Abstract
Although it has been shown that non-monotonic reasoning is presumably harder than classical reasoning, there are cases where a non-monotonic treatment actually simplifies matters. Indeed, one of the reasons for considering non-monotonic systems is the hope of speeding up reasoning, and not to slow it down. In this paper, we consider proof lengths in a cut-free sequent calculus, and we show that the application of circumscription (or completion) to certain first-order formulae leads to a non-elementary speed-up of proof length. This is possible because the introduction of the completion formula can simulate the cut rule.
The authors would like to thank Georg Gottlob and Thomas Eiter for their useful comments and constructive criticisms on an earlier version of this paper. The first author was partly supported by the Christian Doppler Labor für Expertensysteme, Wien, Austria.
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Egly, U., Tompits, H. (1997). Is non-monotonic reasoning always harder. In: Dix, J., Furbach, U., Nerode, A. (eds) Logic Programming And Nonmonotonic Reasoning. LPNMR 1997. Lecture Notes in Computer Science, vol 1265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63255-7_5
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DOI: https://doi.org/10.1007/3-540-63255-7_5
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