Cumulative Inference Relations for JTMS and Logic Programming

This paper makes three main points. We observe first that the inference relation induced by a set of JTMS justification rules under the grounded model semantics (or equivalently, by a logic program with negation under the Gelfond-Lifschitz semantics) is not in general cumulative: the addition to a set of assumptions of some of the derivable conclusions may lead to a loss of others.