Till Mossakowski

Otto-von-Guericke-Universität Magdeburg | OvGU · Department of Knowledge and Language Engineering (IWS)

Image schemas are mental patterns learned from perceptual experiences capturing conceptual constructions in expressions. In linguistic analysis, their visualizations are often context-dependent without a generalizable structure. Addressing this, we introduce The Diagrammatic Image Schema Language: a formal representation language that systematizes...

Connecting chemical structural representations with meaningful categories and semantic annotations representing existing knowledge enables data-driven digital discovery from chemistry data. Ontologies are semantic annotation resources that provide definitions and a classification hierarchy for a domain. They are widely used throughout the life scie...

Integrating human knowledge into neural networks has the potential to improve their robustness and interpretability. We have developed a novel approach to integrate knowledge from ontologies into the structure of a Transformer network which we call ontology pre-training: we train the network to predict membership in ontology classes as a way to emb...

Ontologies represent human domain expertise symbolically in a way that is accessible to human experts and suitable for a variety of applications. As a result, they are widely used in scientific research. A challenge for the neuro-symbolic field is how to use the knowledge encoded in ontologies together with sub-symbolic learning approaches. In this...

Reference ontologies provide a shared vocabulary and knowledge resource for their domain. Manual construction and annotation enables them to maintain high quality, allowing them to be widely accepted across their community. However, the manual ontology development process does not scale for large domains. We present a new methodology for automatic...

Integrating human knowledge into neural networks has the potential to improve their robustness and interpretability. We have developed a novel approach to integrate knowledge from ontologies into the structure of a Transformer network which we call ontology pre-training: we train the network to predict membership in ontology classes as a way to emb...

We formalise some aspects of the neural-symbol design patterns of van Bekkum et al., such that we can formally define notions of refinement of patterns, as well as modular combination of larger patterns from smaller building blocks. These formal notions are being implemented in the heterogeneous tool set (Hets), such that patterns and refinements c...

Reference ontologies provide a shared vocabulary and knowledge resource for their domain. Manual construction enables them to maintain a high quality, allowing them to be widely accepted across their community. However, the manual development process does not scale for large domains. We present a new methodology for automatic ontology extension and...

Heterogeneous data, different definitions and incompatible models are a huge problem in many domains, with no exception for the field of energy systems analysis. Hence, it is hard to re-use results, compare model results or couple models at all. Ontologies provide a precisely defined vocabulary to build a common and shared conceptualisation of the...

Chemical data is increasingly openly available in databases such as PubChem, which contains approximately 110 million compound entries as of February 2021. With the availability of data at such scale, the burden has shifted to organisation, analysis and interpretation. Chemical ontologies provide structured classifications of chemical entities that...

In this chapter we propose Generic Ontology Design Patterns, GODPs, as a methodology for representing and instantiating ontology design patterns in a way that is adaptable, and allows domain experts (and other users) to safely use them without cluttering their ontologies.

Chemical data is increasingly openly available in databases such as PubChem, which contains more than 110 million compound entries as of October 2020. With the availability of data at such scale, the burden has shifted to organisation, analysis and interpretation. Chemical ontologies provide structured classifications of chemical entities that can...

Generic Ontology Design Patterns, GODPs, are defined in GENERICDOL, an extension of theDistributed Ontology, Model and Specification Language,and implemented using theHeterogeneous Tool Set. Parameters such as classes,properties, individuals, or whole ontologies may be instantiated with arguments ina host ontology.The potential of GENERICDOLis illu...

Databases and the query language SQL play a major role in modern applications. In this paper we present an institution-based formalisation of relational databases that uses structures close to those used in SQL. This is the essential difference to other category-theoretical formalisations of databases, which often depart quite far from the SQL stan...

Generic Ontology Design Patterns, GODPs, are defined in Generic DOL, an extension of DOL, the Distributed Ontology, Model and Specification Language, and implemented using Heterogeneous Tool Set. Parameters such as classes, properties, individuals, or whole ontologies may be instantiated with arguments in a host ontology. The potential of Generic D...

Generic ontologies were introduced as an extension (Generic DOL) of the Distributed Ontology, Modeling and Specification Language, DOL, with the aim to provide a language for Generic Ontology Design Patterns. In this paper we present a number of new language constructs that increase the expressivity and the generality of Generic DOL, among them seq...

We combine CASL's pushout-style generic specification with DOL's filtering, the latter being a syntactic removal of parts of a specification. The challenge is that now the body of a generic specification can remove parts of the formal parameter. This cannot be handled with usual pushout semantics, but calls for a semantics of “match, delete, glue i...

This paper addresses the semantics of weighted argumentation graphs that are bipolar, i.e. contain both attacks and supports for arguments. We build on previous work by Amgoud, Ben-Naim et. al. We study the various characteristics of acceptability semantics that have been introduced in these works. We provide a simplified and mathematically elegant...

We study the question of consistency of multi-view models in UML and OCL. We critically survey the large amount of literature that already exists. We find that only limited subsets of the UML/OCL have been covered so far and that consistency checks mostly only cover structural aspects, whereas only few methods also address behaviour. We also give a...

In cognitive science the theory of conceptual blending provides an explanation of the human ability to invent concepts. This cognitive theory provides an inspiration for computational concept invention theory, which has the goal of building creative systems that generate new concepts automatically. In Chapter 3 we discuss a workflow for a system th...

Over the last decades, the WADT community has studied the formal specification of software (and hardware) in great detail [1, 9, 42].

Colimits are a powerful tool for the combination of objects in a category. In the context of modeling and specification, they are used in the institution-independent semantics (1) of instantiations of parameterised specifications (e.g. in the specification language CASL), and (2) of combinations of networks of specifications (in the OMG standardise...

Ontology matching and alignment are key mechanism for linking the diverse datasets and ontologies arising in the Semantic Web and other application areas for formalised ontologies. We show that category theory provides the powerful abstractions needed for a uniform treatment of ontology alignment at various levels: semantics, language design, reaso...

Cognitive linguistics introduced image schemas as a missing link between embodied experiences and high-level conceptualisation in language and metaphorical thinking. They are described as the abstract spatio-temporal relationships that function as conceptual building blocks for everyday concepts and events. Although there is increasing interest in...

A qualitative representation of space and/or time provides mechanisms which characterize the essential properties of objects or configurations. The advantages over quantitative representations can be: (1) a better match with human concepts related to natural language, and (2) better efficiency for reasoning. The two main trends in qualitative spati...

Colimits are a powerful tool for the combination of objects in a category. In the context of modeling and specification, they are used in the institution-independent semantics (1) of instantiations of parameterised specifications (e.g. in the specification language CASL), and (2) of combinations of networks of specifications (in the OMG standardise...

We propose and study a framework for systematic development of software systems (or models) from their formal specifications. We introduce a language for formal development by refinement and decomposition, as an extension to CASL. We complement it with a notion of refinement tree and present proof calculi for checking correctness of refinements as...

Solid decision making should be ideally based on clear arguments that can be justified by trustworthy information sources. However, argument spaces can quickly get quite complex and it is very often hard to trace the line of arguments found in literature or social media such as blogs and forums. In this paper, we propose a framework for a decision...

Ontohub is a repository engine for managing distributed heterogeneous ontologies. The distributed nature enables communities to share and exchange their contributions easily. The heterogeneous nature makes it possible to integrate ontologies written in various ontology languages. Ontohub supports a wide range of formal logical and ontology language...

This paper discusses the semantics of weighted argumentation graphs that are biplor, i.e. contain both attacks and support graphs. The work builds on previous work by Amgoud, Ben-Naim et. al., which presents and compares several semantics for argumentation graphs that contain only supports or only attacks relationships, respectively.

We study the question of consistency of multi-view models in UML and OCL. We first critically survey the large amount of literature that already exists. We find that only limited subsets of the UML/OCL have been covered so far and that consistency checks mostly only cover structural aspects, whereas only few methods also address behaviour. We also...

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 qualitat...

The Distributed Ontology, Model, and Specification Language DOL provides logic-independent structuring, linking, and modu-larity constructs. Its homogeneous OWL fragment, DOWL, we argue, can be seen as an ideal language for formalising ontology patterns in description logics. It naturally consumes earlier formalisms such as C-OWL or DDL, and extend...

In some cases it may be useful to represent a problem in many logical domains, since they provide different perspectives for addressing formal verification. However, the maintenance of multiple representations in separate domains can be expensive if there is neither automated assistance nor a clear formal relation between these domains. We have add...

Qualitative spatial descriptions characterize essential properties of spatial objects or configurations by relying on relative comparisons rather than measuring. Typically, in qualitative approaches only relatively coarse distinctions between configurations are made. Qualitative spatial knowledge can be used to represent incomplete and underdetermi...

The notion of signature morphism is basic to the theory of institutions. It provides a powerful primitive for the study of specifications, their modularity and their relations in an abstract setting. The notion of derived signature morphism generalises signature morphisms to more complex constructions, where symbols may be mapped not only to symbol...

The notion of module extraction has been studied extensively in the ontology community. The idea is to extract, from a large ontology, those axioms that are relevant to certain concepts of interest (formalised as a subsignature). The technical concept used for the definition of module extraction is that of inseparability, which is related to indist...

There is a diversity of ontology languages in use, among them \(\mathsf{OWL}\), RDF, OBO, Common Logic, and F-logic. Related languages such as UML class diagrams, entity-relationship diagrams and object role modeling provide bridges from ontology modeling to applications, e.g., in software engineering and databases. Also in model-driven engineering...

Conceptual blending has been employed very successfully to understand the process of concept invention, studied particularly within cognitive psychology and linguistics. However, despite this influential research, within computational creativity little effort has been devoted to fully formalise these ideas and to make them amenable to computational...

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...

In this essay we analyse and elucidate the method to establish and clarify the scope of logic theorems offered within the theory of institutions. The method presented pervades a lot of abstract model the- oretic developments carried out within institution theory. The power of the proposed general method is illustrated with the examples of (Craig) i...

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, whic...

We provide an ontology for OpenStreetMap tags, called OSMonto, which can be used in different ways: (1) browsing of the hierarchy of tags is eased, (2) tags can be related with other ontologies, let it be tool-specific ontologies or more general ontologies like the recent Schema.org ontology supported by the dominant search engines, and (3) concept...

We have defined a unified environment that allows formal verification within the Model-Driven Engineering (MDE) paradigm using heterogeneous verification approaches. The environment is based on the Theory of Institutions, which provides a sound basis for representing MDE elements and a way for specifying translations from these elements to other lo...

Proof calculi for structured specifications have been developed independently of the underlying logical system (formalised as institution). Typically, completeness of these calculi requires interpolation properties of the underlying logic. We develop a relatively complete calculus for structured heterogeneous specifications that does not need inter...

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 i...

This paper addresses issues arising in the systematic construction of large logical systems. We rely on a model-theoretic view of logical systems, captured by institutions that are in turn presented by parchments. We define their categories, and study constructions that may be carried out in these categories. In particular we show how limits of par...

Ontology matching and alignment is a key mechanism for linking the diverse datasets and ontologies arising in the Semantic Web. We show that category theory provides the powerful abstractions needed for a uniform treatment at various levels: semantics, language design, reasoning and tools. The Distributed Ontology Language DOL is extended in a natu...

We present the theoretical background for an extension of the Heterogeneous Tool Set Hets that enables proof support for Common Logic. This is achieved via logic translations that relate Common Logic and some of its sublogics to already supported logics and automated theorem proving systems. We thus provide the first theorem proving support for Com...

Reasoning over spatial descriptions involving relations that can be described as left, right and inline has been studied extensively during the last two decades. While the fundamental nature of these relations makes reasoning about them applicable to a number of interesting problems, it also makes reasoning about them computationally hard. The key...

Conservative extension is an important notion in the theory of formal specification [8]. If we can implement a specification SP, we can implement any conservative extension of SP as well. Hence, a specification can be shown consistent by starting with a consistent specification and extending it using a number of conservative extension steps. This i...

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 qu...

We present an architecture that permits compiling declarative logic specifications (given in some type theory like LF) into implementations of that logic within the heterogeneous tool set hets. The central contributions are the use of declaration patterns for singling out a suitable subset of signatures for a particular logic, and the automatic gen...

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 investig...

CoCasl (11), a recently developed coalgebraic extension of the algebraic specica- tion language Casl (2), allows for modelling systems in terms of inductive datatypes as well as of co-inductive process types. Here, we demonstrate how to specify pro- cess algebras, namely CCS (10) and CSP (8,17), within such an algebraic-coalgebraic framework. It tu...

The distributed ontology language (DOL) is a recent development within the ISO standardisation initiative 17347 ontology integration and interoperability (OntoIOp). In DOL, heterogeneous and distributed ontologies can be expressed, i.e. ontologies that are made up of parts written in ontology languages based on various logics. In order to make the...

Domain modelling based on UML class diagrams is an established industrial practice. In the context of the Railway industry, we show how to utilize such diagrams for verification. This involves the translation of UML class diagrams into the algebraic specification language CASL. To this end, we define new class diagram institutions and provide suita...

There is a diversity of ontology languages in use, among them OWL, RDF, OBO, Common Logic, and F-logic. Related languages such as UML class diagrams, entity-relationship diagrams and object role modelling provide bridges from ontology modelling to applications, e.g. in software engineering and databases. Another diversity appears at the level of on...

We present the integration of the refinement method of the VSE verification tool, successfully used in industrial applications, in the Heterogeneous Tool Set HETS. The connection is done via introducing the dynamic logic underlying VSE and two logic translations in the logic graph of HETS. Thus the proof management formalism provided by HETS can be...

Methods for automated classification of chemical data depend on identifying interesting parts and properties. However, classes of chemical entities which are highly symmetrical and contain large numbers of homogeneous parts (such as carbon atoms) are not straightforwardly classified in this fashion. One such class of molecules is the fullerene fami...

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. Thi...

Increasing availability of GPS-enabled devices technically enables a broad variety of people to participate in the volunteered geographic information (VGI) movement and to collect and share information about places and spatial entities. But in order to be useful, geo-data has to be correctly classified, and inexperienced users need assistance to be...

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. Thi...

The Distributed Ontology Language DOL, which is currently being stan-dardised as ISO WD 17347 within the OntoIOp (Ontology Integration and Inter-operability) activity of ISO/TC 37/SC 3, aims at providing a unified framework for (1) ontologies formalised in heterogeneous logics, (2) modular ontologies, (3) links between ontologies, and (4) annotatio...

The Distributed Ontology Language (DOL), currently being standardised within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37/SC 3, aims at providing a unified framework for (1) ontologies formalised in heterogeneous logics, (2) modular ontologies, (3) links between ontologies, and (4) annotation of ontologies. This pap...