. L O ] 1 9 Ju n 20 06 Pivotal and Pivotal - discriminative Consequence

In the present paper, we investigate consequence relations that are both paraconsistent and plausible (but still monotonic). More precisely, we lay the focus on pivotal consequence relations, i.e. those relations that can be defined by a pivot (in the style of e.g. D. Makinson). A pivot is a fixed subset of valuations which are considered to be the important ones in the absolute sense. We will provide characterizations for families of pivotal consequence relations, in a general framework that covers e.g. the ones of the well-known paraconsistent logics J3 and FOUR. In addition, we will provide, again in a general framework, characterizations for families of pivotal-discriminative consequence relations. The latter are defined exactly as the plain versions, except that among the conclusions, a formula is rejected if its negation is also present. We will also answer negatively a representation problem that was left open by Makinson. And, finally, we will put in evidence a connexion with X-logics from Forget, Risch, and Siegel. The motivations and the framework of the present paper are very similar to the ones of another paper of the same author which is about preferential consequence relations. A previous version of this paper has been published: The Journal of Logic and Computation, 15(5):679-700, 2005. The present version contains improvements about the presentation. Consequently, section ordering, definition numbers, proposition numbers, etc. are different according to whether the present or the previous version is considered.