Abstract
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.
We then show how cumulativity may be restored by adapting a technique recently applied by Brewka to default logic. The basic idea is to upgrade the universe of discourse: replace the elementary propositions, between which inference customarily takes place, by more complex items consisting of elementary propositions indexed by certain of the ”reasons” that lead to their acceptance.
However, as we finally show, the indexed JTMS still has a shortcoming: it does not give an adequate treatment of the phenomenon of ”floating conclusions”. The problem of finding an alternative aproach that handles floating conclusions adequately without losing cumulativity again, remains open.
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© 1991 Springer-Verlag Berlin Heidelberg
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Brewka, G., Makinson, D., Schlechta, K. (1991). Cumulative inference relations for JTMS and logic programming. In: Dix, J., Jantke, K.P., Schmitt, P.H. (eds) Nonmonotonic and Inductive Logic. NIL 1990. Lecture Notes in Computer Science, vol 543. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023314
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DOI: https://doi.org/10.1007/BFb0023314
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