In many areas of Logic, Computer Science, and Artificial Intelligence, there is a need for specialized formalisms and inference mechanisms to solve domain-specific tasks. For this reason, various methods and systems have been developed that allow for an efficient and adequate treatment of such restricted problems. In most realistic applications, however, one is faced with a complex combination of different problems, which means that a system tailored to solving a single problem can only be applied if it is possible to combine it both with other specialized systems and with general purpose systems.
A well-investigated instance of this general combination task is the problem of combining constraint systems and the respective solvers. The lecture will give a short overview of the available methods and results, and then describe in detail two of the most prominent combination approaches in this area:
We will discuss similarities and differences of the two approaches, both from a syntactic (logical) and a semantic (algebraic) point of view, and comment on possibilities and principal limitations for optimizations.