Nonmonotonic reasoning, neural-symbolic integration, conceptual structures, domain theory, topology, fixed-point theory.
I'm involved in the SmartWeb project.
The following are some of the research topics which I am currently investigating.
Logic programming and connectionist systems, i.e. artificial neural networks, are two very diverse AI paradigms, with very different strengths and weaknesses. The interplay between both is the subject of our investigations. In particular, we are interested in aspects involving first-order and nonmonotonic logics, which have only played a minor role in this area so far. We build heavily on an approach proposed by Hölldobler, Kalinke and Störr which was further extended in collaboration with Anthony K. Seda from Cork, Ireland, and Sebastian Bader. Our investigations also involve methods and tools from the theory of topological dynamical systems and other aspects of the interplay between logic and connectionism.
The representation and processing of conceptual knowledge plays an important role in data- and textmining, and also in semantic web research. Our work focusses on the integration and interaction of nonmonotonic and rule based reasoning systems with conceptual knowledge as provided e.g. by formal conept analysis and description logics.
We develop a uniform approach to different declarative semantics in logic programming and nonmonotonic reasoning. For normal logic programs, a unifying framework has already been developed. We are currently further analysing and extending our approach to more general paradigms. We perceive the study of decidability of answer set programming for first-order syntax to be a application area of our investigations.
We develop applications of generalized metric fixed-point theorems and other tools from topology and (quantitative) domain theory to the semantic analysis of logic programming and nonmonotonic reasoning. The work builds on investigations by Batharek and Subrahmanian, Fitting, and Seda. Amongst other things we develop topological tools for the analysis of nonmontonic semantic operators. A large body of publications on this topic has already appeared in joint work Anthony K. Seda from Cork, Ireland. A monograph on our joint work (which includes the main aspects of my dissertation) is in preparation.
Besides my teaching duties and my research I have an active interest in furthering particularly able students at early stages of their career. This includes (more or less frequent) teaching activities for enhancement programmes as well as the supervision of (a small number of) very good undergraduate students in early research projects.