arXiv subjects

Till Mossakowski

Publications and source records attributed to Till Mossakowski.

28 records · Page 2Linked to original sources

arXiv2016

A Survey of Qualitative Spatial and Temporal Calculi -- Algebraic and Computational Properties

Qualitative Spatial and Temporal Reasoning (QSTR) is concerned with symbolic knowledge representation, typically over infinite domains. The motivations for employing QSTR techniques range from exploiting computational properties that allow efficient reasoning to capture human cognitive concepts in a computational framework. The notion of a qualitative calculus is one of the most prominent QSTR formalisms. This article presents the first overview of all qualitative calculi developed to date and their computational properties, together with generalized definitions of the fundamental concepts and methods, which now encompass all existing calculi. Moreover, we provide a classification of calculi according to their algebraic properties.

cs.AI↗

arXiv2015

Query Answering over Contextualized RDF/OWL Knowledge with Forall-Existential Bridge Rules: Decidable Finite Extension Classes (Post Print)

The proliferation of contextualized knowledge in the Semantic Web (SW) has led to the popularity of knowledge formats such as \emph{quads} in the SW community. A quad is an extension of an RDF triple with contextual information of the triple. In this paper, we study the problem of query answering over quads augmented with forall-existential bridge rules that enable interoperability of reasoning between triples in various contexts. We call a set of quads together with such expressive bridge rules, a quad-system. Query answering over quad-systems is undecidable, in general. We derive decidable classes of quad-systems, for which query answering can be done using forward chaining. Sound, complete and terminating procedures, which are adaptations of the well known chase algorithm, are provided for these classes for deciding query entailment. Safe, msafe, and csafe class of quad-systems restrict the structure of blank nodes generated during the chase computation process to be directed acyclic graphs (DAGs) of bounded depth. RR and restricted RR classes do not allow the generation of blank nodes during the chase computation process. Both data and combined complexity of query entailment has been established for the classes derived. We further show that quad-systems are equivalent to forall-existential rules whose predicates are restricted to ternary arity, modulo polynomial time translations. We subsequently show that the technique of safety, strictly subsumes in expressivity, some of the well known and expressive techniques, such as joint acyclicity and model faithful acyclicity, used for decidability guarantees in the realm of forall-existential rules.

cs.DB↗

arXiv2014

An Institution for Simple UML State Machines

We present an institution for UML state machines without hierarchical states. The interaction with UML class diagrams is handled via institutions for guards and actions, which provide dynamic components of states (such as valuations of attributes) but abstract away from details of class diagrams. We also study a notion of interleaving product, which captures the interaction of several state machines. The interleaving product construction is the basis for a semantics of composite structure diagrams, which can be used to specify the interaction of state machines. This work is part of a larger effort to build a framework for formal software development with UML, based on a heterogeneous approach using institutions.

cs.SE↗

arXiv2014

An Institutional Framework for Heterogeneous Formal Development in UML

We present a framework for formal software development with UML. In contrast to previous approaches that equip UML with a formal semantics, we follow an institution based heterogeneous approach. This can express suitable formal semantics of the different UML diagram types directly, without the need to map everything to one specific formalism (let it be first-order logic or graph grammars). We show how different aspects of the formal development process can be coherently formalised, ranging from requirements over design and Hoare-style conditions on code to the implementation itself. The framework can be used to verify consistency of different UML diagrams both horizontally (e.g., consistency among various requirements) as well as vertically (e.g., correctness of design or implementation w.r.t. the requirements).

cs.SE↗

arXiv2013

Algebraic Properties of Qualitative Spatio-Temporal Calculi

Qualitative spatial and temporal reasoning is based on so-called qualitative calculi. Algebraic properties of these calculi have several implications on reasoning algorithms. But what exactly is a qualitative calculus? And to which extent do the qualitative calculi proposed meet these demands? The literature provides various answers to the first question but only few facts about the second. In this paper we identify the minimal requirements to binary spatio-temporal calculi and we discuss the relevance of the according axioms for representation and reasoning. We also analyze existing qualitative calculi and provide a classification involving different notions of a relation algebra.

cs.AI↗

arXiv2013

A Qualitative Comparison of the Suitability of Four Theorem Provers for Basic Auction Theory

Novel auction schemes are constantly being designed. Their design has significant consequences for the allocation of goods and the revenues generated. But how to tell whether a new design has the desired properties, such as efficiency, i.e. allocating goods to those bidders who value them most? We say: by formal, machine-checked proofs. We investigated the suitability of the Isabelle, Theorema, Mizar, and Hets/CASL/TPTP theorem provers for reproducing a key result of auction theory: Vickrey's 1961 theorem on the properties of second-price auctions. Based on our formalisation experience, taking an auction designer's perspective, we give recommendations on what system to use for formalising auctions, and outline further steps towards a complete auction theory toolbox.

cs.LO↗

arXiv2012

The Distributed Ontology Language (DOL): Use Cases, Syntax, and Extensibility

The Distributed Ontology Language (DOL) is currently being standardized within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37/SC 3. It aims at providing a unified framework for (1) ontologies formalized in heterogeneous logics, (2) modular ontologies, (3) links between ontologies, and (4) annotation of ontologies. This paper presents the current state of DOL's standardization. It focuses on use cases where distributed ontologies enable interoperability and reusability. We demonstrate relevant features of the DOL syntax and semantics and explain how these integrate into existing knowledge engineering environments.

cs.AI↗

arXiv2012

The Distributed Ontology Language (DOL): Ontology Integration and Interoperability Applied to Mathematical Formalization

The Distributed Ontology Language (DOL) is currently being standardized within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37/SC 3. It aims at providing a unified framework for (1) ontologies formalized in heterogeneous logics, (2) modular ontologies, (3) links between ontologies, and (4) annotation of ontologies. This paper focuses on an application of DOL's meta-theoretical features in mathematical formalization: validating relationships between ontological formalizations of mathematical concepts in COLORE (Common Logic Repository), which provide the foundation for formalizing real-world notions such as spatial and temporal relations.

cs.LO↗

arXiv2010

Qualitative Reasoning about Relative Direction on Adjustable Levels of Granularity

An important issue in Qualitative Spatial Reasoning is the representation of relative direction. In this paper we present simple geometric rules that enable reasoning about relative direction between oriented points. This framework, the Oriented Point Algebra OPRA_m, has a scalable granularity m. We develop a simple algorithm for computing the OPRA_m composition tables and prove its correctness. Using a composition table, algebraic closure for a set of OPRA statements is sufficient to solve spatial navigation tasks. And it turns out that scalable granularity is useful in these navigation tasks.

cs.AI↗

arXiv2009

Oriented Straight Line Segment Algebra: Qualitative Spatial Reasoning about Oriented Objects

Nearly 15 years ago, a set of qualitative spatial relations between oriented straight line segments (dipoles) was suggested by Schlieder. This work received substantial interest amongst the qualitative spatial reasoning community. However, it turned out to be difficult to establish a sound constraint calculus based on these relations. In this paper, we present the results of a new investigation into dipole constraint calculi which uses algebraic methods to derive sound results on the composition of relations and other properties of dipole calculi. Our results are based on a condensed semantics of the dipole relations. In contrast to the points that are normally used, dipoles are extended and have an intrinsic direction. Both features are important properties of natural objects. This allows for a straightforward representation of prototypical reasoning tasks for spatial agents. As an example, we show how to generate survey knowledge from local observations in a street network. The example illustrates the fast constraint-based reasoning capabilities of the dipole calculus. We integrate our results into two reasoning tools which are publicly available.

cs.AI↗