<span style="font-size: 10pt; font-family: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">Automatic acquisition of ISA relations is a basic problem in knowled</span><span style="font-size: 10pt; font-family: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">ge acquisition from text. We present a</span><span style="font-size: 10pt; font-family: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">n</span><span style="font-size: 10pt; font-family: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US"> </span><span style="font-size: 10pt; font-family: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">iterative </span><span style="font-size: 10pt; font-family: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">method </span><span style="font-size: 10pt; font-family: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">extracting </span><span style="font-size: 10pt; font-family: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">ISA relations from large Chinese free text</span><span style="font-size: 10pt; font-family: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US"> for ontology learning</span><span style="font-size: 10pt; font-family: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">. </span><span style="font-size: 10pt; font-family: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">Firstly, i</span><span style="font-size: 10pt; font-family: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">t initially discovers a set of sentences using </span><span style="font-size: 10pt; font-family: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-ansi-language: EN...

Based on preimage sampleable functions and hard problems for lattices, we propose two lattice-based multi-signature schemes, which include the trivial broadcasting multi-signature scheme and the sequential multi-signature scheme. In the broadcasting multi-signature scheme, the length of the multi-signature varies linearly with the number of the signers. In the sequential multi-signature scheme, the length of the multi-signature is fixed and independent of the number of the signers. These two multi-signature schemes can allow multiple signers to sign the same message cooperatively.

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