Description Logic Knowledge Bases Research Articles

A Dual Description Logic for the Relations in Databases

This paper introduced a dual description logic for relations, in order to represent the difference of tuples and attribute values. In the logic, concepts are classified into two classes as follows: tuple-concepts and attribute-value concepts. This paper firstly gives the logical language, syntax and semantics of the logic, and secondly defines a transformation of a relation in a database into a knowledge base in the dual description logic, and last proposes a transformation of a model for the dual description logic into a relation.

Extending description logics with uncertainty reasoning in possibilistic logic

Possibilistic logic provides a convenient tool for dealing with uncertainty and handling inconsistency. In this paper, we propose possibilistic description logics as an extension of description logics, which are a family of well-known ontology languages. We first give the syntax and semantics of possibilistic description logics and define several inference services in possibilistic description logics. We show that these inference serviced can be reduced to the task of computing the inconsistency degree of a knowledge base in possibilistic description logics. Since possibilistic inference services suffer from the drowning problem, that is, axioms whose confidence degrees are less than or equal to the inconsistency are not used, we consider a drowning-free variant of possibilistic inference, called linear order inference. We propose an algorithm for computing the inconsistency degree of a possibilistic description logic knowledge base and an algorithm for the linear order inference. We consider the impact of our possibilistic description logics on ontology learning and ontology merging. Finally, we implement these algorithms and provide some interesting evaluation results. © 2011 Wiley Periodicals, Inc.

Well-founded semantics for description logic programs in the semantic web

The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms. In particular, combining logic programming with the Web Ontology Language (OWL), which is a standard based on description logics, emerged as an important issue for linking the Rules and Ontology Layers of the Semantic Web. Nonmonotonic description logic programs (dl-programs) were introduced for such a combination, in which a pair(L,P)of a description logic knowledge baseLand a set of rulesPwith negation as failure is given a model-based semantics that generalizes the answer set semantics of logic programs. In this article, we reconsider dl-programs and present a well-founded semantics for them as an analog for the other main semantics of logic programs. It generalizes the canonical definition of the well-founded semantics based on unfounded sets, and, as we show, lifts many of the well-known properties from ordinary logic programs to dl-programs. Among these properties, our semantics amounts to a partial model approximating the answer set semantics, which yields for positive and stratified dl-programs, a total model coinciding with the answer set semantics; it has polynomial data complexity provided the access to the description logic knowledge base is polynomial; under suitable restrictions, it has lower complexity and even first-order rewritability is achievable. The results add to previous evidence that dl-programs are a versatile and robust combination approach, which moreover is implementable using legacy engines.

A New Approach to Knowledge Base Revision in DL-Lite

Revising knowledge bases (KBs) in description logics (DLs) in a syntax-independent manner is an important, nontrivial problem for the ontology management and DL communities. Several attempts have been made to adapt classical model-based belief revision and update techniques to DLs, but they are restricted in several ways. In particular, they do not provide operators or algorithms for general DL KB revision. The key difficulty is that, unlike propositional logic, a DL KB may have infinitely many models with complex (and possibly infinite) structures, making it difficult to define and compute revisions in terms of models. In this paper, we study general KBs in a specific DL in the DL-Lite family. We introduce the concept of features for such KBs, develop an alternative semantic characterization of KBs using features (instead of models), define two specific revision operators for KBs, and present the first algorithm for computing best approximations for syntax-independent revisions of KBs.

Automata-Based Axiom Pinpointing

Axiom pinpointing has been introduced in description logics (DL) to help the user understand the reasons why consequences hold by computing minimal subsets of the knowledge base that have the consequence in question (MinA). Most of the pinpointing algorithms described in the DL literature are obtained as extensions of tableau-based reasoning algorithms for computing consequences from DL knowledge bases. In this paper, we show that automata-based algorithms for reasoning in DLs and other logics can also be extended to pinpointing algorithms. The idea is that the tree automaton constructed by the automata-based approach can be transformed into a weighted tree automaton whose so-called behaviour yields a pinpointing formula, i.e., a monotone Boolean formula whose minimal valuations correspond to the MinAs. We also develop an approach for computing the behaviour of a given weighted tree automaton. We use the DL $\mathcal{SI}$ as well as Linear Temporal Logic (LTL) to illustrate our new pinpointing approach.

The role of semantics in mining frequent patterns from knowledge bases in description logics with rules

AbstractWe propose a new method for mining frequent patterns in a language that combines both Semantic Web ontologies and rules. In particular, we consider the setting of using a language that combines description logics (DLs) with DL-safe rules. This setting is important for the practical application of data mining to the Semantic Web. We focus on the relation of the semantics of the representation formalism to the task of frequent pattern discovery, and for the core of our method, we propose an algorithm that exploits the semantics of the combined knowledge base. We have developed a proof-of-concept data mining implementation of this. Using this we have empirically shown that using the combined knowledge base to perform semantic tests can make data mining faster by pruning useless candidate patterns before their evaluation. We have also shown that the quality of the set of patterns produced may be improved: the patterns are more compact, and there are fewer patterns. We conclude that exploiting the semantics of a chosen representation formalism is key to the design and application of (onto-)relational frequent pattern discovery methods.

CREATING AND QUERYING FORMAL ONTOLOGIES VIA CONTROLLED NATURAL LANGUAGE

Formal ontologies are difficult to read and understand for domain experts who do not have a background in formal logic. This severely restricts the ability of this user group to determine whether an ontology conforms to the requirements of the application domain or not. We argue that a formal ontology—in our case a description logic knowledge base—should be created in a linguistically motivated way so that domain experts can understand and query the ontology. We first show that this can be partially achieved with the help of a naming convention which is based on those linguistic expressions that occur in the application domain. We then go a step further and suggest the use of a controlled natural language for creating and querying formal ontologies that follows the syntactic structure of a well-defined subset of English.

Axiom Pinpointing in General Tableaux

Axiom pinpointing has been introduced in description logics (DLs) to help the user to understand the reasons why consequences hold and to remove unwanted consequences by computing minimal (maximal) subsets of the knowledge base that have (do not have) the consequence in question. Most of the pinpointing algorithms described in the DLliterature are obtained as extensions of the standard tableau-based reasoning algorithms for computing consequences from DL knowledge bases. Although these extensions are based on similar ideas, they are all introduced for a particular tableau-based algorithm for a particular DL. The purpose of this article is to develop a general approach for extending a tableau-based algorithm to a pinpointing algorithm. This approach is based on a general definition of ‘tableau algorithms,’ which captures many of the known tableau-based algorithms employed in DLs, but also other kinds of reasoning procedures.

Exploiting conjunctive queries in description logic programs

Towards combining rules and ontologies for the Semantic Web, nonmonotonic Description Logic Programs (dl-programs) have been proposed as a powerful formalism to couple nonmonotonic logic programming and Description Logic reasoning on a clear semantic basis. In this paper, we present cq-programs, which enhance dl-programs with conjunctive queries (CQ) and union of conjunctive queries (UCQ) over Description Logics knowledge bases, as well as with disjunctive rules. The novel formalism has two advantages. First, it offers increased expressivity because it allows for (U)CQs in the bodies of the rules. The (U)CQs allow one to access unnamed individuals in the rules and they increase the expressivity of the formalism, as evident from the increase in complexity from NEXP to 2-EXP. And second, when implemented as a combination between a logic programming system and a DL-reasoner, this integration of rules and ontologies gives rise to strategies for optimizing calls to the DL-reasoner, by exploiting specific support for (U)CQs. To this end, we present equivalence preserving transformations which can be used for program rewriting, and we present respective generic rewriting algorithms. Experimental results for a cq-program prototype show that this can lead to significant performance improvements, and suggest that cq-programs and program rewriting provide a useful basis for dl- and cq-program optimization.

Evolutionary Conceptual Clustering Based on Induced Pseudo-Metrics

We present a method based on clustering techniques to detect possible/probable novel concepts or concept drift in a Description Logics knowledge base. The method exploits a semi-distance measure defined for individuals, that is based on a finite number of dimensions corresponding to a committee of discriminating features (concept descriptions). A maximally discriminating group of features is obtained with a randomized optimization method. In the algorithm, the possible clusterings are represented as medoids (w.r.t. the given metric) of variable length. The number of clusters is not required as a parameter, the method is able to find an optimal choice by means of evolutionary operators and a proper fitness function. An experimentation proves the feasibility of our method and its effectiveness in terms of clustering validity indices. With a supervised learning phase, each cluster can be assigned with a refined or newly constructed intensional definition expressed in the adopted language.

Guarded hybrid knowledge bases

AbstractRecently, there has been a lot of interest in the integration of Description Logics (DL) and rules on the Semantic Web. We defineguarded hybrid knowledge bases(org-hybrid knowledge bases) as knowledge bases that consist of a Description Logic knowledge base and aguardedlogic program, similar to the$\mathcal{DL}$+logknowledge bases from Rosati (In Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning, AAAI Press, Menlo Park, CA, 2006, pp. 68–78.). g-Hybrid knowledge bases enable an integration of Description Logics and Logic Programming where, unlike in other approaches, variables in the rules of a guarded program do not need to appear in positive non-DL atoms of the body, i.e., DL atoms can act asguardsas well. Decidability of satisfiability checking of g-hybrid knowledge bases is shown for the particular DL$\mathcal{DLRO}^{\-{le}}$, which is close to OWL DL, by a reduction to guarded programs under the open answer set semantics. Moreover, we show 2-Exptime-completeness for satisfiability checking of such g-hybrid knowledge bases. Finally, we discuss advantages and disadvantages of our approach compared with$\mathcal{DL}$+logknowledge bases.

Combining answer set programming with description logics for the Semantic Web

We propose a combination of logic programming under the answer set semantics with the description logics SHIF ( D ) and SHOIN ( D ) , which underly the Web ontology languages OWL Lite and OWL DL, respectively. To this end, we introduce description logic programs (or dl-programs), which consist of a description logic knowledge base L and a finite set P of description logic rules (or dl-rules). Such rules are similar to usual rules in nonmonotonic logic programs, but they may also contain queries to L, possibly under default negation, in their bodies. They allow for building rules on top of ontologies but also, to a limited extent, building ontologies on top of rules. We define a suite of semantics for various classes of dl-programs, which conservatively extend the standard semantics of the respective classes and coincide with it in absence of a description logic knowledge base. More concretely, we generalize positive, stratified, and arbitrary normal logic programs to dl-programs, and define a Herbrand model semantics for them. We show that they have similar properties as ordinary logic programs, and also provide fixpoint characterizations in terms of (iterated) consequence operators. For arbitrary dl-programs, we define answer sets by generalizing Gelfond and Lifschitz's notion of a transform, leading to a strong and a weak answer set semantics, which are based on reductions to the semantics of positive dl-programs and ordinary positive logic programs, respectively. We also show how the weak answer sets can be computed utilizing answer sets of ordinary normal logic programs. Furthermore, we show how some advanced reasoning tasks for the Semantic Web, including different forms of closed-world reasoning and default reasoning, as well as DL-safe rules, can be realized on top of dl-programs. Finally, we give a precise picture of the computational complexity of dl-programs, and we describe efficient algorithms and a prototype implementation of dl-programs which is available on the Web.

Conjunctive Query Answering for the Description Logic SHIQ

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, conjunctive query answering over DL knowledge bases is only poorly understood if transitive roles are admitted in the query. In this paper, we consider unions of conjunctive queries over knowledge bases formulated in the prominent DL SHIQ and allow transitive roles in both the query and the knowledge base. We show decidability of query answering in this setting and establish two tight complexity bounds: regarding combined complexity, we prove that there is a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query, which is optimal. Regarding data complexity, we prove containment in co-NP.

Decomposition-based reasoning for large knowledge bases in description logics

Reasoning in a Knowledge Base (KB) is one of the most important applications of Description Logic (DL) reasoners. The execution time and storage space requirements are both significant factors that directly influence the performance of a reasoning al

Tractable Reasoning and Efficient Query Answering in Description Logics: The DL-Lite Family

We propose a new family of description logics (DLs), called DL-Lite, specifically tailored to capture basic ontology languages, while keeping low complexity of reasoning. Reasoning here means not only computing subsumption between concepts and checking satisfiability of the whole knowledge base, but also answering complex queries (in particular, unions of conjunctive queries) over the instance level (ABox) of the DL knowledge base. We show that, for the DLs of the DL-Lite family, the usual DL reasoning tasks are polynomial in the size of the TBox, and query answering is LogSpace in the size of the ABox (i.e., in data complexity). To the best of our knowledge, this is the first result of polynomial-time data complexity for query answering over DL knowledge bases. Notably our logics allow for a separation between TBox and ABox reasoning during query evaluation: the part of the process requiring TBox reasoning is independent of the ABox, and the part of the process requiring access to the ABox can be carried out by an SQL engine, thus taking advantage of the query optimization strategies provided by current database management systems. Since even slight extensions to the logics of the DL-Lite family make query answering at least NLogSpace in data complexity, thus ruling out the possibility of using on-the-shelf relational technology for query processing, we can conclude that the logics of the DL-Lite family are the maximal DLs supporting efficient query answering over large amounts of instances.

Variable-strength conditional preferences for ranking objects in ontologies

We introduce conditional preference bases as a means for ranking objects in ontologies. Conditional preference bases consist of a description logic knowledge base and a finite set of conditional preferences, which are statements of the form “generally, in the context ϕ , property α is preferred over property ¬ α with strength s”. They are inspired by variable-strength defaults in conditional knowledge bases. We define the notion of consistency for conditional preference bases, and we show how consistent conditional preference bases can be used for ranking objects in ontologies, where every object represents essentially a set of individuals that are sharing the same ranking-relevant properties. More concretely, we define two object rankings, denoted κ sum and κ lex , which evaluate the strengths of conditional preferences in an additive and a lexicographic way, respectively. Furthermore, we provide algorithms for the main computational tasks for ranking objects under conditional preference bases, we analyze the complexity of these tasks, and we delineate a tractable special case. To give evidence of the usefulness of this approach in practice, we describe two applications in the areas of product and literature search, where it allows especially for a flexible user-defined ranking of the query results reflecting personal preferences.

Variable-Strength Conditional Preferences for Ranking Objects in Ontologies

We introduce conditional preference bases as a means for ranking objects in ontologies. Conditional preference bases consist of a description logic knowledge base and a finite set of conditional preferences, which are statements of the form generally, in the context φ, property α is preferred over property -α with strength s. They are inspired by variable-strength defaults in conditional knowledge bases. We define the notion of consistency for conditional preference bases, and we show how consistent conditional preference bases can be used for ranking objects in ontologies, where every object represents essentially a set of individuals that are sharing the same ranking-relevant properties. More concretely, we define two object rankings, denoted κsum and κlex, which evaluate the strengths of conditional preferences in an additive and a lexicographic way, respectively. Furthermore, we provide algorithms for the main computational tasks for ranking objects under conditional preference bases, we analyze the complexity of these tasks, and we delineate a tractable special case. To give evidence of the usefulness of this approach in practice, we describe two applications in the areas of product and literature search, where it allows especially for a flexible user-defined ranking of the query results reflecting personal preferences.

A revision-based approach to handling inconsistency in description logics

Recently, the problem of inconsistency handling in description logics has attracted a lot of attention. Many approaches have been proposed to deal with this problem based on existing techniques for inconsistency management. In this paper, we first define two revision operators in description logics; one is called a weakening-based revision operator and the other is its refinement. Based on the revision operators, we then propose an algorithm to handle inconsistency in a stratified description logic knowledge base. We show that when the weakening-based revision operator is chosen, the resulting knowledge base of our algorithm is semantically equivalent to the knowledge base obtained by applying refined conjunctive maxi-adjustment (RCMA) which refines disjunctive maxi-adjusment (DMA), known to be a good strategy for inconsistency handling in classical logic.

A hybrid reasoning system for terminologies and first-order clauses in knowledge bases

Description Logics (DLs) theoretically explore knowledge representation and reasoning in concept languages. However, since they are conceptually oriented, they are not equipped with rule-based reasoning mechanisms for assertional knowledge bases - specifically, rules and facts in Logic Programming (LP), or the interaction of rules and facts with terminological knowledge. To combine rule-based reasoning with terminological knowledge, this paper presents a hybrid reasoning system for DL knowledge bases (TBox and ABox) and first-order clause sets. The primary result of this study involves the design of a sound and complete resolution method for the composed knowledge bases, and this method possesses features of an effective deduction procedure such as Robinson's Resolution Principle.

Reducing OWL entailment to description logic satisfiability

We show how to reduce ontology entailment for the OWL DL and OWL Lite ontology languages to knowledge base satisfiability in (respectively) the S H O I N ( D ) and S H I F ( D ) description logics. This is done by first establishing a correspondence between OWL ontologies and description logic knowledge bases and then by showing how knowledge base entailment can be reduced to knowledge base satisfiability.