摘要
研究了王国俊教授建立的模糊命题演算的形式演绎系统L*和与之在语义上相匹配的R0-代数,以及Petr Hajek建立的模糊命题演算系统BL和BL-代数,提出了基础R0-代数和基础L*系统的观点,讨论了基础R0-代数与BL代数,基础L*系统与BL系统之间的相互关系及相对独立性,讨论了基础L*系统关于基础R0-代数的完备性问题,证明了MV-代数是特殊的基础R0-代数,指出了Lukasiewicz模糊命题演算系统是基础L*系统的扩张,最后作为基础R0-代数与基础L*系统的一个应用,证明了L*系统关于语义ΩW的完备性,并在将模糊命题演算系统中的推演证明转化为相应逻辑代数中的代数运算方面作了一些尝试.
The formal deductive system L* for fuzzy propositional calculus and R0-algebra have been studied. The concepts of basis Ro-algebra, and basis L* system are proposed. The independances between basis R0o-algebra and BL-algebra, basis L* system and BL system have been discussed. The completeness of basis L* system about basis R0-algebra has been investigated. As an example of their application, we have proved the completeness of L* system about semantics ΩW, and we make a try to change the deductions and proofs in system L* into operation in relevant logic algebra.
出处
《数学进展》
CSCD
北大核心
2003年第5期565-576,共12页
Advances in Mathematics（China）
