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On WLI-ideal space and the properties of WLI-ideals in lattice implication algebra (LIA)

机译:关于WLI理想空间和格蕴涵代数(LIA)中WLI理想的性质

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In classical logic and non-classical logic, Modus Ponens (MP rule) is very useful for a formal deduction. Firstly, we focus on the properties of WLI-ideal of lattice implication algebras based on the definition of ⊕ operation and ? operation, which are abstraction of MP rule. On the other hand, we consider the WLI-ideal topological space (L,T W(L)) based on LIA, and its topological properties are investigated, it is an abstraction of MP rule-base. Finally, we consider the fuzzification of WLI-ideals in lattice implication algebras, and the properties of FWLI-ideals are investigated.
机译:在古典逻辑和非古典逻辑中,形式规则(MP规则)对于形式推论非常有用。首先,我们基于⊕运算和σ的定义,着重研究WLI理想的格蕴涵代数的性质。操作,这是MP规则的抽象。另一方面,我们考虑了基于LIA的WLI理想拓扑空间(L,T W(L)),并对其拓扑性质进行了研究,它是MP规则库的抽象。最后,我们考虑了格蕴涵代数中WLI理想化的模糊化,并研究了FWLI理想化的性质。

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