Search

We study the relative expressiveness of ontology-mediated queries (OMQs) formulated in the expressive Description Logic ALCHOIQ extended with closed predicates. In particular, we present a polynomial time translation from OMQs into Datalog with negation under the stable model semantics, the formalism that underlies Answer Set Programming. This is a novel and non-trivial result: the considered OMQs are not only non-monotonic, but also feature a tricky combination of nominals, inverse roles, and counting. We start with atomic queries and then lift our approach to a large class of first-order queries where quantification is “guarded” by closed predicates. Our translation is based on a characterization of the query answering problem via integer programming, and a specially crafted program in Datalog with negation that finds solutions to dynamically generated systems of integer inequalities. As an important by-product of our translation we get that the query answering problem is co-NP-complete in data complexity for the considered class of OMQs. Thus, answering these OMQs in the presence of closed predicates is not harder than answering them in the standard setting. This is not obvious as closed predicates are known to increase data complexity for some existing ontology languages.

We study the relative expressiveness of ontology-mediated queries (OMQs) formulated in the expressive Description Logic ALCHOIQ extended with closed predicates. In particular, we present a polynomial time translation from OMQs into Datalog with negation under the stable model semantics, the formalism that underlies Answer Set Programming. This is a novel and non-trivial result: the considered OMQs are not only non-monotonic, but also feature a tricky combination of nominals, inverse roles, and counting. We start with atomic queries and then lift our approach to a large class of first-order queries where quantification is “guarded” by closed predicates. Our translation is based on a characterization of the query answering problem via integer programming, and a specially crafted program in Datalog with negation that finds solutions to dynamically generated systems of integer inequalities. As an important by-product of our translation we get that the query answering problem is co-NP-complete in data complexity for the considered class of OMQs. Thus, answering these OMQs in the presence of closed predicates is not harder than answering them in the standard setting. This is not obvious as closed predicates are known to increase data complexity for some existing ontology languages.

Information modelling for databases and object-oriented information systems avails of conceptual data modelling languages such as EER and UML Class Diagrams. Many attempts exist to add logical rigour to them, for various reasons and with disparate strengths. In this paper we aim to provide a structured overview of the many efforts. We focus on aims, approaches to the formalisation, including key dimensions of choice points, popular logics used, and the main relevant reasoning services. We close with current challenges and research directions.

Motivated by an application where we try to make proofs for Description Logic inferences smaller by rewriting, we consider the following decision problem, which we call the small term reachability problem: given a term rewriting system R, a term s, and a natural number n, decide whether there is a term t of size ≤ n reachable from s using the rules of R. We investigate the complexity of this problem depending on how termination of R can be established. We show that the problem is NP-complete for length-reducing term rewriting systems. Its complexity increases to N2ExpTime-complete (NExpTime-complete) if termination is proved using a (linear) polynomial order and to PSpace-complete for systems whose termination can be shown using a restricted class of Knuth-Bendix orders. Confluence reduces the complexity to P for the length-reducing case, but has no effect on the worst-case complexity in the other two cases.

We study the relative expressiveness of ontology-mediated queries (OMQs) formulated in the expressive Description Logic ALCHOIQ extended with closed predicates. In particular, we present a polynomial time translation from OMQs into Datalog with negation under the stable model semantics, the formalism that underlies Answer Set Programming. This is a novel and non-trivial result: the considered OMQs are not only non-monotonic, but also feature a tricky combination of nominals, inverse roles, and counting. We start with atomic queries and then lift our approach to a large class of first-order queries where quantification is “guarded” by closed predicates. Our translation is based on a characterization of the query answering problem via integer programming, and a specially crafted program in Datalog with negation that finds solutions to dynamically generated systems of integer inequalities. As an important by-product of our translation we get that the query answering problem is co-NP-complete in data complexity for the considered class of OMQs. Thus, answering these OMQs in the presence of closed predicates is not harder than answering them in the standard setting. This is not obvious as closed predicates are known to increase data complexity for some existing ontology languages.

We study the relative expressiveness of ontology-mediated queries (OMQs) formulated in the expressive Description Logic ALCHOIQ extended with closed predicates. In particular, we present a polynomial time translation from OMQs into Datalog with negation under the stable model semantics, the formalism that underlies Answer Set Programming. This is a novel and non-trivial result: the considered OMQs are not only non-monotonic, but also feature a tricky combination of nominals, inverse roles, and counting. We start with atomic queries and then lift our approach to a large class of first-order queries where quantification is “guarded” by closed predicates. Our translation is based on a characterization of the query answering problem via integer programming, and a specially crafted program in Datalog with negation that finds solutions to dynamically generated systems of integer inequalities. As an important by-product of our translation we get that the query answering problem is co-NP-complete in data complexity for the considered class of OMQs. Thus, answering these OMQs in the presence of closed predicates is not harder than answering them in the standard setting. This is not obvious as closed predicates are known to increase data complexity for some existing ontology languages.

The complexity and relative expressiveness of Ontology-mediated Queries (OMQs) is quite well understood by now. In this paper, we study the expressive power of OMQs from a descriptive complexity perspective, where the central question is to understand whether a given OMQ language is powerful enough to express all queries that can be computed within some bound on time or space. We show that the OMQ language that pairs instance queries with ontologies in the very expressive DL ALCHOI with closed predicates cannot express all coNP-computable Boolean queries, despite being coNP-complete in data complexity. We, then, propose an extension of this OMQ language that is expressive enough to precisely capture the class of all Boolean queries computable in coNP. This involves adding functionality as well as path expressions and nominal schemata, which are restricted in a way that allows us to carefully incorporate them into the existing mosaic technique for the DL ALCHOIF with closed predicates without affecting the coNP upper bound in data complexity.

The complexity and relative expressiveness of Ontology-mediated Queries (OMQs) is quite well understood by now. In this paper, we study the expressive power of OMQs from a descriptive complexity perspective, where the central question is to understand whether a given OMQ language is powerful enough to express all queries that can be computed within some bound on time or space. We show that the OMQ language that pairs instance queries with ontologies in the very expressive DL ALCHOI with closed predicates cannot express all coNP-computable Boolean queries, despite being coNP-complete in data complexity. We, then, propose an extension of this OMQ language that is expressive enough to precisely capture the class of all Boolean queries computable in coNP. This involves adding functionality as well as path expressions and nominal schemata, which are restricted in a way that allows us to carefully incorporate them into the existing mosaic technique for the DL ALCHOIF with closed predicates without affecting the coNP upper bound in data complexity.

The complexity and relative expressiveness of Ontology-mediated Queries (OMQs) is quite well understood by now. In this paper, we study the expressive power of OMQs from a descriptive complexity perspective, where the central question is to understand whether a given OMQ language is powerful enough to express all queries that can be computed within some bound on time or space. We show that the OMQ language that pairs instance queries with ontologies in the very expressive DL ALCHOI with closed predicates cannot express all coNP-computable Boolean queries, despite being coNP-complete in data complexity. We, then, propose an extension of this OMQ language that is expressive enough to precisely capture the class of all Boolean queries computable in coNP. This involves adding functionality as well as path expressions and nominal schemata, which are restricted in a way that allows us to carefully incorporate them into the existing mosaic technique for the DL ALCHOIF with closed predicates without affecting the coNP upper bound in data complexity.

The complexity and relative expressiveness of Ontology-mediated Queries (OMQs) is quite well understood by now. In this paper, we study the expressive power of OMQs from a descriptive complexity perspective, where the central question is to understand whether a given OMQ language is powerful enough to express all queries that can be computed within some bound on time or space. We show that the OMQ language that pairs instance queries with ontologies in the very expressive DL ALCHOI with closed predicates cannot express all coNP-computable Boolean queries, despite being coNP-complete in data complexity. We, then, propose an extension of this OMQ language that is expressive enough to precisely capture the class of all Boolean queries computable in coNP. This involves adding functionality as well as path expressions and nominal schemata, which are restricted in a way that allows us to carefully incorporate them into the existing mosaic technique for the DL ALCHOIF with closed predicates without affecting the coNP upper bound in data complexity.

Knowledge Graphs (KGs) are becoming increasingly popular in the industry and academia. They can be represented as labelled graphs conveying structured knowledge in a domain of interest, where nodes and edges are enriched with metaknowledge such as time validity, provenance, language, among others. Once the data is structured as a labelled graph one can apply reasoning techniques to extract relevant and insightful information. We provide an overview of deductive and inductive reasoning approaches for reasoning in KGs.

This report documents the program and the outcomes of Dagstuhl Seminar 21361 "Extending the Synergies Between SAT and Description Logics". Propositional satisfiability (SAT) and description logics (DL) are two successful areas of computational logic where automated reasoning plays a fundamental role. While they share a common core (formalised on logic), the developments in both areas have diverged in their scopes, methods, and applications. The goal of this seminar was to reconnect the SAT and DL communities (understood in a broad sense) so that they can benefit from each other. The seminar thus focused on explaining the foundational principles, main results, and open problems of each area, and discussing potential avenues for collaborative progress.

In this paper we study instance-level update in DL-LiteA , a well-known description logic that influenced the OWL 2 QL standard. Instance-level update regards insertions and deletions in the ABox of an ontology. In particular we focus on formula-based approaches to instance-level update. We show that DL-LiteA , which is well-known for enjoying first-order rewritability of query answering, enjoys a first-order rewritability property also for instance-level update. That is, every update can be reformulated into a set of insertion and deletion instructions computable through a non-recursive Datalog program with negation. Such a program is readily translatable into a first-order query over the ABox considered as a database, and hence into SQL. By exploiting this result, we implement an update component for DL-LiteA-based systems and perform some experiments showing that the approach works in practice., This work was partly supported by the EU within the H2020 Programme under the grant agreement 834228 (ERC Advanced Grant WhiteMech), the grant agreement 952215 (TAILOR), and the grant agreement 825333 (MOSAICrOWN). Moreover, it is partly supported by Ministerio de Economia, Industria y Competitividad under the grant agreement TIN2017-87610-R (REMEDiAL), by the Generalitat de Catalunya under the grant agreement 2017-SGR-1749, and by Regione Lombardia within the Call Hub Ricerca e Innovazione under the grant agreement 1175328 (WATCHMAN)., Peer Reviewed, Postprint (published version)

Fuzzy DL-Lite has been studied as a means to answer queries w.r.t. vague or imprecise knowledge and facts. Existing approaches consider only the Zadeh semantics or are limited to precise terminological knowledge, where only facts are graded. We study the problem of answering conjunctive queries over fuzzy DL-Lite ontologies which allow also graded axioms, and whose semantics is based on mathematical fuzzy logic. We show that for the Gödel t-norm, the degree of an answer is computable through repeated calls to a classical query answering engine. For non-idempotent t-norms, we show the difficulty in dealing with degrees, and provide some partial solutions.

In this paper we present an approach to defeasible reasoning for the description logic ALC. The results discussed here are based on work done by Kraus, Lehmann and Magidor (KLM) on defeasible conditionals in the propositional case. We consider versions of a preferential semantics for two forms of defeasible subsumption, and link these semantic constructions formally to KLM-style syntactic properties via representation results. In addition to showing that the semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. With the semantics of the defeasible version of ALC in place, we turn to the investigation of an appropriate form of defeasible entailment for this enriched version of ALC. This investigation includes an algorithm for the computation of a form of defeasible entailment known as rational closure in the propositional case. Importantly, the algorithm relies completely on classical entailment checks and shows that the computational complexity of reasoning over defeasible ontologies is no worse than that of the underlying classical ALC. Before concluding, we take a brief tour of some existing work on defeasible extensions of ALC that go beyond defeasible subsumption.

In this paper we propose an algorithm that generalises existing procedures for the implementation of defeasible reasoning in the framework of Description Logics (DLs). One of the well-known approaches to defeasible reasoning, the so-called KLM approach, is based on constructing specific rankings of defeasible information, and using these rankings to determine priorities in case of conflicting information. Here we propose a procedure that allows us to input any possible ranking of the defeasible concept inclusions contained in the knowledge base. We analyse and investigate the forms of defeasible reasoning obtained when conclusions drawn are obtained using these rankings.

In this paper we propose an algorithm that generalises existing procedures for the implementation of defeasible reasoning in the framework of Description Logics (DLs). One of the well-known approaches to defeasible reasoning, the so-called KLM approach, is based on constructing specific rankings of defeasible information, and using these rankings to determine priorities in case of conflicting information. Here we propose a procedure that allows us to input any possible ranking of the defeasible concept inclusions contained in the knowledge base. We analyse and investigate the forms of defeasible reasoning obtained when conclusions drawn are obtained using these rankings.

In this paper we present an approach to defeasible reasoning for the description logic ALC. The results discussed here are based on work done by Kraus, Lehmann and Magidor (KLM) on defeasible conditionals in the propositional case. We consider versions of a preferential semantics for two forms of defeasible subsumption, and link these semantic constructions formally to KLM-style syntactic properties via representation results. In addition to showing that the semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. With the semantics of the defeasible version of ALC in place, we turn to the investigation of an appropriate form of defeasible entailment for this enriched version of ALC. This investigation includes an algorithm for the computation of a form of defeasible entailment known as rational closure in the propositional case. Importantly, the algorithm relies completely on classical entailment checks and shows that the computational complexity of reasoning over defeasible ontologies is no worse than that of the underlying classical ALC. Before concluding, we take a brief tour of some existing work on defeasible extensions of ALC that go beyond defeasible subsumption.

We show that the finite satisfiability problem for the unary negation fragment with an arbitrary number of transitive relations is decidable and 2-ExpTime-complete. Our result actually holds for a more general setting in which one can require that some binary symbols are interpreted as arbitrary transitive relations, some as partial orders and some as equivalences. We also consider finite satisfiability of various extensions of our primary logic, in particular capturing the concepts of nominals and role hierarchies known from description logic. As the unary negation fragment can express unions of conjunctive queries, our results have interesting implications for the problem of finite query answering, both in the classical scenario and in the description logics setting.

Concept similarity measure aims at identifying a degree of commonality of two given concepts and is often regarded as a generalization of the classical reasoning problem of equivalence. That is, any two concepts are equivalent if and only if their similarity degree is one. However, existing measures are often devised based on objective factors, e.g. structural-based measures and interpretation-based measures. When these measures are employed to characterize similar concepts in an ontology, they may lead to unintuitive results. In this work, we introduce a new notion called concept similarity measure under preference profile with a set of formally defined properties in Description Logics. This new notion may be interpreted as measuring the similarity of two concepts under subjective factors (e.g. the agent's preferences and domain-dependent knowledge). We also develop a measure of the proposed notion and show that our measure satisfies all desirable properties. Two algorithmic procedures are introduced for top-down and bottom-up implementation, respectively, and their computational complexities are intensively studied. Finally, the paper discusses the usefulness of the approach to potential use cases., identifier:https://dspace.jaist.ac.jp/dspace/handle/10119/16202

Conceptual blending is a mental process that serves a variety of cognitive purposes, including human creativity. In this line of thinking, human creativity is modeled as a process that takes different mental spaces as input and combines them into a new mental space, called a blend. According to this form of combinational creativity, a blend is constructed by taking the commonalities among the input mental spaces into account, to form a so-called generic space, and by projecting the non-common structure of the input spaces in a selective way to the novel blended space. Since input spaces for interesting blends are often initially incompatible, a generalisation step is needed before they can be blended. In this paper, we apply this idea to blend input spaces specified in the description logic EL¿¿++ and propose an upward refinement operator for generalising EL¿¿++ concepts. We show how the generalisation operator is translated to Answer Set Programming (ASP) in order to implement a search process that finds possible generalisations of input concepts. The generalisations obtained by the ASP process are used in a conceptual blending algorithm that generates and evaluates possible combinations of blends. We exemplify our approach in the domain of computer icons

Concept similarity measure aims at identifying a degree of commonality of two given concepts and is often regarded as a generalization of the classical reasoning problem of equivalence. That is, any two concepts are equivalent if and only if their similarity degree is one. However, existing measures are often devised based on objective factors, e.g. structural-based measures and interpretation-based measures. When these measures are employed to characterize similar concepts in an ontology, they may lead to unintuitive results. In this work, we introduce a new notion called concept similarity measure under preference profile with a set of formally defined properties in Description Logics. This new notion may be interpreted as measuring the similarity of two concepts under subjective factors (e.g. the agent's preferences and domain-dependent knowledge). We also develop a measure of the proposed notion and show that our measure satisfies all desirable properties. Two algorithmic procedures are introduced for top-down and bottom-up implementation, respectively, and their computational complexities are intensively studied. Finally, the paper discusses the usefulness of the approach to potential use cases.

The World Wide Web contains large amounts of data, and in most cases this data has no explicit structure. The lack of structure makes it difficult for automated agents to understand and use such data. A step towards a more structured World Wide Web is the Semantic Web, which aims at introducing semantics to data on the World Wide Web. One of the key technologies in this endeavour are ontologies, which provide a means for modeling a domain of interest and are used for search and integration of data. In recent years many ontologies have been developed. To be able to use multiple ontologies it is necessary to align them, i.e., find inter-ontology relationships. However, developing and aligning ontologies is not an easy task and it is often the case that ontologies and their alignments are incorrect and incomplete. This can be a problem for semantically-enabled applications. Incorrect and incomplete ontologies and alignments directly influence the quality of the results of such applications, as wrong results can be returned and correct results can be missed. This thesis focuses on the problem of completing ontologies and ontology networks. The contributions of the thesis are threefold. First, we address the issue of completing the is-a structure and alignment in ontologies and ontology networks. We have formalized the problem of completing the is-a structure in ontologies as an abductive reasoning problem and developed algorithms as well as systems for dealing with the problem. With respect to the completion of alignments, we have studied system performance in the Ontology Alignment Evaluation Initiative, a yearly evaluation campaign for ontology alignment systems. We have also addressed the scalability of ontology matching, which is one of the current challenges, by developing an approach for reducing the search space when generating the alignment.Second, high quality completion requires user involvement. As users' time and effort are a limited resource we address the

Recent extensions of description logics for dealing with different forms of non-monotonic reasoning don’t take us beyond the case of defeasible subsumption. In this paper we enrich the DL EL⊥ with a (constrained version of) a typicality operator •, the intuition of which is to capture the most typical members of a class, providing us with the DL EL•⊥. We argue that EL•⊥ is the smallest step one can take to increase the expressivity beyond the case of defeasible subsumption for DLs, while still retaining all the rationality properties an appropriate notion of defeasible subsumption is required to satisfy, and investigate what an appropriate notion of non-monotonic entailment for EL•⊥ should look like.

Recent extensions of description logics for dealing with different forms of non-monotonic reasoning don’t take us beyond the case of defeasible subsumption. In this paper we enrich the DL EL⊥ with a (constrained version of) a typicality operator •, the intuition of which is to capture the most typical members of a class, providing us with the DL EL•⊥. We argue that EL•⊥ is the smallest step one can take to increase the expressivity beyond the case of defeasible subsumption for DLs, while still retaining all the rationality properties an appropriate notion of defeasible subsumption is required to satisfy, and investigate what an appropriate notion of non-monotonic entailment for EL•⊥ should look like.

The World Wide Web contains large amounts of data, and in most cases this data has no explicit structure. The lack of structure makes it difficult for automated agents to understand and use such data. A step towards a more structured World Wide Web is the Semantic Web, which aims at introducing semantics to data on the World Wide Web. One of the key technologies in this endeavour are ontologies, which provide a means for modeling a domain of interest and are used for search and integration of data. In recent years many ontologies have been developed. To be able to use multiple ontologies it is necessary to align them, i.e., find inter-ontology relationships. However, developing and aligning ontologies is not an easy task and it is often the case that ontologies and their alignments are incorrect and incomplete. This can be a problem for semantically-enabled applications. Incorrect and incomplete ontologies and alignments directly influence the quality of the results of such applications, as wrong results can be returned and correct results can be missed. This thesis focuses on the problem of completing ontologies and ontology networks. The contributions of the thesis are threefold. First, we address the issue of completing the is-a structure and alignment in ontologies and ontology networks. We have formalized the problem of completing the is-a structure in ontologies as an abductive reasoning problem and developed algorithms as well as systems for dealing with the problem. With respect to the completion of alignments, we have studied system performance in the Ontology Alignment Evaluation Initiative, a yearly evaluation campaign for ontology alignment systems. We have also addressed the scalability of ontology matching, which is one of the current challenges, by developing an approach for reducing the search space when generating the alignment.Second, high quality completion requires user involvement. As users' time and effort are a limited resource we address the

The World Wide Web contains large amounts of data, and in most cases this data has no explicit structure. The lack of structure makes it difficult for automated agents to understand and use such data. A step towards a more structured World Wide Web is the Semantic Web, which aims at introducing semantics to data on the World Wide Web. One of the key technologies in this endeavour are ontologies, which provide a means for modeling a domain of interest and are used for search and integration of data. In recent years many ontologies have been developed. To be able to use multiple ontologies it is necessary to align them, i.e., find inter-ontology relationships. However, developing and aligning ontologies is not an easy task and it is often the case that ontologies and their alignments are incorrect and incomplete. This can be a problem for semantically-enabled applications. Incorrect and incomplete ontologies and alignments directly influence the quality of the results of such applications, as wrong results can be returned and correct results can be missed. This thesis focuses on the problem of completing ontologies and ontology networks. The contributions of the thesis are threefold. First, we address the issue of completing the is-a structure and alignment in ontologies and ontology networks. We have formalized the problem of completing the is-a structure in ontologies as an abductive reasoning problem and developed algorithms as well as systems for dealing with the problem. With respect to the completion of alignments, we have studied system performance in the Ontology Alignment Evaluation Initiative, a yearly evaluation campaign for ontology alignment systems. We have also addressed the scalability of ontology matching, which is one of the current challenges, by developing an approach for reducing the search space when generating the alignment.Second, high quality completion requires user involvement. As users' time and effort are a limited resource we address the

The World Wide Web contains large amounts of data, and in most cases this data has no explicit structure. The lack of structure makes it difficult for automated agents to understand and use such data. A step towards a more structured World Wide Web is the Semantic Web, which aims at introducing semantics to data on the World Wide Web. One of the key technologies in this endeavour are ontologies, which provide a means for modeling a domain of interest and are used for search and integration of data. In recent years many ontologies have been developed. To be able to use multiple ontologies it is necessary to align them, i.e., find inter-ontology relationships. However, developing and aligning ontologies is not an easy task and it is often the case that ontologies and their alignments are incorrect and incomplete. This can be a problem for semantically-enabled applications. Incorrect and incomplete ontologies and alignments directly influence the quality of the results of such applications, as wrong results can be returned and correct results can be missed. This thesis focuses on the problem of completing ontologies and ontology networks. The contributions of the thesis are threefold. First, we address the issue of completing the is-a structure and alignment in ontologies and ontology networks. We have formalized the problem of completing the is-a structure in ontologies as an abductive reasoning problem and developed algorithms as well as systems for dealing with the problem. With respect to the completion of alignments, we have studied system performance in the Ontology Alignment Evaluation Initiative, a yearly evaluation campaign for ontology alignment systems. We have also addressed the scalability of ontology matching, which is one of the current challenges, by developing an approach for reducing the search space when generating the alignment.Second, high quality completion requires user involvement. As users' time and effort are a limited resource we address the

The World Wide Web contains large amounts of data, and in most cases this data has no explicit structure. The lack of structure makes it difficult for automated agents to understand and use such data. A step towards a more structured World Wide Web is the Semantic Web, which aims at introducing semantics to data on the World Wide Web. One of the key technologies in this endeavour are ontologies, which provide a means for modeling a domain of interest and are used for search and integration of data. In recent years many ontologies have been developed. To be able to use multiple ontologies it is necessary to align them, i.e., find inter-ontology relationships. However, developing and aligning ontologies is not an easy task and it is often the case that ontologies and their alignments are incorrect and incomplete. This can be a problem for semantically-enabled applications. Incorrect and incomplete ontologies and alignments directly influence the quality of the results of such applications, as wrong results can be returned and correct results can be missed. This thesis focuses on the problem of completing ontologies and ontology networks. The contributions of the thesis are threefold. First, we address the issue of completing the is-a structure and alignment in ontologies and ontology networks. We have formalized the problem of completing the is-a structure in ontologies as an abductive reasoning problem and developed algorithms as well as systems for dealing with the problem. With respect to the completion of alignments, we have studied system performance in the Ontology Alignment Evaluation Initiative, a yearly evaluation campaign for ontology alignment systems. We have also addressed the scalability of ontology matching, which is one of the current challenges, by developing an approach for reducing the search space when generating the alignment.Second, high quality completion requires user involvement. As users' time and effort are a limited resource we address the

Integrity constraints play a central role in databases and, among other applications, are fundamental for preserving data integrity when databases evolve as a result of operations manipulating the data. In this context, an important task is that of static verification, which consists in deciding whether a given set of constraints is preserved after the execution of a given sequence of operations, for every possible database satisfying the initial constraints. In this paper, we consider constraints over graph-structured data formulated in an expressive Description Logic (DL) that allows for regular expressions over binary relations and their inverses, generalizing many of the well-known path constraint languages proposed for semi-structured data in the last two decades. In this setting, we study the problem of static verification, for operations expressed in a simple yet flexible language built from additions and deletions of complex DL expressions. We establish undecidability of the general setting, and identify suitable restricted fragments for which we obtain tight complexity results, building on techniques developed in our previous work for simpler DLs. As a by-product, we obtain new (un)decidability results for the implication problem of path constraints, and improve previous upper bounds on the complexity of the problem.

The cognitive theory of conceptual blending models human creativity as a mental process that combines two mental spaces into a new mental space, called a blend. According to this theory, a blend is constructed by taking the commonalities among the input mental spaces into account, to form a so-called generic space, and by projecting their non-common structure in a selective way to the novel blended space. In this paper, we apply this idea to blend input spaces modeled as complex EL++ concepts. To construct the generic space of two EL++ concepts, these need to be generalised in a controlled manner. For this, we propose an upward refinement operator that is used for finding common generalisations of EL++ concepts. © 2016, CEUR-WS. All rights reserved.

We address the problem on how newly invented concepts are evaluated with respect to a background ontology of conceptual knowl- edge so as to decide which of them are to be accepted into a system of familiar concepts, and how this, in turn, may affect the previously ac- cepted conceptualisation. As technique to tackle this problem we explore the applicability of Paul Thagard¿s computational theory of coherence. In particular, we propose a formalisation of Thagard¿s notion of conceptual coherence for concepts represented in the AL description logic and explore by means of an illustrative example the role coherence may play in the process of conceptual blending. Copyright © 2016 for this paper by its authors.

Similarity assessment is a key operation in several areas of artificial intelligence. This paper focuses on measuring similarity in the context of Description Logics (DL), and specifically on similarity between individuals. The main contribution of this paper is a novel approach based on measuring similarity in the space of Conjunctive Queries, rather than in the space of concepts. The advantage of this approach is two fold. On the one hand, it is independent of the underlying DL and therefore there is no need to design similarity measures for different DL, and, on the other hand, the approach is computationally more efficient than searching in the space of concepts. © 2015, Springer Science+Business Media New York.

This paper is a contribution to the study of similarity relations between objects represented as attribute-value pairs in Fuzzy Description Logics. For this purpose we use concrete domains in the fuzzy description logic IALCEF(D) associated either with a left-continuous or with a finite t-norm. We propose to expand this fuzzy description logic by adding a Similarity Box (SBox) including axioms expressing properties of fuzzy equalities. We also define a global similarity between objects from similarities between the values of each object attribute (local similarities) and we prove that the global similarity defined using a t-norm inherits the usual properties of the local similarities (reflexivity, symmetry or transitivity). We also prove a result relative to global similarities expressing that, in the context of the logic MTL, similar objects have similar properties, being these properties expressed by predicate formulas evaluated in these objects.

This dissertation is concerned with the development of new methodologies and semantics for model-based systems engineering (MBSE) procedures for the behavior modeling of cyber-physical systems (CPS). Our main interest is to enhance system-level safety through effective reasoning capabilities embedded in procedures for CPS design. This class of systems is defined by a tight integration of software and physical processes, the need to satisfy stringent constraints on performance, safety and a reliance on automation for the management of system functionality. Our approach employs semantic–driven modeling and reasoning : (1) for the design of cyber that can understand the physical world and reason with physical quantities, time and space, (2) to improve synthesis of component-based CPS architectures, and (3) to prevent under-specification of system requirements (the main cause of safety failures in software). We investigate and understand metadomains, especially temporal and spatial theories, and the role ontologies play in deriving formal, precise models of CPS. Description logic-based semantics and metadomain ontologies for reasoning in CPS and an integrated approach to unify the semantic foundations for decision making in CPS are covered. The research agenda is driven by Civil Systems design and operation applications, especially the dilemma zone problem. Semantic models of time and space supported respectively by Allen’s Temporal Interval Calculus (ATIC) and Region Connectedness Calculus (RCC-8) are developed and demonstrated thanks to the capabilities of Semantic Web technologies. A modular, flexible, and reusable reasoning-enabled semantic-based platform for safety-critical CPS modeling and analysis is developed and demonstrated. The platform employs formal representations of domains (cyber, physical) and metadomains (temporal and spatial) entities using decidable web ontology language (OWL) formalisms. Decidable fragments of temporal and spatial calculus are found

In recent years, various approaches have been developed for representing and reasoning with exceptions in OWL. The price one pays for such capabilities, in terms of practical performance, is an important factor that is yet to be quantified comprehensively. A major barrier is the lack of naturally occurring ontologies with defeasible features - the ideal candidates for evaluation. Such data is unavailable due to absence of tool support for representing defeasible features. In the past, defeasible reasoning implementations have favoured automated generation of defeasible ontologies. While this suffices as a preliminary approach, we posit that a method somewhere in between these two would yield more meaningful results. In this work, we describe a systematic approach to modify real-world OWL ontologies to include defeasible features, and we apply this to the Manchester OWL Repository to generate defeasible ontologies for evaluating our reasoner DIP (Defeasible-Inference Platform). The results of this evaluation are provided together with some insights into where the performance bottle-necks lie for this kind of reasoning. We found that reasoning was feasible on the whole, with surprisingly few bottle-necks in our evaluation.

In recent years, various approaches have been developed for representing and reasoning with exceptions in OWL. The price one pays for such capabilities, in terms of practical performance, is an important factor that is yet to be quantified comprehensively. A major barrier is the lack of naturally occurring ontologies with defeasible features - the ideal candidates for evaluation. Such data is unavailable due to absence of tool support for representing defeasible features. In the past, defeasible reasoning implementations have favoured automated generation of defeasible ontologies. While this suffices as a preliminary approach, we posit that a method somewhere in between these two would yield more meaningful results. In this work, we describe a systematic approach to modify real-world OWL ontologies to include defeasible features, and we apply this to the Manchester OWL Repository to generate defeasible ontologies for evaluating our reasoner DIP (Defeasible-Inference Platform). The results of this evaluation are provided together with some insights into where the performance bottle-necks lie for this kind of reasoning. We found that reasoning was feasible on the whole, with surprisingly few bottle-necks in our evaluation.

Unification in Description Logics has been introduced as a means to detect redundancies in ontologies. We try to extend the known decidability results for unification in the Description Logic EL to disunification since negative constraints on unifiers can be used to avoid unwanted unifiers. While decidability of the solvability of general EL-disunification problems remains an open problem, we obtain NP-completeness results for two interesting special cases: dismatching problems, where one side of each negative constraint must be ground, and local solvability of disunification problems, where we restrict the attention to solutions that are built from so-called atoms occurring in the input problem. More precisely, we first show that dismatching can be reduced to local disunification, and then provide two complementary NP-algorithms for finding local solutions of (general) disunification problems.

Areas in which graph databases are applied - such as the semantic web, social networks and scientific databases - are prone to inconsistency, mainly due to interoperability issues. This raises the need for understanding query answering over inconsistent graph databases in a framework that is simple yet general enough to accommodate many of its applications. We follow the well-known approach of consistent query answering (CQA), and study the data complexity of CQA over graph databases for regular path queries (RPQs) and regular path constraints (RPCs), which are frequently used. We concentrate on subset, superset and symmetric difference repairs. Without further restrictions, CQA is undecidable for the semantics based on superset and symmetric difference repairs, and Pi_2^P-complete for subset repairs. However, we provide several tractable restrictions on both RPCs and the structure of graph databases that lead to decidability, and even tractability of CQA. We also compare our results with those obtained for CQA in the context of relational databases.

The validation and the verification of conceptual schemas have attracted a lot of interest during the last years, and several tools have been developed to automate this process as much as possible. This is achieved, in general, by assessing whether the schema satisfies different kinds of desirable properties which ensure that the schema is correct. In this paper we describe AuRUS, a tool we have developed to analyze UML/OCL conceptual schemas and to explain their (in)correctness. When a property is satisfied, AuRUS provides a sample instantiation of the schema showing a particular situation where the property holds. When it is not, AuRUS provides an explanation for such unsatisfiability, i.e., a set of integrity constraints which is in contradiction with the property., Peer Reviewed, Postprint (author’s final draft)

Operational commanders and intelligence professionals are provided with a continually-increasing volume of data from numerous sources. Effective utilization of this data can be hampered by difficulties in fusing different data streams for presentation, correlating related data from various sources and developing reliable summary and predictive products. An opportunity presently exists to improve this situation through the incorporation of Semantic Web technologies into Department of Defense (DOD) systems. This report provides a didactic overview of Description Logics (DL) and their implementation in Semantic Web languages and technologies to include the mathematical properties supporting robust knowledge representation. Subsequently, the algorithms for automated reasoning and inferencing with DLs are discussed. Included in this discussion is a comparison of available Semantic Web applications for ontology development and realization or DL reasoning capabilities with real-world knowledge bases. Finally, mechanisms for applying artificial intelligence techniques to ontological DL information are presented., The original document contains color images.

Description Logics are a family of logics used to represent and reason about conceptual and terminological knowledge. One of the most basic description logics is ALC , used as a basis from which to obtain others. Description logics are particularly important to provide a logical basis for the web ontology languages (such as OWL) used in the Semantic Web. In order to increase the reliability of the Semantic Web, formal methods can be applied, and in particular formal verification of its reasoning services can be carried out. In this paper, we present the formal verification of a tableau-based satisfiability algorithm for the logic ALC . The verification has been completed in several stages. First, we develop an abstract formalization of satisfiability-checking of ALC -concepts. Secondly, we define and formally verify a tableau-based algorithm in which the order of rule application and branch selection can be flexibly specified, using a methodology of refinements to transfer the main properties from the ALC abstract formalization. Finally, we obtain verified and executable reasoners from the algorithm via a process of instantiation.

The World Wide Web contains large amounts of data and in most cases this data is without any explicit structure. The lack of structure makes it difficult for automated agents to understand and use such data. A step towards a more structured World Wide Web is the idea of the Semantic Web which aims at introducing semantics to data on the World Wide Web. One of the key technologies in this endeavour are ontologies which provide means for modeling a domain of interest. Developing and maintaining ontologies is not an easy task and it is often the case that defects are introduced into ontologies. This can be a problem for semantically-enabled applications such as ontology-based querying. Defects in ontologies directly influence the quality of the results of such applications as correct results can be missed and wrong results can be returned. This thesis considers one type of defects in ontologies, namely the problem of completing the is-a structure in ontologies represented in description logics. We focus on two variants of description logics, the EL family and ALC, which are often used in practice. The contributions of this thesis are as follows. First, we formalize the problem of completing the is-a structure as a generalized TBox abduction problem (GTAP) which is a new type of abduction problem in description logics. Next, we provide algorithms for solving GTAP in the EL family and ALC description logics. Finally, we describe two implemented systems based on the introduced algorithms. The systems were evaluated in two experiments which have shown the usefulness of our approach. For example, in one experiment using ontologies from the Ontology Alignment Evaluation Initiative 58 and 94 detected missing is-a relations were repaired by adding 54 and 101 is-a relations, respectively, introducing new knowledge to the ontologies.

Restricted access! The contents are blocked by the system. Please consult the technical assistant.

Description Logics are a family of logics used to represent and reason about conceptual and terminological knowledge. One of the most basic description logics is ALC , used as a basis from which to obtain others. Description logics are particularly important to provide a logical basis for the web ontology languages (such as OWL) used in the Semantic Web. In order to increase the reliability of the Semantic Web, formal methods can be applied, and in particular formal verification of its reasoning services can be carried out. In this paper, we present the formal verification of a tableau-based satisfiability algorithm for the logic ALC . The verification has been completed in several stages. First, we develop an abstract formalization of satisfiability-checking of ALC -concepts. Secondly, we define and formally verify a tableau-based algorithm in which the order of rule application and branch selection can be flexibly specified, using a methodology of refinements to transfer the main properties from the ALC abstract formalization. Finally, we obtain verified and executable reasoners from the algorithm via a process of instantiation.

Restricted access! The contents are blocked by the system. Please consult the technical assistant.