“…This approach enables the reuse of existing, interactive and automated, theorem proving technology for HOL to mechanize also non-classical higher-order reasoning. Some of the findings reported in this article have, at an abstract level, already been summarized in the literature before [24,6,17], but they have not been published in full detail yet (for example, the notions of "modal" ultrafilters, as employed in our analysis, have not been made precise in these papers). This is the contribution of this article.…”