Some properties of state filters in state residuated lattices

summary:We consider properties of state filters of state residuated lattices and prove that for every state filter $F$ of a state residuated lattice $X$: \begin {itemize} \item [(1)] $F$ is obstinate $\Leftrightarrow$ $L/F \cong \{0,1\}$; \item [(2)] $F$ is primary $\Leftrightarrow$ $L/F$ is a state local residuated lattice; \end {itemize} and that every g-state residuated lattice $X$ is a subdirect product of $\{X/P_{\lambda } \}$, where $P_{\lambda }$ is a prime state filter of $X$. \endgraf Moreover, we show that the quotient MTL-algebra $X/P$ of a state residuated lattice $X$ by a state prime filter $P$ is not always totally ordered, although the quotient MTL-algebra by a prime filter is totally ordered

Intuitionistic logic with a Galois connection has the finite model property

We show that the intuitionistic propositional logic with a Galois connection (IntGC), introduced by the authors, has the finite model property.Comment: 6 page

© Hindawi Publishing Corp. ON THE CLASS OF QS-ALGEBRAS

We consider some fundamental properties of QS-algebras and show that (1) the theory of QS-algebras is logically equivalent to the theory of Abelian groups, that is, each theorem of QS-algebras is provable in the theory of Abelian groups, and conversely, each theorem of Abelian groups is provable in the theory of QS-algebras; and (2) a G-part G(X) of a QSalgebra X is a normal subgroup generated by the class of all elements of order 2 of X when it is considered as a group. 2000 Mathematics Subject Classification: 06F35, 03G25, 03C07. 1. Introduction. In [3

On the transfer principle in fuzzy theory

We show in this paper that almost all results proved in many papers about fuzzy algebras can be proved uniformly and immediately by using so-called “Transfer Principle”