Abstract
Determining whether a given formula holds in any extension of a Default Logic (DL) theory is called in [8] goal directed reasoning. Reiter [14] presented a goal-directed proof theory for normal default theories. But Reiter and Criscuolo [15] showed that semi-normal defaults were needed in DL to give priorities between defaults to eliminate anomalous extensions. Moreover, Marek and Truszczynski [11] showed that any DL theory can be represented as a seminormal default theory. Etherington [4, 5] developed a forward procedure for constructing default extensions of a subclass of semi-normal default theories. Since a theory may have many extensions, it seems wasteful to compute an entire extension when one is only concerned with goal directed reasoning. Moreover, the given formula may not be contained in the currently computed extension.This paper presents a goal-directed proof theory for semi-normal default theories. A proof of soundness is presented for plain ordered network semi-normal default theories. We show that if there is a proof of a given formula, then an extension containing this formula can be constructed by Etherington's procedure. We also present a goal-directed proof procedure to compute a default proof.
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© 1995 Springer-Verlag Berlin Heidelberg
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Zaverucha, G., Veloso, S.R.M. (1995). A goal directed reasoning for semi-normal default theories. In: Wainer, J., Carvalho, A. (eds) Advances in Artificial Intelligence. SBIA 1995. Lecture Notes in Computer Science, vol 991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034804
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DOI: https://doi.org/10.1007/BFb0034804
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