NExpTime-Complete Description Logics with Concrete Domains

Concrete domains have been introduced in description logic (DL) to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. The primary research goal in this context was to find restrictions on the concrete domain such that its integration into certain DLs preserves decidability or tractability. In this article, we complement these investigations by studying the abstract expressive power of both first-order and description logics extended with concrete domains, i.e., we analyze which classes of first-order interpretations can be expressed using these logics, compared to what their counterparts without concrete domains can express. We demonstrate that, under natural conditions on the concrete domain D (which also play a role for decidability), extensions of first-order logic (FOL) or the well-known DL ALC with D share important formal characteristics with FOL, such as the compactness and the Löwenheim-Skolem properties. Nevertheless, these conditions do not ensure that the abstract expressive power of the extensions we consider is contained in that of FOL, though in some cases it is. To be more precise, we show, on the one hand, that unary concrete domains leave the abstract expressive power within FOL if we are allowed to introduce auxiliary predicates. As a by-product, we obtain (semi-)decidability results for some fragments of FOL extended with the concrete domains considered in this article. On the other hand, we show that the ability to express equality between elements of D , another condition employed in the context of showing decidability of ALC ( D ), is sufficient to push the abstract expressive power of most first-order fragments with concrete domains beyond that of FOL. While for such concrete domains D decidability is retained for ALC ( D ), we show that the availability of equality in D causes undecidability of the two-variable fragment of FOL( D ), although the two-variable fragment of FOL is decidable.

All currently available Network-based Intrusion Detection Systems (NIDS) rely upon passive protocol analysis which is fundamentally flawed as an attack can evade detection by exploiting ambiguities in the traffic stream as seen by the NIDS. We observe that different attack variations can be derived from the original attack using simple transformations. This paper proposes a semantic model for attack mutation based on dynamic description logics (DDL(X)), extensions of description logics (DLs) with a dynamic dimension, and explores the possibility of using DDL(X) as a basis for evasion composition. The attack mutation model describes all the possible transformations and how they can be applied to the original attack to generate a large number of attack variations. Furthermore, this paper presents a heuristics planning algorithm for the automation of evasion composition at the functional level based on DDL(X). Our approach employs classical DL-TBoxes to capture the constraints of the domain, DL-ABoxes to present the attack, and DL-formulas to encode the objective sequence of packets respectively. In such a way, the evasion composition problem is solved by a decidable tableau procedure. The preliminary results certify the potential of the approach.KeywordsIntrusion Detection/Prevention SystemsMulti-protocol EvasionsAdvanced Evasion TechniquesKnowledge Representation and ReasoningDynamic Description Logics

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.

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.

In order to capture the full fledge semantic of complicated product data model, the expressive language ALCNHR+K(D) is introduced. It cannot only be able to represent knowledge about concrete domain and constraints, but also rules in some sense of closed world semantic model hypothesis. Also the paper investigates an extension to description logic (DL) based knowledge reasoning by means of decomposing and rewriting complicated hybrid concepts into partitions. We present an approach that automatically decomposes the whole knowledge base into description logic compatible one and constraints solver one. Our arguments are two-fold. First, complex DLs with powerful representation ability lack effective reasoning ability. Second, we are concerned with how to reason effectively with the combination of inferences from distributed heterogeneous reasoner.

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.

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.

We consider an extension of linear-time temporal logic (LTL) with constraints interpreted over a concrete domain. We use a new automata-theoretic technique to show pspace decidability of the logic for the constraint systems (ℤ,<, =) and (ℕ,<, =).We also give an automata-theoretic proof of a result of Balbiani and Condotta [] for constraint systems that satisfy a “completion” property.

Handling exceptions in a knowledge-based system is an important issue in many application domains, such as medical domain. Recently, there is an increasing interest in nonmonotonic extension of description logics to handle exceptions in ontologies. In this paper, we propose three preferential semantics for plausible subsumption to deal with exceptions in description logic-based knowledge bases. Our preferential semantics are defined in the framework of possibility theory, which is an uncertainty theory devoted to handling incomplete information. We consider the properties of these semantics and their relationships. We also discuss the relationship between two of our preferential semantics and two existing preferential semantics. We extend a description logic-based knowledge base by adding preferential subsumptions. Entailment of plausible subsumptions relative to an extended knowledge base is defined. Properties of the preferential subsumption relations relative to an extended description logic-based knowledge base are discussed. Finally, we show that our semantics for plausible subsumption can be reduced to standard semantics of an expressive description logic. Thus, the problem of plausible subsumption checking under our semantics can be reduced to the problem of subsumption checking under the classical semantics.

Bipolarity is an important feature of spatial information, involved in the expression of preferences and constraints about spatial positioning or in pairs of opposite spatial relations such as left and right. Another important feature is imprecision which has to be taken into account to model vagueness, inherent to many spatial relations (as for instance vague expressions such as close to, to the right of), and to gain in robustness in the representations. In previous works, we have shown that fuzzy sets and fuzzy mathematical morphology are appropriate frameworks, on the one hand, to represent bipolarity and imprecision of spatial relations and, on the other hand, to combine qualitative and quantitative reasoning in description logics extended with fuzzy concrete domains. The purpose of this paper is to integrate the bipolarity feature in the latter logical framework based on bipolar and fuzzy mathematical morphology and description logics with fuzzy concrete domains. Two important issues are addressed in this paper: the modeling of the bipolarity of spatial relations at the terminological level and the integration of bipolar notions in fuzzy description logics. At last, we illustrate the potential of the proposed formalism for spatial reasoning on a simple example in brain imaging.

Concept languages based on KL-ONE [Brachman and Schmolze, 1985] are used to represent the taxonomical and conceptual knowledge of a particular problem domain on an abstract logical level. To describe this kind of knowledge, one starts with atomic concepts and roles, and defines new concepts using the operations provided by the language. Concepts can be considered as unary predicates which are interpreted as sets of individuals, and roles as binary predicates which are interpreted as binary relations bdtween individuals. Examples for atomic concepts may be Human and Male, and for roles child. If the logical connective of conjunction "n" is present as a language construct, one may describe the concept Man as "humans who are male", and represent it by the expression Human N Male. Many languages provide quantification over role fillers which allows for example to describe the concept Father by the expression Man N 3child.Human. KL-ONE was first developed for the purpose of natural language processing [Brazhman et al., 1979], and some of the existing systems are still mostly used in this context (see e.g., SB-ONE [Kobsa, 1989]). However, its success in this area has also led to applications in other fields (see e.g., MESON [Edelmann and Owsnicki, 1986] which is used for computer configuration tasks, CLASSIC [Borgida et al., 1989] which is e.g. used in the area of CAD/CAM, or K-REP [Mays et al., 1988] which is used in a financial marketing domain).

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.

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.

To represent and reason about contextualized knowledge often two-dimensional Description Logics (DLs) are employed, where one DL is used to describe contexts (or possible worlds) and the other DL is used to describe the objects, i.e. the relational structure of the specific contexts. Previous approaches for DLs of context that combined pairs of DLs resulted in undecidability in those cases where so-called rigid roles are admitted, i.e. if parts of the relational structure are the same in all contexts. In this paper, we present a novel combination of pairs of DLs and show that reasoning stays decidable even in the presence of rigid roles. We give complexity results for various combinations of DLs including \(\mathcal{ALC}\), \(\mathcal{SHOQ}\), and \(\mathcal{EL}\).KeywordsDescription LogicReasoning TaskConsistency ProblemObject LogicBinary CounterThese 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.