Paraconsistent Query Answering Systems

Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in query answering systems. We compare the paraconsistent and the non-monotonic solutions to the problem of contradictions. We propose a many-valued paraconsistent logic based on a simple notion of indeterminacy. In particular we describe the semantics of the logic using key equalities for the logical operators. We relate our approach to works on bilattices. We also discuss and provide formalizations of two case studies, notably the well-known example involving penguins and a more interesting example in the domain of medicine. Paraconsistent logic can be seen as an alternative, for example, to nonmonotonic logic. Non-monotonists reject monotony because they think that there are experiences (most of the time involving birds) which show that monotony is wrong and in particular leads to some contradictions. But one who thinks the paraconsistent way would reject the principle of non contradiction and not monotony. The strategy of the paraconsistentist is more imaginative, he accepts to see penguins flying in the sky of Hawai’s beaches and pink floyds surfing on Antarctica’s permafrost. It seems to us that the future shall give the preference to paraconsistent logic taking in account the progress of genitical biology which already produces chicken without feathers, and in the future we may have flying pigs. In such an absurd world, it will make no sense to reason by default, because everything could be true by default. J.-Y. Béziau The Future of Paraconsistent Logic Logical Studies Online Journal 2 (1999) p. 12