Adding abductive reasoning to a propositional logic

We present a technique for obtaining a logic with abductive reasoning extending a given propositional logic. Abduction, along with deduction and induction, is recognized as important for machine learning, namely in identifying possible causes that may lead to the occurrence of an event and in providing new ways for a computational device to achieve a certain objective. Each rule in the original calculus induces a set of multiple-conclusion abductive rules. Moreover, rules stating generic properties of abduction have to be added. In the induced logic, the deductive mechanism of the base logic coexists with this abductive component. A new notion of a multiple-conclusion derivation had to be developed. Due to the canonical nature of obtaining such a logic, we prove the preservation of soundness, completeness, decidability and computational complexity. These concepts and results are illustrated in a robot navigation problem using a multimodal logic.