Is It Important to Explain a Theorem? A Case Study on UML and $\mathcal{ALCQI}$

In the process of information semantic integration for product design and manufacturing, it is very important to express the product information semantic. Description logics (DLs) are a family of state-of-the-art knowledge representation languages, and a decidable subset of first-order logic. Firstly, by analyzing the characteristics of product information, proposed a semantic information description framework based on description logics for product information integration, which is divided into three levels: basic description logic, classic extended logic and unusual extended logic. Then, in the framework, reducer was taken for example to illustrate the application of their description logic in product design and manufacturing formal semantic information. Finally, based on description logic, discussed reasoning problems of product design and manufacturing information.

Level of detail in UML models and its impact on model comprehension: A controlled experiment

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.

6 - Normalization

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.

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.

Manufacturing companies across multiple industries face an increasingly dynamic and unpredictable environment. This development can be seen on both the market and supply side. To respond to these challenges, manufacturing companies must implement smart manufacturing systems and become more flexible and agile. The flexibility in operational planning regarding the scheduling and sequencing of customer orders needs to be increased and new structures must be implemented in manufacturing systems’ fundamental design as they constitute much of the operational flexibility available. To this end, smart and more flexible solutions for production planning and control (PPC) are developed. However, scheduling or sequencing is often only considered isolated in a predefined stable environment. Moreover, their orientation on the fundamental logic of the existing IT solutions and their applicability in a dynamic environment is limited. This paper presents a conceptual model for a task-based description logic that can be applied to factory planning, technology planning, and operational control. By using service-oriented architectures, the goal is to generate smart manufacturing systems. The logic is designed to allow for easy and automated maintenance. It is compatible with the existing resource and process allocation logic across operational and strategic factory and production planning.

For designing Entity-relationship(ER) schemas, an interesting topic is how to transform ER schemas into knowledge bases (KBs) in description logics (DLs). It is significance in translations that one can use automated DL reasoning services to support the development and maintenance of correct ER schemas. This paper proposed a faithful translation, which translates ER schemas into KBs in the description logic ALDL and allows us to reduce reasoning on ER schemas to finite models reasoning on ALDL KBs.

In recent years, there has been a significant increase in the popularity of ontological analysis of conceptual modelling techniques. To date, related research explores the ontological deficiencies of classical techniques such as ER or UML modelling, as well as business process modelling techniques such as ARIS or even Web Services standards such as BPEL4WS, BPML, ebXML, BPSS and WSCI. While the ontologies that form the basis of these analyses are reasonably mature, it is the actual process of an ontological analysis that still lacks rigour. The current procedure is prone to individual interpretations and is one reason for criticism of the entire ontological analysis. This paper presents a procedural model for ontological analysis based on the use of meta models, multiple coders and metrics. The model is supported by examples from various ontological analyses.

In the last two decades, modal and description logics have provided a theoretical framework for important applications in many areas of computer science. For this reason, the problem of automated reasoning in modal and description logics has been thoroughly investigated. In this chapter we show how efficient Boolean reasoning techniques have been imported, used and integrated into reasoning tools for modal and description logics. To this extent, we focus on modal logics, and in particular mainly on K(m). In particular, we provide some background in modal logics; we describe a basic theoretical framework and we present and analyze the basic tableau-based and DPLL-based techniques; we describe optimizations and extensions of the DPLL-based procedures; we introduce the automata-theoretic/OBDD-based approach; finally, we present the eager approach.

Throughout its history, deontic logic had to face the question whether it is a logic of descriptions or a logic of prescriptions, namely of imperatives. The paper describes how the idea that there is a ‘logic of imperatives’ first came about, what proposals there have been to explain it and what problems it has had difficulties to solve. The paper argues that the idea of a logic of imperatives rests on a mistaken parallelism between imperative and indicative language and that there is, as a matter of fact, no such logic. However, we can argue about what ought to be done or need not be done according to given imperatives, and appeal to existing imperatives to motivate new ones. Descriptively interpreted deontic logic suffices to explain the reasoning involved.

Under the complex operational environment of the antimissile operation, the application of Systems Modeling Language (SysML) parametric model in weapon system effectiveness evaluation is explored. The function of parametric graph model, the construction process of the model and the optimization method of the model are researched. Using feedback mechanism to collect, collate and calculate the parameters of the model, and realize the leap from the index relationship description to the calculation of the index. Finally, the feasibility and effectiveness of the proposed method is verified by using the system of antimissile weapon system as an example.

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.

Concrete domains are an extension of Description Logics (DLs) allowing to integrate reasoning about conceptual knowledge with reasoning about “concrete properties” of objects such as sizes, weights, and durations. It is known that reasoning with ALC(D), the basic DL admitting concrete domains, is PSpace-complete. In this paper, it is shown that the upper bound is not robust: we give three examples for seemingly harmless extensions of ALC(D)—namely acyclic TBoxes, inverse roles, and a role-forming concrete domain constructor—that make reasoning NExpTime-hard. As a corresponding upper bound, we show that reasoning with all three extensions together is in NExpTime.KeywordsDescription LogicConcrete PropertyAbstract FeatureConcrete DomainConcrete FeatureThese 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.

Standard graphical representations have played a crucial role in science and engineering throughout the last century. Without electrical symbolism, it is very likely that our industrial society would not have evolved at the same pace. Similarly, specialised notations such as the Feynmann notation or the process flow diagrams did a lot for the adoption of concepts in their own fields. With the advent of Systems Biology, and more recently of Synthetic Biology, the need for precise and unambiguous descriptions of biochemical interactions has become more pressing. While some ideas have been advanced over the last decade, with a few detailed proposals, no actual community standard has emerged. The Systems Biology Graphical Notation (SBGN) is a graphical representation crafted over several years by a community of biochemists, modellers and computer scientists. Three orthogonal and complementary languages have been created, the Process Descriptions, the Entity Relationships and the Activity Flows. Using these three idioms a scientist can represent any network of biochemical interactions, which can then be interpreted in an unambiguous way. The set of symbols used is limited, and the grammar quite simple, to allow its usage in textbooks and its teaching directly in high schools. The first level of the SBGN Entity Relationship language has been publicly released. Shared by the communities of biochemists, genomicians, theoreticians and computational biologists, SBGN languages will foster efficient storage, exchange and reuse of information on signalling pathways, metabolic networks and gene regulatory maps.