Description Logic Programs (dl-programs) proposed by constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the notions of completion and loop formulas of logic programs to description logic programs and show that the answer sets of a dl-program can be precisely captured by the models of its completion and loop formulas. Furthermore, we propose a new, alternative semantics for dl-programs, called the canonical answer set semantics, which is defined by the models of completion that satisfy what are called canonical loop formulas. A desirable property of canonical answer sets is that they are free of circular justifications. Some properties of canonical answer sets are also explored.
Integrating ASP with description logics has attracted a great deal of attention recently. The existing approaches can be roughly classified into three categories. The first is to adopt a nonmonotonic formalism that covers both ASP and first-order logic (if not for the latter, then extend it to the first-order case) @cite_21 @cite_18 , where ontologies and rules are written in the same language, resulting in a tight coupling. The second is a loose approach: An ontology knowledge base and the rules share the same constants but not the same predicates, and the communication is via a well-defined interface, such as dl-atoms @cite_13 . The third is to combine ontologies with hybrid rules @cite_5 @cite_9 @cite_12 , where predicates in the language of ontologies are interpreted classically, whereas those in the language of rules are interpreted nonmonotonically.
@cite_18 @cite_9 @cite_21 @cite_5 @cite_13 @cite_12
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In the context of the Semantic Web, several approaches to the combination of ontologies, given in terms of theories of classical first-order logic, and rule bases have been proposed. They either cast rules into classical logic or limit the interaction between rules and ontologies. Autoepistemic logic (AEL) is an attractive formalismwhich allows to overcome these limitations, by serving as a uniform host language to embed ontologies and nonmonotonic logic programs into it. For the latter, so far only the propositional setting has been considered. In this paper, we present several embeddings of normal and disjunctive non-ground logic programs under the stable-model semantics into first-order AEL, and compare them in combination with classical theories, with respect to stable expansions and autoepistemic consequences. Our results reveal differences and correspondences of the embeddings and provide a useful guidance in the choice of a particular embedding for knowledge combination. 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 base L and a set of rules P with 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. In the ongoing discussion about combining rules and Ontologies on the Semantic Web a recurring issue is how to combine first-order classical logic with nonmonotonic rule languages. Whereas several modular approaches to define a combined semantics for such hybrid knowledge bases focus mainly on decidability issues, we tackle the matter from a more general point of view. In this paper we show how Quantified Equilibrium Logic (QEL) can function as a unified framework which embraces classical logic as well as disjunctive logic programs under the (open) answer set semantics. In the proposed variant of QEL we relax the unique names assumption, which was present in earlier versions of QEL. Moreover, we show that this framework elegantly captures the existing modular approaches for hybrid knowledge bases in a unified way. 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. Description logics (DLs) and rules are formalisms that emphasize different aspects of knowledge representation: whereas DLs are focused on specifying and reasoning about conceptual knowledge, rules are focused on nonmonotonic inference. Many applications, however, require features of both DLs and rules. Developing a formalism that integrates DLs and rules would be a natural outcome of a large body of research in knowledge representation and reasoning of the last two decades; however, achieving this goal is very challenging and the approaches proposed thus far have not fully reached it. In this paper, we present a hybrid formalism of MKNFp knowledge bases, which integrates DLs and rules in a coherent semantic framework. Achieving seamless integration is nontrivial, since DLs use an open-world assumption, while the rules are based on a closed-world assumption. We overcome this discrepancy by basing the semantics of our formalism on the logic of minimal knowledge and negation as failure (MKNF) by Lifschitz. We present several algorithms for reasoning with MKNFp knowledge bases, each suitable to different kinds of rules, and establish tight complexity bounds. In recent years, there has been a growing interest in the adoption of ontologies and ontological reasoning to automatically recognize complex context data such as human activities. In particular, the Web Ontology Language (OWL) emerged as the language of choice, being a standard for the Semantic Web, and supported by a number of tools for knowledge engineering and reasoning. However, the limitations of OWL 1 in terms of expressiveness have been recognized in various fields, and important research efforts have been made to extend the language while preserving decidability of its OWL 1 DL fragment. The result of such work is OWL 2. In this paper we investigate the use of OWL 2 for modeling complex activities and reasoning with them. We show that the new language constructors of OWL 2 overcome the main limitations of OWL 1 for the representation of activities; OWL 2 axioms can be used to represent certain rules and rule-based reasoning previously demanded to hybrid approaches, with the advantage of having a unique semantics, avoiding potential inconsistencies. Then, we propose a system architecture showing the integration of a novel OWL 2 activity ontology and reasoning modules with distributed modules for sensor data aggregation and reasoning. The feasibility of our solution is shown by an extensive experimental evaluation with simulations of different intelligent environments. We describe the strategy currently pursued for verbalising OWL ontologies by sentences in Controlled Natural Language (i.e., combining generic rules for realising logical patterns with ontology-specific lexicons for realising atomic terms for individuals, classes, and properties) and argue that its success depends on assumptions about the complexity of terms and axioms in the ontology. We then show, through analysis of a corpus of ontologies, that although these assumptions could in principle be violated, they are overwhelmingly respected in practice by ontology developers. With the fast development of Semantic Web, more and more RDF and OWL ontologies are created and shared. The effective management, such as storage, inference and query, of these ontologies on databases gains increasing attention. This paper addresses ontology query answering on databases by means of Datalog programs. Via epistemic operators, integrity constraints are introduced, and used for conveying semantic aspects of OWL that are not covered by Datalog-style rule languages. We believe such a processing suitable to capture ontologies in the database flavor, while keeping reasoning tractable. Here, we present a logically equivalent knowledge base whose (sound and complete) inference system appears as a Datalog program. As such, SPARQL query answering on OWL ontologies could be solved in databases. Bi-directional strategies, taking advantage of both forward and backward chaining, are then studied to support this kind of customized Datalog programs, returning exactly answers to the query within our logical framework. In this paper, we present a brief overview of Pellet: a complete OWL-DL reasoner with acceptable to very good performance, extensive middleware, and a number of unique features. Pellet is the first sound and complete OWL-DL reasoner with extensive support for reasoning with individuals (including nominal support and conjunctive query), user-defined datatypes, and debugging support for ontologies. It implements several extensions to OWL-DL including a combination formalism for OWL-DL ontologies, a non-monotonic operator, and preliminary support for OWL Rule hybrid reasoning. Pellet is written in Java and is open source. It is claimed in [45] that first-order theorem provers are not efficient for reasoning with ontologies based on description logics compared to specialised description logic reasoners. However, the development of more expressive ontology languages requires the use of theorem provers able to reason with full first-order logic and even its extensions. So far, theorem provers have extensively been used for running experiments over TPTP containing mainly problems with relatively small axiomatisations. A question arises whether such theorem provers can be used to reason in real time with large axiomatisations used in expressive ontologies such as SUMO. In this paper we answer this question affirmatively by showing that a carefully engineered theorem prover can answer queries to ontologies having over 15,000 first-order axioms with equality. Ontologies used in our experiments are based on the language KIF, whose expressive power goes far beyond the description logic based languages currently used in the Semantic Web. Practical description logic systems play an ever-growing role for knowledge representation and reasoning research even in distributed environments. In particular, the ontology layer of the often-discussed semantic web is based on description logics (DLs) and defines important challenges for current system implementations. The article introduces and evaluates optimization techniques for the instance retrieval problem w.r.t. the description logic @math , which covers large parts of the Web Ontology Language (OWL). We demonstrate that sound and complete query engines for OWL-DL can be built for practically significant query classes. Experience with ontologies derived from database content has shown that it is often necessary to effectively solve instance retrieval problems with respect to huge amounts of data descriptions that make up major parts of ontologies. We present and analyze the main results about how to address this kind of scalability problem. The last two decades has seen the emergence of many different probabilistic logics that use logical languages to specify, and sometimes reason, with probability distributions. Probabilistic logics that support reasoning with probability distributions, such as ProbLog, use an implicit definition of an interaction rule to combine probabilistic evidence about atoms. In this paper, we show that this interaction rule is an example of a more general class of interactions that can be described by nonmonotonic logics. We furthermore show that such local interactions about the probability of an atom can be described by convolution. The resulting extended probabilistic logic supports nonmonotonic reasoning with probabilistic information. Ontology evolution is an important problem in the Semantic Web research. Recently, Alchourron, Gardenfors and Markinson's (AGM) theory on belief change has been applied to deal with this problem. However, most of current work only focuses on the feasibility of the application of AGM postulates on contraction to description logics (DLs), a family of ontology languages. So the explicit construction of a revision operator is ignored. In this paper, we first generalize the AGM postulates on revision to DLs. We then define two revision operators in DLs. One is the weakening-based revision operator which is defined by weakening of statements in a DL knowledge base and the other is its refinement. We show that both operators capture some notions of minimal change and satisfy the generalized AGM postulates for revision. We are researching the interaction between the rule and the ontology layers of the Semantic Web, by comparing two options: 1) using OWL and its rule extension SWRL to develop an integrated ontology rule language, and 2) layering rules on top of an ontology with RuleML and OWL. Toward this end, we are developing the SWORIER system, which enables efficient automated reasoning on ontologies and rules, by translating all of them into Prolog and adding a set of general rules that properly capture the semantics of OWL. We have also enabled the user to make dynamic changes on the fly, at run time. This work addresses several of the concerns expressed in previous work, such as negation, complementary classes, disjunctive heads, and cardinality, and it discusses alternative approaches for dealing with inconsistencies in the knowledge base. In addition, for efficiency, we implemented techniques called extensionalization, avoiding reanalysis, and code minimization. Abstract To support the sharing and reuse of formally represented knowledge among AI systems, it is useful to define the common vocabulary in which shared knowledge is represented. A specification of a representational vocabulary for a shared domain of discourse—definitions of classes, relations, functions, and other objects—is called an ontology. This paper describes a mechanism for defining ontologies that are portable over representation systems. Definitions written in a standard format for predicate calculus are translated by a system called Ontolingua into specialized representations, including frame-based systems as well as relational languages. This allows researchers to share and reuse ontologies, while retaining the computational benefits of specialized implementations. We discuss how the translation approach to portability addresses several technical problems. One problem is how to accommodate the stylistic and organizational differences among representations while preserving declarative content. Another is how to translate from a very expressive language into restricted languages, remaining system-independent while preserving the computational efficiency of implemented systems. We describe how these problems are addressed by basing Ontolingua itself on an ontology of domain-independent, representational idioms. Ontologies provide a conceptualization of a domain of interest. Nowadays, they are typically represented in terms of Description Logics (DLs), and are seen as the key technology used to describe the semantics of information at various sites. The idea of using ontologies as a conceptual view over data repositories is becoming more and more popular, but for it to become widespread in standard applications, it is fundamental that the conceptual layer through which the underlying data layer is accessed does not introduce a significant overhead in dealing with the data. Based on these observations, in recent years a family of DLs, called DL-Lite, has been proposed, which is specifically tailored to capture basic ontology and conceptual data modeling languages, while keeping low complexity of reasoning and of answering complex queries, in particular when the complexity is measured w.r.t. the size of the data. In this article, we present a detailed account of the major results that have been achieved for the DL-Lite family. Specifically, we concentrate on @math , an expressive member of this family, present algorithms for reasoning and query answering over @math ontologies, and analyze their computational complexity. Such algorithms exploit the distinguishing feature of the logics in the DL-Lite family, namely that ontology reasoning and answering unions of conjunctive queries is first-order rewritable, i.e., it can be delegated to a relational database management system. We analyze also the effect of extending the logic with typical DL constructs, and show that for most such extensions, the nice computational properties of the DL-Lite family are lost. We address then the problem of accessing relational data sources through an ontology, and present a solution to the notorious impedance mismatch between the abstract objects in the ontology and the values appearing in data sources. The solution exploits suitable mappings that create the objects in the ontology from the appropriate values extracted from the data sources. Finally, we discuss the QUONTO system that implements all the above mentioned solutions and is wrapped by the DIG-QUONTO server, thus providing a standard DL reasoner for @math with extended functionality to access external data sources. This paper presents a revision of Real Logic and its implementation with Logic Tensor Networks and its application to Semantic Image Interpretation. Real Logic is a framework where learning from numerical data and logical reasoning are integrated using first order logic syntax. The symbols of the signature of Real Logic are interpreted in the data-space, i.e, on the domain of real numbers. The integration of learning and reasoning obtained in Real Logic allows us to formalize learning as approximate satisfiability in the presence of logical constraints, and to perform inference on symbolic and numerical data. After introducing a refined version of the formalism, we describe its implementation into Logic Tensor Networks which uses deep learning within Google's T ensor F low ™. We evaluate LTN on the task of classifying objects and their parts in images, where we combine state-of-the-art-object detectors with a part-of ontology. LTN outperforms the state-of-the-art on object classification, and improves the performances on part-of relation detection with respect to a rule-based baseline. When deploying Answer Set Programming ASP in an industrial context, for instance for re-configurationi¾ź[5], knowledge engineers need debugging support on non-ground programs. Current approaches to ASP debugging, however, do not cover extended modeling features of ASP, such as choice rules, conditional literals, cardinality and weight constraintsi¾ź[13]. To this end, we encode non-ground ASP programs using extended modeling features into normal logic progams; this encoding extends existing encodings for the case of ground programs [4,10,11] to the non-ground case. We subsequently deploy this translation on top of an existing ASP debugging approach for non-ground normal logic programsi¾ź[14]. We have implemented and tested the approach and provide evaluation results. The majority of knowledge on the Web is encoded in unstructured text and is not linked to formalized knowledge, such as ontologies and rules. A potential solution to this problem is to acquire this knowledge through natural language processing and text mining methods. Prior work has focused on automatically extracting RDF- or OWL-based ontologies from text; however, the type of knowledge acquired is generally restricted to simple term hierarchies. This paper presents a general-purpose framework for acquiring more complex relationships from text and then encoding this knowledge as rules. Our approach starts with existing domain knowledge in the form of OWL ontologies and Semantic Web Rule Language (SWRL) rules and applies natural language processing and text matching techniques to deduce classes and properties. It then captures deductive knowledge in the form of new rules. We have evaluated our framework by applying it to web-based text on car rental requirements. We show that our approach can automatically and accurately generate rules for requirements of car rental companies not in the knowledge base. Our framework thus rapidly acquires complex knowledge from free text sources. We are expanding it to handle richer domains, such as medical science. Ontologies play a crucial role in the development of the Semantic Web as a means for defining shared terms in web resources. They are formulated in web ontology languages, which are based on expressive description logics. Significant research efforts in the semantic web community are recently directed towards representing and reasoning with uncertainty and vagueness in ontologies for the Semantic Web. In this paper, we give an overview of approaches in this context to managing probabilistic uncertainty, possibilistic uncertainty, and vagueness in expressive description logics for the Semantic Web.