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Journal of Logic and Computation

Volume 12, Issue 6, December 2002: pp. 1027-1060

Labelled Tableaux for Nonmonotonic Reasoning: Cumulative Consequence Relations

Alberto Artosi1, Guido Governatori2 and Antonino Rotolo3

1Department of Philosophy, University of Bologna, via Zamboni 38, I-40126 Bologna, Italy. E-mail: artosi@cirfid.unibo.it
2School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane, QLD 4072, Australia. E-mail: guido@itee.uq.edu.au
3CIRSFID, University of Bologna, Via Galliera 3, I-40121 Bologna, Italy. E-mail: rotolo@cirfid.unibo.it

In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method exploits the strong connection between these deductive relations and conditional logics, and it is based on the usual possible world semantics devised for the latter. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The basic inference rules are provided by the propositional system KE+-a tableau-like analytic proof system devised to be used both as a refutation method and a direct method of proof-that is the classical core of KEM which is thus enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications.

Keywords: Labelled tableaux; nonmonotonic reasoning; conditional logic

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