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Proving Theorems in a Multi-Source Environment

This paper describes a logic for reasoning in a multi-source environment and a theorem prover for this logic. We assume the existence of several sources of information (data/knowledge bases), each of them providing information. The main problem dealt with here is the problem of the consistency of the information : even if each separate source is consistent, the global set of information may be inconsistent. In our approach, we assume that the different sources are totally ordered, according to their reliability. This order is then used in order to avoid inconsistency. The logic we define for reasoning in this case is based on a classical logic augmented with pseudo-modalities. Its semantic is first detailed. Then a sound and complete axiomatic is given. Finally, a theorem prover is specified at the meta-level. We prove that it is correct with regard to the logic. We then implement it in a PROLOG-like language.