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Logic Journal of IGPL Advance Access originally published online on November 17, 2008
Logic Journal of IGPL 2008 16(6):537-560; doi:10.1093/jigpal/jzn020
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Vol. 16 No. 6, © The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Cut-Based Abduction

Marcello D’Agostino, Marcelo Finger * and Dov Gabbay


  Abstract

In this paper we explore a generalization of traditional abduction which can simultaneously perform two different tasks: (i) given an unprovable sequent {Gamma} {vdash} G, find a sentence H such that {Gamma}, H {vdash} G is provable (hypothesis generation); (ii) given a provable sequent {Gamma} {vdash} G, find a sentence H such that {Gamma} {vdash} H and the proof of {Gamma}, H {vdash} G is simpler than the proof of {Gamma} {vdash} G (lemma generation). We argue that the two tasks should not be distinguished, and present a general procedure for finding suitable hypotheses or lemmas. When the original sequent is provable, the abduced formula can be seen as a cut formula with respect to Gentzen's sequent calculus, so the abduction method is cut-based. Our method is based on the tableau-like system KE and we argue for its advantages over existing abduction methods based on traditional Smullyan-style Tableaux.

Received for publication 8 September 2008.

*Partly supported by CNPq grant PQ 301294/2004-6 and FAPESP project 04/14107-2.


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