Abstract

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.

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