ZHOU Jianren, WU Hongbo. Schematic Extensions of MTL by Adding Weak Divisibility Axiom[J]. Chinese Journal of Electronics, 2016, 25(5): 824-831. doi: 10.1049/cje.2016.06.032
Citation: ZHOU Jianren, WU Hongbo. Schematic Extensions of MTL by Adding Weak Divisibility Axiom[J]. Chinese Journal of Electronics, 2016, 25(5): 824-831. doi: 10.1049/cje.2016.06.032

Schematic Extensions of MTL by Adding Weak Divisibility Axiom

doi: 10.1049/cje.2016.06.032
Funds:  This work is supported by National Natural Science Foundation of China (No.61572016, No.11531009), and the Fundamental Research Funds for the Central Universities (No.GK201501001).
  • Received Date: 2014-07-21
  • Rev Recd Date: 2014-09-10
  • Publish Date: 2016-09-10
  • MTL is a Monoidal t-norm based logic introduced by Esteva and Godo by omitting divisibility axiom from Hájek's Basic logic (BL). Many logics can be obtained by adding axioms to MTL logic. Logic system WBL is obtained by adding weak divisibility axiom to logic system MTL. Logic system WMV is obtained by adding involution axiom to logic system WBL. WBL-algebra corresponding to logic system WBL and WMV-algebra to logic systemWMV are defined respectively. It is proved that the both of logic system Luk and logic system Nilpotent minimum (NM) are the schematic extensions of logic system WMV. Weak Wajsberg algebra and the simplified form of logic system WMV are obtained.
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