jul 1, 2005

In this paper we consider an extension of the answer set semantics allowing arbitrary use of stro... more In this paper we consider an extension of the answer set semantics allowing arbitrary use of strong negation. We prove that the strong negation extension of any intermediate logic provides a suitable basis for reasoning under the answer set semantics. We propose two new notions of equivalence that are more general than strong equivalence: substitution equivalence and contextualized equivalence.

In many applications of Description Logic (DL) ontologies, complete information—e.g., stemming fr... more In many applications of Description Logic (DL) ontologies, complete information—e.g., stemming from relational databases—interacts with incomplete knowledge. Closed predicates allow to leverage information completeness within the standard open-world semantics of DLs. In this paper we study the (combined) complexity of query answering in the presence of closed predicates, establishing tight complexity results for a range of DLs and query languages. Our results show that consistency testing and instance query answering in the presence of closed predicates is NP-complete even for rich dialects of the DL-Lite family. For EL, in contrast, they are EXPTIME-complete, thus as hard as for ALC and some of its extensions. If (unions of) conjunctive queries (UCQs) are considered, the picture is rather bleak, as 2EXPTIME-hardness holds even for DL-LiteR and EL. Our results also imply 2EXPTIME-hardness of query answering in ALCO for the standard open-world setting. Despite these negative results,...

The goal of this paper is to understand the relative expressiveness of the query language in whic... more The goal of this paper is to understand the relative expressiveness of the query language in which queries are specified by a set of guarded (disjunctive) tuple-generating dependencies (TGDs) and an output (or 'answer') predicate. Our main result is to show that every such query can be translated into a polynomially-sized (disjunctive) Datalog program if the maximal number of variables in the (disjunctive) TGDs is bounded by a constant. To overcome the challenge that Datalog has no direct means to express the existential quantification present in TGDs, we define a two-player game that characterizes the satisfaction of the dependencies, and design a Datalog query that can decide the existence of a winning strategy for the game. For guarded disjunctive TGDs, we can obtain Datalog rules with disjunction in the heads. However, the use of disjunction is limited, and the resulting rules fall into a fragment that can be evaluated in deterministic single exponential time. We proceed...

Description Logics, 2017

Answer Set Programming (ASP) and ontology languages like Description Logics (DLs) play leading ro... more Answer Set Programming (ASP) and ontology languages like Description Logics (DLs) play leading roles in Knowledge Representation and Reasoning (KR&R). ASP and DLs have largely orthogonal features because they make very different assumptions regarding the completeness of information, and thus reasoning techniques and algorithms that are deployed in ASP are significantly different from the ones used in DLs. Combining ASP, which makes the closed-world assumption (CWA), with DLs, which make the open-world assumption (OWA), into expressive hybrid languages that would enjoy the positive features of both has received significant attention in the last decade (see, e.g., [23, 24, 7, 20, 19]). However, progress on understanding the relationship between different hybrid languages, and their relationship with more standard languages like plain ASP, has been limited, as has the development of efficient reasoning algorithms and implementations. These and related problems are investigated in this ...

The Shape Constraint Language (SHACL) was recently standardized by the W3C as a formalism for che... more The Shape Constraint Language (SHACL) was recently standardized by the W3C as a formalism for checking the quality of RDF graphs; we refer to [7] for an introduction. In SHACL, the main problem is to check whether a given RDF graph G validates a SHACL document (C, T ), where C is a set of constraints, also called shapes graph, each associated to a so-called shape name, and T (targets) is a specification of nodes from the data graph which should validate certain shapes from C. For illustration, consider a graph G = {enrolledIn(Ben,C1)} and a SHACL document (C, T ), where C = {Student ↔ ∃enrolledIn.Course}, and T is the shape atom Student(Ben). The constraint states that each Student must be enrolled in some course; Student is a shape name, and enrolledIn and Course are data predicates, i.e., property and class name, respectively. Clearly, G does not validate (C, T ), but the extended graph G′ = G∪{Course(C1)} does. The standard specifies a syntax for expressing SHACL constraints and ...

In this paper, we introduce a navigational query language that extends binary frontier-guarded Da... more In this paper, we introduce a navigational query language that extends binary frontier-guarded Datalog by allowing regular expressions in rule bodies and a limited use of higher-arity intensional predicates. Our query language strictly extends conjunctive two-way regular path queries (C2RPQs) and captures some of the key features advocated in recent works aimed at extending C2RPQs. We compare our language to existing proposals and establish decidability with elementary complexity of query evaluation in the presence of ontologies.

International Joint Conference on Artificial Intelligence, Jul 16, 2011

Query containment has been studied extensively in KR and databases, for different kinds of query ... more Query containment has been studied extensively in KR and databases, for different kinds of query languages and domain constraints. We address the longstanding open problem of containment under expressive description logic (DL) constraints for two-way regular path queries (2RPQs) and their conjunctions, which generalize conjunctive queries with the ability to express regular navigation. We show that, surprisingly, functionality constraints alone make containment of 2RPQs already EXPTIME-hard. By employing automatatheoretic techniques, we also provide a matching upper bound that extends to very expressive DL constraints. For conjunctive 2RPQs we prove a further exponential jump in complexity, and provide again a matching upper bound for expressive DLs. Our techniques provide also a solution to the problem of query entailment over DL knowledge bases in which individuals in the ABox may be related through regular role-paths.

In this work we describe the theoretical foundations and the implementation of a new automata-bas... more In this work we describe the theoretical foundations and the implementation of a new automata-based technique for reasoning over expressive Description Logics that is worst-case optimal and lends itself to an efficient implementation. In order to show the feasibility of the approach, we have realized a working prototype of a reasoner based upon these techniques. An experimental evaluation of this prototype shows encouraging results.

Lecture Notes in Computer Science, 2009

In the recent years, query answering over Description Logic (DL) knowledge bases has been receivi... more In the recent years, query answering over Description Logic (DL) knowledge bases has been receiving increasing attention, and various methods and techniques have been presented for this problem. In this paper, we consider knots, which are an instance of the mosaic technique from Modal Logic. When annotated with suitable query information, knots are a flexible tool for query answering that allows for solving the problem in a simple and intuitive way. The knot approach yields optimal complexity bounds, as we illustrate on the DLs ALCH and ALCHI, and can be easily extended to accommodate other constructs.

Lecture Notes in Computer Science

We provide an ExpTime algorithm for answering conjunc- tive queries (CQs) in Horn-SHIQ, a Horn fr... more We provide an ExpTime algorithm for answering conjunc- tive queries (CQs) in Horn-SHIQ, a Horn fragment of the well-known Description Logic SHIQ underlying the OWL-Lite standard. The al- gorithm employs a domino system for model representation, which is constructed via a worst-case optimal tableau algorithm for Horn-SHIQ; the queries are answered by reasoning over the domino system. Our al- gorithm

Lecture Notes in Computer Science

The deployment of Description Logics (DLs) and Answer Set Programming (ASP), which are well-known... more The deployment of Description Logics (DLs) and Answer Set Programming (ASP), which are well-known knowledge representation and reasoning formalisms, to a growing range of applications has created the need for novel reasoning algorithms and methods. Recently, knots have been introduced as a tool to facilitate reasoning tasks in extensions of ASP with functions symbols. They were then also fruitfully applied for query answering in Description Logics, hinging on the forest-shaped model property of knowledge bases. This paper ...

Journal of Computer and System Sciences, 2012

Answering conjunctive queries (CQs) has been recognized as an important task for the widening use... more Answering conjunctive queries (CQs) has been recognized as an important task for the widening use of Description Logics (DLs) in a number of applications. The problem has been studied by many authors, who developed a number of different techniques for its solution. We present a novel method for CQ answering based on knots, which are schematic subtrees of depth at most one. The method yields an algorithm for CQ answering in the DL SH which handles CQs with distinguished (i.e., output) variables in a direct manner. It proceeds by first compiling the knowledge base into a set of knots, and then constructing a set of simple knowledge bases, which contain only assertional data, over which a given query is answered. Notably, the knot compilation can be reused for varying queries and is amenable to an implementation in disjunctive Datalog. The algorithm works in double exponential time in general but in single exponential time under various restrictions on the occurrence of transitive roles in queries, including CQ answering in the DL ALCH. The results are worst-case optimal, given that CQ answering is 2EXPTIME-complete for SH and EXPTIME-hard already for the core expressive DL ALC. In particular, the result for ALCH reconfirms Lutz's result that adding inverse roles to ALC causes an exponential jump in complexity, while adding role hierarchies does not. Furthermore, a nondeterministic version of our algorithm runs in CONP under data complexity, which is worst-case optimal in this setting as well.

Information and Computation, 2014

Automata on infinite trees Expressive Description Logics (DLs) have been advocated as formalisms ... more Automata on infinite trees Expressive Description Logics (DLs) have been advocated as formalisms for modeling the domain of interest in various application areas, including the Semantic Web, data and information integration, peer-to-peer data management, and ontology-based data access. An important requirement there is the ability to answer complex queries beyond instance retrieval, taking into account constraints expressed in a knowledge base. We consider this task for positive 2-way regular path queries (P2RPQs) over knowledge bases in the expressive DL ZIQ. P2RPQs are more general than conjunctive queries, union of conjunctive queries, and regular path queries from the literature. They allow regular expressions over roles and data joins that require inverse paths. The DL ZIQ extends the core DL ALC with qualified number restrictions, inverse roles, safe Boolean role expressions, regular expressions over roles, and concepts of the form ∃S.Self in the style of the DL SRIQ. Using techniques based on two-way tree-automata, we first provide as a stepping stone an elegant characterization of TBox and ABox satisfiability testing which gives us a tight ExpTime bound for this problem (under unary number encoding). We then establish a double exponential upper bound for answering P2RPQs over ZIQ knowledge bases; this bound is tight. Our result significantly pushes the frontier of 2ExpTime decidability of query answering in expressive DLs, both with respect to the query language and the considered DL. Furthermore, by reducing the well known DL SRIQ to ZIQ (with an exponential blow-up in the size of the knowledge base), we also provide a tight 2ExpTime upper bound for knowledge base satisfiability in SRIQ and establish the decidability of query answering for this significant fragment of the new OWL 2 standard.

In order to meet usability requirements, most logic-based applications provide explanation facili... more In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for DLs, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for (conjunctive) query answering over DL-Lite ontologies, by adopting abductive reasoning, that is, we look for ...

Description Logics, 2012

Query answering has become a prominent reasoning task in Description Logics. This is witnessed no... more Query answering has become a prominent reasoning task in Description Logics. This is witnessed not only by the high number of publications on the topic in the last decade, but also by the increasing number of query answering engines. A number of systems provide full conjunctive query (CQ) answering capabilities, including [1, 23, 25, 4, 11]. A common feature of these approaches is that they rely on existing technologies for relational or deductive databases. They focus on lightweight DLs like DL-Lite and EL, and they use query ...

Proc. of AAAI, Jul 13, 2008

Answering conjunctive queries (CQs) has been recognized as a key task for the usage of Descriptio... more Answering conjunctive queries (CQs) has been recognized as a key task for the usage of Description Logics (DLs) in a number of applications, and has thus been studied by many authors. In this paper, we present an algorithm for this problem in the DL ALCH which works in exponential time. It improves over previous algorithms which require double exponential time and is worst-case optimal, as already satisfiability testing in ALC is EXPTIME-complete. Furthermore, it shows that inverse roles cause an exponential jump in ...

Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI 2009), Jul 11, 2009

Reasoning over complex queries in the DLs underlying OWL 2 is of importance in several applicatio... more Reasoning over complex queries in the DLs underlying OWL 2 is of importance in several application domains. We provide decidability and (tight) upper bounds for the problem of checking entailment and containment of positive regular path queries under various combinations of constructs used in such expressive DLs; specifically: regular expressions and (safe) Booleans over roles, and allowing for the combination of any two constructs among inverse roles, qualified number restrictions, and nominals. Our results ...

Answer Set Programming: Advances in Theory and Implementation ASP’05, Jul 1, 2005

In this paper we consider an extension of the answer set semantics allowing arbitrary use of stro... more In this paper we consider an extension of the answer set semantics allowing arbitrary use of strong negation. We prove that the strong negation extension of any intermediate logic provides a suitable basis for reasoning under the answer set semantics. We propose two new notions of equivalence that are more general than strong equivalence: substitution equivalence and contextualized equivalence.

In many applications of Description Logic (DL) ontologies, complete information—e.g., stemming fr... more In many applications of Description Logic (DL) ontologies, complete information—e.g., stemming from relational databases—interacts with incomplete knowledge. Closed predicates allow to leverage information completeness within the standard open-world semantics of DLs. In this paper we study the (combined) complexity of query answering in the presence of closed predicates, establishing tight complexity results for a range of DLs and query languages. Our results show that consistency testing and instance query answering in the presence of closed predicates is NP-complete even for rich dialects of the DL-Lite family. For EL, in contrast, they are EXPTIME-complete, thus as hard as for ALC and some of its extensions. If (unions of) conjunctive queries (UCQs) are considered, the picture is rather bleak, as 2EXPTIME-hardness holds even for DL-LiteR and EL. Our results also imply 2EXPTIME-hardness of query answering in ALCO for the standard open-world setting. Despite these negative results,...

The goal of this paper is to understand the relative expressiveness of the query language in whic... more The goal of this paper is to understand the relative expressiveness of the query language in which queries are specified by a set of guarded (disjunctive) tuple-generating dependencies (TGDs) and an output (or 'answer') predicate. Our main result is to show that every such query can be translated into a polynomially-sized (disjunctive) Datalog program if the maximal number of variables in the (disjunctive) TGDs is bounded by a constant. To overcome the challenge that Datalog has no direct means to express the existential quantification present in TGDs, we define a two-player game that characterizes the satisfaction of the dependencies, and design a Datalog query that can decide the existence of a winning strategy for the game. For guarded disjunctive TGDs, we can obtain Datalog rules with disjunction in the heads. However, the use of disjunction is limited, and the resulting rules fall into a fragment that can be evaluated in deterministic single exponential time. We proceed...

Description Logics, 2017

Answer Set Programming (ASP) and ontology languages like Description Logics (DLs) play leading ro... more Answer Set Programming (ASP) and ontology languages like Description Logics (DLs) play leading roles in Knowledge Representation and Reasoning (KR&R). ASP and DLs have largely orthogonal features because they make very different assumptions regarding the completeness of information, and thus reasoning techniques and algorithms that are deployed in ASP are significantly different from the ones used in DLs. Combining ASP, which makes the closed-world assumption (CWA), with DLs, which make the open-world assumption (OWA), into expressive hybrid languages that would enjoy the positive features of both has received significant attention in the last decade (see, e.g., [23, 24, 7, 20, 19]). However, progress on understanding the relationship between different hybrid languages, and their relationship with more standard languages like plain ASP, has been limited, as has the development of efficient reasoning algorithms and implementations. These and related problems are investigated in this ...

The Shape Constraint Language (SHACL) was recently standardized by the W3C as a formalism for che... more The Shape Constraint Language (SHACL) was recently standardized by the W3C as a formalism for checking the quality of RDF graphs; we refer to [7] for an introduction. In SHACL, the main problem is to check whether a given RDF graph G validates a SHACL document (C, T ), where C is a set of constraints, also called shapes graph, each associated to a so-called shape name, and T (targets) is a specification of nodes from the data graph which should validate certain shapes from C. For illustration, consider a graph G = {enrolledIn(Ben,C1)} and a SHACL document (C, T ), where C = {Student ↔ ∃enrolledIn.Course}, and T is the shape atom Student(Ben). The constraint states that each Student must be enrolled in some course; Student is a shape name, and enrolledIn and Course are data predicates, i.e., property and class name, respectively. Clearly, G does not validate (C, T ), but the extended graph G′ = G∪{Course(C1)} does. The standard specifies a syntax for expressing SHACL constraints and ...

In this paper, we introduce a navigational query language that extends binary frontier-guarded Da... more In this paper, we introduce a navigational query language that extends binary frontier-guarded Datalog by allowing regular expressions in rule bodies and a limited use of higher-arity intensional predicates. Our query language strictly extends conjunctive two-way regular path queries (C2RPQs) and captures some of the key features advocated in recent works aimed at extending C2RPQs. We compare our language to existing proposals and establish decidability with elementary complexity of query evaluation in the presence of ontologies.

International Joint Conference on Artificial Intelligence, Jul 16, 2011

Query containment has been studied extensively in KR and databases, for different kinds of query ... more Query containment has been studied extensively in KR and databases, for different kinds of query languages and domain constraints. We address the longstanding open problem of containment under expressive description logic (DL) constraints for two-way regular path queries (2RPQs) and their conjunctions, which generalize conjunctive queries with the ability to express regular navigation. We show that, surprisingly, functionality constraints alone make containment of 2RPQs already EXPTIME-hard. By employing automatatheoretic techniques, we also provide a matching upper bound that extends to very expressive DL constraints. For conjunctive 2RPQs we prove a further exponential jump in complexity, and provide again a matching upper bound for expressive DLs. Our techniques provide also a solution to the problem of query entailment over DL knowledge bases in which individuals in the ABox may be related through regular role-paths.

In this work we describe the theoretical foundations and the implementation of a new automata-bas... more In this work we describe the theoretical foundations and the implementation of a new automata-based technique for reasoning over expressive Description Logics that is worst-case optimal and lends itself to an efficient implementation. In order to show the feasibility of the approach, we have realized a working prototype of a reasoner based upon these techniques. An experimental evaluation of this prototype shows encouraging results.

Lecture Notes in Computer Science, 2009

In the recent years, query answering over Description Logic (DL) knowledge bases has been receivi... more In the recent years, query answering over Description Logic (DL) knowledge bases has been receiving increasing attention, and various methods and techniques have been presented for this problem. In this paper, we consider knots, which are an instance of the mosaic technique from Modal Logic. When annotated with suitable query information, knots are a flexible tool for query answering that allows for solving the problem in a simple and intuitive way. The knot approach yields optimal complexity bounds, as we illustrate on the DLs ALCH and ALCHI, and can be easily extended to accommodate other constructs.

Lecture Notes in Computer Science

We provide an ExpTime algorithm for answering conjunc- tive queries (CQs) in Horn-SHIQ, a Horn fr... more We provide an ExpTime algorithm for answering conjunc- tive queries (CQs) in Horn-SHIQ, a Horn fragment of the well-known Description Logic SHIQ underlying the OWL-Lite standard. The al- gorithm employs a domino system for model representation, which is constructed via a worst-case optimal tableau algorithm for Horn-SHIQ; the queries are answered by reasoning over the domino system. Our al- gorithm

Lecture Notes in Computer Science

The deployment of Description Logics (DLs) and Answer Set Programming (ASP), which are well-known... more The deployment of Description Logics (DLs) and Answer Set Programming (ASP), which are well-known knowledge representation and reasoning formalisms, to a growing range of applications has created the need for novel reasoning algorithms and methods. Recently, knots have been introduced as a tool to facilitate reasoning tasks in extensions of ASP with functions symbols. They were then also fruitfully applied for query answering in Description Logics, hinging on the forest-shaped model property of knowledge bases. This paper ...

Journal of Computer and System Sciences, 2012

Answering conjunctive queries (CQs) has been recognized as an important task for the widening use... more Answering conjunctive queries (CQs) has been recognized as an important task for the widening use of Description Logics (DLs) in a number of applications. The problem has been studied by many authors, who developed a number of different techniques for its solution. We present a novel method for CQ answering based on knots, which are schematic subtrees of depth at most one. The method yields an algorithm for CQ answering in the DL SH which handles CQs with distinguished (i.e., output) variables in a direct manner. It proceeds by first compiling the knowledge base into a set of knots, and then constructing a set of simple knowledge bases, which contain only assertional data, over which a given query is answered. Notably, the knot compilation can be reused for varying queries and is amenable to an implementation in disjunctive Datalog. The algorithm works in double exponential time in general but in single exponential time under various restrictions on the occurrence of transitive roles in queries, including CQ answering in the DL ALCH. The results are worst-case optimal, given that CQ answering is 2EXPTIME-complete for SH and EXPTIME-hard already for the core expressive DL ALC. In particular, the result for ALCH reconfirms Lutz's result that adding inverse roles to ALC causes an exponential jump in complexity, while adding role hierarchies does not. Furthermore, a nondeterministic version of our algorithm runs in CONP under data complexity, which is worst-case optimal in this setting as well.

Information and Computation, 2014

Automata on infinite trees Expressive Description Logics (DLs) have been advocated as formalisms ... more Automata on infinite trees Expressive Description Logics (DLs) have been advocated as formalisms for modeling the domain of interest in various application areas, including the Semantic Web, data and information integration, peer-to-peer data management, and ontology-based data access. An important requirement there is the ability to answer complex queries beyond instance retrieval, taking into account constraints expressed in a knowledge base. We consider this task for positive 2-way regular path queries (P2RPQs) over knowledge bases in the expressive DL ZIQ. P2RPQs are more general than conjunctive queries, union of conjunctive queries, and regular path queries from the literature. They allow regular expressions over roles and data joins that require inverse paths. The DL ZIQ extends the core DL ALC with qualified number restrictions, inverse roles, safe Boolean role expressions, regular expressions over roles, and concepts of the form ∃S.Self in the style of the DL SRIQ. Using techniques based on two-way tree-automata, we first provide as a stepping stone an elegant characterization of TBox and ABox satisfiability testing which gives us a tight ExpTime bound for this problem (under unary number encoding). We then establish a double exponential upper bound for answering P2RPQs over ZIQ knowledge bases; this bound is tight. Our result significantly pushes the frontier of 2ExpTime decidability of query answering in expressive DLs, both with respect to the query language and the considered DL. Furthermore, by reducing the well known DL SRIQ to ZIQ (with an exponential blow-up in the size of the knowledge base), we also provide a tight 2ExpTime upper bound for knowledge base satisfiability in SRIQ and establish the decidability of query answering for this significant fragment of the new OWL 2 standard.

In order to meet usability requirements, most logic-based applications provide explanation facili... more In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for DLs, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for (conjunctive) query answering over DL-Lite ontologies, by adopting abductive reasoning, that is, we look for ...

Description Logics, 2012

Query answering has become a prominent reasoning task in Description Logics. This is witnessed no... more Query answering has become a prominent reasoning task in Description Logics. This is witnessed not only by the high number of publications on the topic in the last decade, but also by the increasing number of query answering engines. A number of systems provide full conjunctive query (CQ) answering capabilities, including [1, 23, 25, 4, 11]. A common feature of these approaches is that they rely on existing technologies for relational or deductive databases. They focus on lightweight DLs like DL-Lite and EL, and they use query ...

Proc. of AAAI, Jul 13, 2008

Answering conjunctive queries (CQs) has been recognized as a key task for the usage of Descriptio... more Answering conjunctive queries (CQs) has been recognized as a key task for the usage of Description Logics (DLs) in a number of applications, and has thus been studied by many authors. In this paper, we present an algorithm for this problem in the DL ALCH which works in exponential time. It improves over previous algorithms which require double exponential time and is worst-case optimal, as already satisfiability testing in ALC is EXPTIME-complete. Furthermore, it shows that inverse roles cause an exponential jump in ...

Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI 2009), Jul 11, 2009

Reasoning over complex queries in the DLs underlying OWL 2 is of importance in several applicatio... more Reasoning over complex queries in the DLs underlying OWL 2 is of importance in several application domains. We provide decidability and (tight) upper bounds for the problem of checking entailment and containment of positive regular path queries under various combinations of constructs used in such expressive DLs; specifically: regular expressions and (safe) Booleans over roles, and allowing for the combination of any two constructs among inverse roles, qualified number restrictions, and nominals. Our results ...