Description Logics in Information Semantic Integration for Product Design and Manufacturing

The Beth definability property, a well-known property from classical logic, is investigated in the context of description logics: if a general L-TBox implicitly defines an L-concept in terms of a given signature, where L is a description logic, then does there always exist over this signature an explicit definition in L for the concept? This property has been studied before and used to optimize reasoning in description logics. In this paper a complete classification of Beth definability is provided for extensions of the basic description logic ALC with transitive roles, inverse roles, role hierarchies, and/or functionality restrictions, both on arbitrary and on finite structures. Moreover, we present a tableau-based algorithm which computes explicit definitions of at most double exponential size. This algorithm is optimal because it is also shown that the smallest explicit definition of an implicitly defined concept may be double exponentially long in the size of the input TBox. Finally, if explicit definitions are allowed to be expressed in first-order logic, then we show how to compute them in single exponential time.

PurposeThe purpose of this paper is to introduce an interpreting schema and semantic description framework for a collection of images of Xilankapu, a traditional Chinese form of embroidered fabric and brocade artwork.Design/methodology/approachFirst, the authors interpret the artwork of Xilankapu through Gillian Rose’s “four site” theory by presenting how the brocades were made, how the patterns of Xilankapu are classified and the geometrical abstraction of visual images. To further describe the images of this type of brocade, this paper presents semantic descriptions that include objective–non-objective relations and a multi-layered semantic framework. Furthermore, the authors developed corresponding methods for scanning, storage and indexing images for retrieval.FindingsAs exploratory research on describing, preserving and indexing images of Xilankapu in the context of the preservation of cultural heritage, the authors collected 1,000+ images of traditional Xilankapu, classifying and storing some of the images in a database. They developed an index schema that combines concept- and content-based approaches according to the proposed semantic description framework. They found that the framework can describe, store and preserve semantic and non-semantic information of the same image. They relate the findings of this paper to future research directions for the digital preservation of traditional cultural heritages.Research limitations/implicationsThe framework has been designed especially for brocade, and it needs to be extended to other types of cultural image.Originality/valueThe semantic description framework can describe connotative semantic information on Xilankapu. It can also assist the later information retrieval work in organizing implicit information about culturally related visual materials.

Semantic Web service matchmaking is the process of searching the space of possible matches between demands and supplies, and finds the best available ones. To achieve this, the semantic Web service matchmaking framework is one of the absolutely necessary components of service oriented architecture. This paper proposes a matchmaking framework based on Description Logic for semantic Web service described by RDF4S model, a novel semantic Web service description which consists of three layers: service oriented knowledge base, semantic description model and semantic description language. We describe the service description and service query conditions by using the ontologies that are included in service oriented knowledge base. The service resource specification is described according to Description Logics syntax and a Description Logic reasoner is used to compare service descriptions. By representing the semantics of service descriptions, the matchmaker enables the behavior of an intelligent agent to approach more closely that of a human user trying to locate suitable Web service resources.

Description Logics (DL) are quite well-established as underlying logics for KR. $\mathcal{ALC}$ is a basic description logic. ER and UML are among the most used semiformal artifacts in computer science. The DL-community has shown that one needs to go a bit further to reason on ER and UML models. $\mathcal{ALCQI}$ is able to express most of the features involved in an ER and UML modeling. DL-Lite would also be taken for doing this, although it might be more verbose.

The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition.We start by investigating a notion ofdefeasible subsumptionin the spirit of defeasible conditionals as studied by Kraus, Lehmann, and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for bothpreferentialandrationalsubsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level ofentailmentand present an algorithm for the computation ofrational closureof a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DLALC.

We propose a formal specification framework for functional aspects of services. We define services as operations which are specified by means of pre- and postconditions, for the specification of which we use extensions of description logic. The (extensions of) description logic and the specification framework itself are defined as institutions. This gives the framework a uniformity of definition and a solid algebraic and logical foundation. The framework can be used for the specification of service requests and service providers. Given a signature morphism from request to provider, we define when a service request is matched by a service provider, which can be used in service discovery. We provide a model-theoretic definition of matching and show that matching can be characterized by a semantic entailment relation which is formulated over a particular standard description logic. Thus proofs of matching can be reduced to standard reasoning in description logic for which one can use description logic reasoners.

Answering regular path queries in expressive Description Logics via alternating tree-automata

Description logics (DLs) and rule-based systems are two prominent families of knowledge representation formalisms. While DLs are focused on describing and reasoning about conceptual knowledge, rules are focused on answering queries about facts in the knowledge base. So far, research on DLs has been largely isolated from the research on rules. With the advent of the Semantic Web, however, it became apparent that neither formalism alone can cover all the practical use cases. The integration between DLs and rules, however, is technically challenging due to significant differences in the underlying semantic assumptions. In particular, DLs are based on standard first-order semantics and open-world assumption, whereas rules typically employ closed-world semantics based on a variant of circumscription. In my talk, I shall present an overview of the benefits of integrating DLs and rules in a coherent semantic framework, and shall discuss the main challenges in achieving a tight integration. I shall present an overview of the approaches currently discussed in literature. Finally, I shall present in more detail the approach that is based on the nonmonotonic logic MKNF by Lifschitz. This approach is tight in the sense that DLs and rules are given a common model-theoretic semantics. Furthermore, it is faithful in the sense that it is compatible with the original semantics of both DLs and rules. Finally, it is expressive and can naturally capture many of the existing proposals. I shall discuss the definitions of the semantics of the hybrid formalism, present a decision procedure for a particular decidable fragment, and discuss the complexity bounds of reasoning.

A framework for modeling Semantic Web Service is proposed. It is based on Description Logic (DL), hence it is endowed with a formal semantics and, in addition, it allows for expressing constraints in service descriptions of different strengths, i.e. Hard and Soft Constraints. Semantic service discovery can be performed by matching DL descriptions, expressing both Hard and Soft constraints, and exploiting DL inferences. Additionally, a method for solving the problem of ranking services is proposed which is based on the use of a semantic similarity measure for DL. This method can rank (matched) service descriptions on the grounds of their semantic similarity w.r.t. the service request, by preferring those that are able to better satisfy both Hard and Soft Constraints.

Standard Description Logics (DLs) can encode quantitative aspects of an application domain through either number restrictions, which constrain the number of individuals that are in a certain relationship with an individual, or concrete domains, which can be used to assign concrete values to individuals using so-called features. These two mechanisms have been extended towards very expressive DLs, for which reasoning nevertheless remains decidable. Number restrictions have been generalized to more powerful comparisons of sets of role successors in $$\mathcal {ALCSCC}$$ ALCSCC , while the comparison of feature values of different individuals in $$\mathcal {ALC} (\mathfrak {D})$$ ALC ( D ) has been studied in the context of $$\omega $$ ω -admissible concrete domains $$\mathfrak {D}$$ D . In this paper, we combine both formalisms and investigate the complexity of reasoning in the thus obtained DL $$\mathcal {ALCOSCC}(\mathfrak {D})$$ ALCOSCC ( D ) , which additionally includes the ability to refer to specific individuals by name. We show that, in spite of its high expressivity, the consistency problem for this DL is ExpTime-complete, assuming that the constraint satisfaction problem of $$\mathfrak {D}$$ D is also decidable in exponential time. It is thus not higher than the complexity of the basic DL $$\mathcal {ALC}$$ ALC . At the same time, we show that many natural extensions to this DL, including a tighter integration of the concrete domain and number restrictions, lead to undecidability.

Although there is an increasing amount of experimental research on learning concepts expressed in first-order logic, there are still relatively few formal results on the polynomial learnability of first-order representations from examples. Most previous analyses in the pac-model have focused on subsets of Prolog, and only a few highly restricted subsets have been shown to be learnable. In this paper, we will study instead the learnability of the restricted first-order logics known as “description logics”, also sometimes called “terminological logics” or “KL-ONE-type languages”. Description logics are also subsets of predicate calculus, but are expressed using a different syntax, allowing a different set of syntactic restrictions to be explored. We first define a simple description logic, summarize some results on its expressive power, and then analyze its learnability. It is shown that the full logic cannot be tractably learned. However, syntactic restrictions exist that enable tractable learning from positive examples alone, independent of the size of the vocabulary used to describe examples. The learnable sublanguage appears to be incomparable in expressive power to any subset of first-order logic previously known to be learnable.

Product manufacturing is currently one of the most important activities that people perform, as it directly or indirectly affects the daily life and economic well-being of countless people around the world. It is likely to continue to have a profound effect on world economies by providing a large source of employment and, ideally, by creating products that positively affect the lives of numerous people. For manufacturing to be successful in the long run, a broad range of factors must be taken into account when products are designed and developed. Product manufacturing today requires skilful decision-making in scenarios that are more complex and demanding than ever before, and the use of optimal system technologies has become essential. Readers of System Design Optimization for Product Manufacturing will learn about detailed concepts and practical technologies that enable successful product design and manufacture. These concepts and technologies are based on system optimization methodologies that consider a broad range of mechanical, as well as human, factors. System Design Optimization for Product Manufacturing explains the methodologies behind current and future product manufacture. Its detailed explanations of key concepts are relevant not only for product design and manufacture, but also for other business fields. These core concepts and methodologies can be applied to practically any field where informed decision-making is important, and where a range of often conflicting factors must be carefully weighed and considered. System Design Optimization for Product Manufacturing can be used as a fundamental reference book by both engineers and students in the fields of manufacturing, design engineering, and product development.

Motivated by a chemical process engineering application, we introduce a new concept constructor in Description Logics (DLs), an n-ary variant of the existential restriction constructor, which generalizes both the usual existential restrictions and so-called qualified number restrictions. We show that the new constructor can be expressed in \(\mathcal{ALCQ}\), the extension of the basic DL \(\mathcal{ALC}\) by qualified number restrictions. However, this representation results in an exponential blow-up. By giving direct algorithms for \(\mathcal{ALC}\) extended with the new constructor, we can show that the complexity of reasoning in this new DL is actually not harder than the one of reasoning in \(\mathcal{ALCQ}\). Moreover, in our chemical process engineering application, a restricted DL that provides only the new constructor together with conjunction, and satisfies an additional restriction on the occurrence of roles names, is sufficient. For this DL, the subsumption problem is polynomial.KeywordsPolynomial TimeDescription LogicConjunctive QueryConcept DescriptionDescription TreeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Description Logic is the logical basis of Semantic Web knowledge representation and reasoning, it has strong capacity of expression, but it is not applicable to uncertain knowledge representation and reasoning. Horn rule is a proper subset of first-order predicate logic, which can be determined, its implication expression makes the description closer to a natural description of the problem, but it can not fully express the abundant and hierarchical knowledge in application fields. Therefore the combination of Description Logic and Horn rule, and utilization of Resolution Principle for Constrained Logics, will effectively solve the problem of Uncertain Reasoning. For the subsistent uncertainty of fact and rules in the reasoning system, credibility can be expressed by the interval between 0 and 1, and Confidence Interval calculation for the querying results can be summarized as a process of solving homologous linear optimization equation.

This handbook provides a systematic survey of the central areas of philosophical logic. It is divided into four volumes, each devoted to a major sub-field within the disciplines. The articles should be of value to general philosophers, linguists, logicians, mathematicians and computer scientists. Volume 1, Elements of Classical Logic, deals with the background to what has come to be considered the standard formulation of predicate logic - both as far as its semantics and proof theory are concerned. The central chapter on predicate logic is followed by chapters outlining various alternative, but essentially equivalent ways of constructing the semantics for first-order logic as well as its proof theory. In addition, this volume contains a discussion of higher-order extensions of first-order logic and a compendium of the algorithmic and decision-theoretic prerequisites in the study of logical systems. Volume 2, Extensions of Classical Logic, surveys the most significant extensions of predicate logic and their applications to various philosophical fields of inquiry. The 12 chapters in this volume together provide a succinct introduction to a variety of intensional frameworks, a discussion of the most well-known logical systems, as well as an overview of major applications and of the open problems in the respective fields. Volume 3, Alternatives to Classical Logic, consists of a series of surveys of some of the alternatives to the basic assumptions of classical logic. These include many-valued logic, partial logic, free logic, relevance and entailment logics, dialogue logic, quantum logic and intuitionism. Volume 4, Topics in the Philosophy of Language, presents a panorama of the applications of logical tools and methods in the formal analysis of natural language. Since a number of developments in philosophical logic were originally stimulated by concern arising in the semantic analysis of natural language discourse, the chapters in this volume provide some criteria of evaluation of the applications of work in philosophical logic. In revealing both the adequacies and inadequacies of logical investigations in the semantic structures of natural discourse, these chapters also point the way to future developments in philosophical logic in general and thus close again the circle of inquiry relating logic and language.