Set-of-support strategy for higher-order logic

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.