The goal of this project is to develop and apply new approximate reasoning methods for expressive description logics as a basis for robot reasoning in the web ontology language OWL. The underlying idea of the approach developed in the project is to compute subsumption between concept expressions on the basis of a subset of the non-logical symbols in the theory. In the course of the project we plan to develop

1. Model-theoretic foundations of approximate subsumption between complex concept expressions.
    
   
2. A prototype of an inference engine implementing sound and complete algorithms for approximate subsumption.
    
   
3. Effective strategies for selecting appropriate subsets of non-logical symbols that lead to a good approximation results.
    
4. Showcases for the use of approximate subsumption for partial matchmaking in different applications areas.

The project is funded by the Ministry of Science of the federal state of Baden-Württemberg for a duration of two years starting from January 2007.

In the first year of the project, we mainly worked on the formal foundations of approximate reasoning for expressive description logics. Based on the work on approximate reasoning in ALC conducted by Cadoli and Schaerf in the early nineties, we have developed a new model theoretic semantics for concepts expressions in the Logic ALCQ that can be parametrized by a subset of the concept and relation names. This semantic provides the basis for a model theoretic notion of approximate subsumption with respect to a certain vocabulary [3].

Further, we have shown that approximate subsumption can be computed by rewriting concept expressions on a syntactic level and testing subsumption between the resulting concept expressions using a standard description logic reasoner as a black box [2]. Recently Schlobach et al have adopted and extended our approach to the case of general T-Boxes. The idea is simply to apply the syntactic rewriting step to every axiom in the T-Box.

In the first we have also investigated the use of approximate subsumption to the problem of computing partial matches between complex concept expressions and developed a first matching prototype. We tested the prototype on a real world data set consisting of complex product descriptions taken from a online hardware store [1].

Another application of approximate reasoning that has been investigated in the context of the project is the verification and debugging of automatically created mappings between description logic ontologies. We have implemented an approximate reasoning system that uses approximate reasoning for improving the performance of mapping  verification. An initial version of this method is described in [4. The methods precomputes implied subusmption relations and uses a sound but incomplete method for verifying the satisfiability of a mapping, reducing the complexity of online reasoning to a linear complexity.

The next steps in the project will include a major re-engineering of the matching prototype. We plan to include the results of Schlobach et al into the implementation and to base the system on the DIG interface to be independent of a specific reasoner as a black box. Further, we will investigate different strategies for selecting a subset of the vocabulary. A first investigation of using the number of occurrence of a concept name as a criterion has been made by Schlobach and others. We will look at criteria more specific to the problem of computing partial matches in different settings.

Further, an improved version of the approximate method for mapping verification is currently being implemented that combines optimal and approximate reasoning methods thus combining the advantages of approximate reaosning in terms of efficiency with the benefits of an optimal solution.