8 Conclusions

19 and complete calculus for DFOL based on ML systems. Finally we have compared our formalism with other formalisms for the representation and integration of distributed knowledge and reasoning systems. Acknowledgments. We thank all the people of the Mechanized Reasoning Group of IRST and DISA for useful discussions and feedback on the paper. We thank Massimo Benerecetti and Sergio Tessaris for carefully proofreading the paper. We also thank the anonymous referees for valuable comments. This work is part of the MRG project Distributed Representations and Systems 18 plus a set of clauses (called amalgamated clauses) which resolve connicts due to inconsistent facts and compose uncertain information of diierent theories. One of the main similarity with our approach is the capability to cope with inconsistent knowledge bases. Annotated logics provide an explicit way to solve connicts. The main diierence between annotated logics and DFOL concerns the ability to represent diierent interpretation domains. Annotated logics has a unique logical language, and the same symbol in diierent knowledge bases is interpreted in the same object. This of course might be trivially solved by indexing the constant with the name of the knowledge base. In this case explicit relational symbols between objects of diierent knowledge bases should be introduced. A Cooperative Information System (CIS) is a formal system based on description logics Donini et al., 1996]. A CIS copes with the semantics for heterogeneous information integration. A CIS is quite similar to a theory in DFOL. A CIS is composed of a set of description languages, a T-BOX for each language, and a set of so-called interschema assertions. Under the usual translation of description logics in rst order logics and the translation of interschema assertion into DFOL compatibility constraints, it can be shown that a CIS can be embedded into DFOL. The main diierence between CIS and DFOL concerns the semantics. A model for a CIS is deened over a \global" domain which is the union of the domains i of the models of each description language. This implies that a constant c in diierent languages is interpreted in the same object c in the CIS. As a consequence various forms of relation between domains, e.g., abstraction, cannot be represented in CIS. A second diierence is that CIS models complete databases and cannot express partiality. Totality aaects directionality. Indeed in CIS every interschema assertion L 1 : ext L 2 (L 1 : int …