This paper presents an algebraic approach of some many-valued generalizations of modal logic. The starting point is the de nition of the [0, 1]-valued Kripke models, where [0, 1] denotes the well known MV-algebra. Two types of structures are used to de ne validity of formulas: the class of frames and the class of Šn-valued frames. The latter structures are frames in which we specify in each wor...

The unit interval in a partially ordered abelian group with order unit forms an interval effect algebra (IEA) and can be regarded as an algebraic model for the semantics of a formal deductive logic. There is a categorical equivalence between the category of IEA’s and the category of unigroups. In this article, we study the IEA-unigroup connection, focusing on the cases in which the IEA is a Boo...

The unit square is regarded as a special kind of dynamical system. It is proved that the square is an MV-algebra, hence the recent results on MValgebra entropy theory can be applied to it.

My talk is based on article [1]. Our aim is to give a unified topological approach to several results about a certain type of fuzzy measures, namely T∞−valuations (2) on clans of fuzzy sets (1) (in the sense of Butnariu and Klement [2]). We will transfer the method of [3], used to study FN-topologies (4) and measures on Boolean rings, to the study of T∞−valuations. So we need, for the domain of...

In this paper, some types of fuzzy filters a strong Sheffer stroke non-associative MV-algebra (for short, NMV-algebra) are introduced. By presenting new properties filters, we define prime filter in algebraic structure. Then (prime) NMV-algebra determined and features proved. Finally, built quotient by filter.

We develop the general theory of RMV-algebras, which are essentially unit intervals in Riesz spaces with strong unit. Since the variety of RMV-algebras is generated by [0, 1], we get an equational characterization of the real product on [0,1] interpreted as scalar multiplication.

The reproducibility over temperature and time of the pull-in voltage of micromechanical structures has been analyzed and verified using fabricated devices in silicon. The pull-in structures are intended for use as an on-chip voltage reference. Microbeams of 100m length, 3m width, and 11m thickness are electrostatically actuated with a very reproducible pull-in voltage at 9.1 V. Devices demonstr...

Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.

Proof. Suppose Mv = λv. We want to show that λ has imaginary value 0. For a complex number x = a + ib, the conjugate of x, is defined as follows: x∗ = a − ib. So, all we need to show is that λ = λ∗. The conjugate of a vector is the conjugate of all of its coordinate. Taking the conjugate transpose of both sides of the above equality, we have v∗M = λ∗v∗, (8.1) where we used that M = M . So, on o...

In this note we prove that it is impossible to extend the natural equivalence between the category of MV-algebras and the category of Abelian `-groups with strong unit described by C. C. Chang, 1958, and Cignoli & Mundici, 1997, to a natural equivalence between the category of m-zeroids and some category containing the category of Abelian `-groups with strong unit.