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In this paper, we summarise our results on Modelling Dynamics in Semantic Web Knowledge Graphs published at WWW 2018 where we proposed a novel data-driven schema for graphs and apply it for the use-case of predicting high-level changes in Wikidata. +
Indexing video data is essential for providing content based access. In this paper, we consider how database technology can offer an integrated framework for modeling and querying video data. As many concerns in video (e.g., modeling and querying) are also found in databases, databases provide an interesting angle to attack many of the problems. From a video applications perspective, database systems provide a nice basis for future video systems. More generally, database research will provide solutions to many video issues even if these are partial or fragmented. From a database perspective, video applications provide beautiful challenges. Next generation database systems will need to provide support for multimedia data (e.g., image, video, audio). These data types require new techniques for their management (i.e., storing, modeling, querying, etc.). Hence new solutions are significant. This paper develops a data model and a rule-based query language for video content based indexing and retrieval. The data model is designed around the object and constraint paradigms. A video sequence is split into a set of fragments. Each fragment can be analyzed to extract the information (i.e., symbolic descriptions) of interest that can be put into a database. This database can then be searched to find information of interest. Two types of information are considered: (1) the entities (i.e., objects) of interest in the domain of a video sequence, (2) video frames which contain these entities. To represent these information, our data model allows facts as well as objects and constraints. We present a declarative, rule-based, constraint query language that can be used to infer relationships about information represented in the model. The language has a clear declarative and operational semantics. +
Indexing video data is essential for providing content based access. In this paper, we consider how database technology can offer an integrated framework for modeling and querying video data. As many concerns in video (e.g., modeling and querying) are also found in databases, databases provide an interesting angle to attack many of the problems. From a video applications perspective, database systems provide a nice basis for future video systems. More generally, database research will provide solutions to many video issues even if these are partial or fragmented. From a database perspective, video applications provide beautiful challenges. Next generation database systems will need to provide support for multimedia data (e.g., image, video, audio). These data types require new techniques for their management (i.e., storing, modeling, querying, etc.). Hence new solutions are significant. This paper develops a data model and a rule-based query language for video content based indexing and retrieval. The data model is designed around the object and constraint paradigms. A video sequence is split into a set of fragments. Each fragment can be analyzed to extract the information (symbolic descriptions) of interest that can be put into a database. This database can then be searched to find information of interest. Two types of information are considered: (1) the entities (objects) of interest in the domain of a video sequence, (2) video frames which contain these entities. To represent these information, our data model allows facts as well as objects and constraints. We present a declarative, rule-based, constraint query language that can be used to infer relationships about information represented in the model. The language has a clear declarative and operational semantics. +
The Bernays-Schönfinkel first-order logic fragment over simple linear real arithmetic constraints BS(SLR) is known to be decidable. We prove that BS(SLR) clause sets with both universally and existentially quantified verification conditions (conjectures) can be translated into BS(SLR) clause sets over a finite set of first-order constants. For the Horn case, we provide a Datalog hammer preserving validity and satisfiability. A toolchain from the BS(LRA) prover SPASS-SPL to the Datalog reasoner VLog establishes an effective way of deciding verification conditions in the Horn fragment. This is exemplified by the verification of supervisor code for a lane change assistant in a car and of an electronic control unit for a supercharged combustion engine. +
We formally introduce a novel, yet ubiquitous, category of norms: norms of instrumentality. Norms of this category describe which actions are obligatory, or prohibited, as instruments for certain results. We propose the Logic of Agency and Norms (LAN) that enables reasoning about actions, instrumentality, and normative principles in a multi-agent setting. Leveraging LAN, we formalize norms of instrumentality and compare them to two prevalent norm categories: norms to be and norms to do. Last, we pose principles describing relations between the three categories and evaluate their validity vis-a-vis notions of deliberative acting. On a technical note, the logic will be shown decidable via the finite model property. +
Complex Event Processing as well as pattern matching against streams have become important in many areas including financial services, mobile devices, sensor-based applications, click stream analysis,real-time processing in Web 2.0 and 3.0 applications and so forth. However, there is a number of issues to be considered in order to enable effective pattern matching in modern applications. A language for describing patterns needs to feature a well-defined semantics, it needs be rich enough to express important classes of complex patterns such as iterative and aggregative patterns, and the language execution model needs to be efficient since event processing is a real-time processing. In this paper, we present an event processing framework which includes an expressive language featuring a precise semantics and a corresponding execution model, expressive enough to represent iterative and aggregative patterns. Our approach is based on a logic, hence we analyse deductive capabilities of such an event processing framework. Finally, we providean open source implementation and present experimental results of our running system. +
We investigate cumulated clauses on a set of attributes consisting of concept descriptions of the description logic FLE. This kind of conceptual statements is argued to be close to intuitive human reasoning. We provide a deduction calculus for cumulated clauses on FLE that is obviously sound and give an elaborated proof for its completeness. +
Motivated by the need for semantically well-founded and algorithmically managable formalisms for describing the functionality of Web services, we introduce an action formalism that is based on description logics (DLs), but is also firmly grounded on research in the reasoning about action community. Our main contribution is an analysis of how the choice of the DL influences the complexity of standard reasoning tasks such as projection and executability, which are important for Web service discovery and composition. +
This paper provides a self-contained first introduction to description logics (DLs). The main concepts and features are explained with examples before syntax and semantics of the DL SROIQ are defined in detail. Additional sections review light-weight DL languages, discuss the relationship to the Web Ontology Language OWL and give pointers to further reading. +
This chapter provides a self-contained first introduction to description logics (DLs). The main concepts and features are explained with examples before syntax and semantics of the DL SROIQ are defined in detail. Additional sections review light-weight DL languages, discuss the relationship to the Web Ontology Language OWL and give pointers to further reading. +
This work introduces the concept language ALC F(M), which is an extension of ALC to many-valued logics. ALC F(M) allows to express vague concepts, e.g. more or less enlarged or very small.
To realize this extension to many-valued logics, the classical notions of satisfiability and subsumption had to be modified appropriately. The main contribution of this paper is a sound and complete method for computing the degree of subsumption between two ALC F(M)-concepts. +
This work introduces the concept language ALC(FM) which is an extension of ALC to many-valued logics. ALC(FM) allows to express vague concepts, e.g. `more or less enlarged' or `very small'. To realize this extension to many-valued logics, the classical notions of satisfiability and subsumption had to be modified appropriately. For example, ALC(FM)-concepts are no longer either satisfiable or unsatisfiable, but they are satisfiable to a certain degree. The main contribution of this paper is a sound and complete method for computing the degree of subsumption between two ALC(FM)-concepts. +
We combine the modal logic S5 with the description logic (DL) ALCQI. The resulting multi-dimensional DL S5-ALCQI supports reasoning about change by allowing to express that concepts and roles change over time. It cannot, however, discriminate between changes in the past and in the future. Our main technical result is that satisfiability of S5-ALCQI concepts with respect to general TBoxes (including GCIs) is decidable and 2-ExpTime-complete. In contrast, reasoning in temporal DLs that are able to discriminate between past and future is inherently undecidable. We argue that our logic is sufficient for reasoning about temporal conceptual models with time-stamping constraints. +
This article presents the description logic ALCRP(D) with concrete domains and a role-forming predicate operator as its prominent aspects. We demonstrate the feasibility of ALCRP(D) for reasoning about spatial objects and their qualitative spatial relationships and provide an appropriate concrete domain for spatial objects. The general significance of ALCRP(D) is demonstrated by adding temporal reasoning to spatial and terminological reasoning using a combined concrete domain. The theory is motivated as a basis for knowledge representation and query processing in the domain of geographic information systems. In contrast to existing work in this domain, which mainly focuses either on conceptual reasoning or on reasoning about qualitative spatial relations, we integrate reasoning about spatial information with terminological reasoning. +
A Description Logic with Transitive and Converse Roles, Role Hierarchies and Qualifying Number Restrictions +
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We successively present algorithms that decides satisfiability of the DL alc extended with transitive and inverse roles, role hierarchies, and qualifying number restrictions. Early experiments indicate that this algorithm is well-suited for implementation. +
The combination of transitive and inverse roles is important in a range of applications, and is crucial for the adequate representation of aggregated objects, allowing the simultaneous description of parts by means of the whole to which they belong and of wholes by means of their constituent parts. In this paper we present tableaux algorithms for deciding concept satisfiability and subsumption in Description Logics that extend alc with both transitive and inverse roles, a role hierarchy, and functional restrictions. In contrast to earlier algorithms for similar logics, those presented here are well-suited for implementation purposes: using transitive roles and role hierarchies in place of the transitive closure of roles enables sophisticated blocking techniques to be used in place of the cut rule, a rule whose high degree of non-determinism strongly discourages its use in an implementation. As well as promising superior computational behaviour, this new approach is shown to be sufficiently powerful to allow subsumption and satisfiability with respect to a (possibly cyclic) knowledge base to be reduced to concept subsumption and satisfiability, and to support reasoning in a Description Logic that no longer has the finite model property. +
Formal Concept Analysis (FCA) can be used to analyze data given in the form of a formal context. In particular, FCA provides efficient algorithms for computing a minimal basis of the implications holding in the context. In this paper, we extend classical FCA by considering data that are represented by relational structures rather than formal contexts, and by replacing atomic attributes by complex formulae defined in some logic. After generalizing some of the FCA theory to this more general form of contexts, we instantiate the general framework with attributes defined in the Description Logic (DL) {EL}, and with relational structures over a signature of unary and binary predicates, i.e., models for {EL}. In this setting, an implication corresponds to a so-called general concept inclusion axiom (GCI) in {EL}, The main technical result of this paper is that, in {EL}, for any finite model there is a emph{finite} set of implications (GCIs) holding in this model from which all implications (GCIs) holding in the model follow. +
The notions `expressive power' or `expressiveness' of knowledge representation languages (KR languages) can be found in most papers on knowledge representation; but these terms are usually just employed in an intuitive sense. The papers contain only informal descriptions of what is meant by expressiveness. There are several reasons that speak in favour of a formal definition of expressiveness: for example, if we want to show that certain expressions in one language cannot be expressed in another language, we need a strict formalism that can be used in mathematical proofs.
Even though we shall only consider terminological KR languages---i.e. KR languages descending from the original system KL-ONE---in our motivation and in the examples, the definition of expressive power that will be given in this paper can be used for all KR languages with Tarski-style model-theoretic semantics. This definition will shed a new light on the tradeoff between expressiveness of a representation language and its computational tractability. There are KR languages with identical expressive power, but different complexity results for reasoning, which comes from the fact that sometimes the tradeoff lies between convenience and computational tractability. The definition of expressive power will be applied to compare various terminological KR languages known from the literature with respect to their expressiveness. This will yield examples for how to utilize the definition both in positive proofs---that is, proofs where it is shown that one language can be expressed by another language---and, more interestingly, in negative proofs---which show that a given language cannot be expressed by the other language. +
We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for extensions with combinations of seriality axioms and what we call "intuitionistic path axioms". We show that each axiomatization is sound and complete with completeness being shown via a typical canonical model construction. +
Description logics are well-known logical formalisms for knowledge representation. We propose to enrich knowledge bases (KBs) with dynamic axioms that specify how the satisfaction of statements from the KBs evolves when the interpretation is decomposed or recomposed, providing a natural means to predict the evolution of interpretations. Our dynamic axioms borrow logical connectives from separation logics, well-known specification languages to verify programs with dynamic data structures. In the paper, we focus on ALC and EL augmented with dynamic axioms, or to their subclass of positive dynamic axioms. The knowledge base consistency problem in the presence of dynamic axioms is investigated, leading to interesting complexity results, among which the problem for EL with positive dynamic axioms is tractable, whereas EL with dynamic axioms is undecidable. +
