Abstract
We have proven in this paper that set-of-support strategy is complete in higher-order system \(\mathcal{L}\). The situation may not apply to other strategies. For example, hyper-resolution which resolve one nuclear clause with several satellite clauses at one time may not be used in system \(\mathcal{L}\). Because \(\mathcal{L}\) does not contain any inference rules similar to hyper-resolution.
Set-of-support strategy has been worked fine in first-order theorem-proving problem. Though complete in system \(\mathcal{L}\), we have not try in too many examples. We have no idea that how the performance is. More experiments need to be done. Of course, other first-order strategy may also work in system \(\mathcal{L}\), which need more future research. Finally, find a total new, pure strategy for higher-order logic is one other direction.
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© 1993 Springer-Verlag Berlin Heidelberg
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Fang, W., Kao, JH. (1993). Set-of-support strategy for higher-order logic. In: Rusinowitch, M., Rémy, JL. (eds) Conditional Term Rewriting Systems. CTRS 1992. Lecture Notes in Computer Science, vol 656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56393-8_40
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DOI: https://doi.org/10.1007/3-540-56393-8_40
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