Lianzhen Liu

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In order to research the logical system whose propositional value is given in a lattice from the semantic viewpoint, Xu [7] proposed the concept of lattice implication algebras, and discussed some of their properties. Xu and Qin [8] introduced the notion of implicative filters in a lattice implication algebra, and investigated some of their properties.(More)
The aim of this paper is to introduce the notion of states on R0 algebras and investigate some of their properties. We prove that every R0 algebra possesses at least one state. Moreover, we investigate states onweak R0 algebras and give some examples to show that, in contrast to R0 algebras, there exist weak R0 algebras which have no states. We also derive(More)
The aim of this paper is to study the existences of Bosbach states and Riečan states on finite monoidal t-norm based algebras (MTL-algebras for short). We give some examples to show that there exist MTL-algebras having no Bosbach states and Riečan states. The conditions under which MTL-algebras have Bosbach states and Riečan states are investigated,(More)