Qualitative spatio-temporal constraint satisfaction problems
Qualitative spatio-temporal is a constraint satisfaction problem with infinite domains. Compared with quantitative methods, it offers serveral advantages: on the one hand, qualitative calculi are often more efficient, on the other hand, they come closer to human orientation in space quantitative methods. Some qualitative spatial calculi even empirically have shown to be cognitively adequate.
Traditionally, qualitative spatio-temporal calculi are modeled as relation algebras. In the last few years there has been a paradigm shift result towards the use of various methods for solving constraint problems. Problems in the area of qualitative spatial inference are often NP-hard. Therefore, often approximation algorithms are used.
Moreover, an important problem is that there has been a profileration of many calculi, varying in topic (mereotopology, absolute orientation, relative orientation) and granularity. An research question is how to heterogeneously combine these calculi, such that problems can be modeled using different calculi in an integrated and coherent way. More...
Institutions and automata for UML, formal methods & ontologies
The main insight is that ontologies, MDE models and specifications can be seens as heterogeneous modular logical theories in some logical system, formalised as institution. For complex systems, an early formal model can checked early for consistency, resulting in possible design changes – instead of doing this later (which means more involved and costly) in the development. We have successfully applied this to ontologies and specifications. Currently, this method is being transferred to the modeling language UML. A heterogeneous formal semantics will respect the specifics of the different UML diagram types in a better way that existing formal semantics of UML.
A formal semantics of UML needs to reach beyond logic, because UML includes different forms of state machines, their composition, and interactions. Here, automata-theoretic methods are used both for the semantics and for ensuring multi-view consistency. The coalgebraic specification of automata allows a uniform treatment of different types of automata while obtaining general results.
The specification and modeling language DOL ("Distributed Ontology, Model and Specification Lnaguage") has been developed within the OMG, led by Prof. Mossakowski. We have built a community around this topic and linked it to other communities. We develop a suitable language with formal semantics, as well as proof methods and tools, among them the Heterogeneous Tool Set and the web platforms ontohub.org, model-hub.org, and spechub.org. More...
Formal Models of Concept Creation
How to capture human creativity with the computer? Is this possible at all? In the EU project “CoInvent: Concept Invention Theory, we study creative analogies and inventions in mathematics and music. A starting point is the theory of conceptual blending, which explains how concepts can be combined in new ways in order to form new concepts. For example, the complex numbers can be obtained by blending the geometric concept of normed real-valued vector space with the algebraic concept of a field. In music,
different harmonic schemes combined by blending into new ones. The Heterogeneous Tool Set, though developed in a completely different context, is a central infrastructure of Coinvent. More...
Modeling for electrical grids and renewable energies
The transition to renewable enegeries leads to challenges for the electrical grid (which will become a smart grid) and the coordination of energy production and concumption - consumers and producers will merge into prosumers. Modeling languages and tools can play a role here, in order to improve design, reliability, testing etc. of complex energy systems. We are involved in a project on open electricity Grid optimization and in one on a renewable energy database; further projects are in preparation.