Combining reasoning systems

Combining logics for modeling purposes has become a rapidly expanding enterprise that is inspired mainly by concerns about modularity and the wish to join together diierent kinds of information. As any interesting real world system is a complex composite entity, decomposing its descriptive requirements (for design, veriication, or maintenance purposes) into simpler, more restricted reasoning tasks is appealing as it is often the only plausible way forward. It would be an exaggeration to claim that we have a thorough understanding of`combined methods.' Nevertheless, a core body of notions, questions and results has emerged for an important class of combined logics, and we are beginning to understand how this core theory behaves when we try to apply it outside this particular class. Does the idea of combining logics actually ooer anything new? Some of the possible objections can be justiied. Logical combination is a relatively new idea: it has been not yet systematically explored, and there is no established body of the results or techniques. Nonetheless, there is a growing body of logic-oriented work in the eld, and there are explorations of their uses in AI, computational linguistics, automated deduction, and computer science. An overly critical reaction seems misguided. The plan of this abstract is as follows. We start with a discussion of a class of problems typically considered in the are. We then take a brief look at actual implementations of combined logics. Transfer Problems Let L 1 and L 2 be two logics|typically, these are special purpose logics with limited expressive power, as it often does not make sense to put together logics with universal expressive power. Let P be a property that logics may have, say decidability, or axiomatic completeness. The transfer problem is this: if L 1 and L 2 enjoy the property P, does their combination L 1 L 1 have P as well? Transfer problems belong to the main mathematical questions that logicians have been concerned with in the area of combining logics. When, and for which properties do we have transfer or failure of transfer? As a rule of {11{