My primary and current research work is in the general spirit of algebras of logic, lattice theory, hyper structures and applications. A partially ordered set, or poset for short is a pair (P, ≤) where P is a set and ≤ a partial order on P. A poset (P, ≤) is called a lattice if every pair x, y ∈ P has a least upper bound x ∨ y and a greatest lowest bound x ∧ y in P. A lattice is bounded if it h...

Peterson’s Intermediate Syllogisms, generalizing Aristotelian syllogisms by intermediate quantifiers ‘Many’, ‘Most’ and ‘Almost all’, are studied. It is demonstrated that, by associating certain values V, W and U on standard Lukasiewicz MV–algebra with the first and second premise and the conclusion, respectively, the validity of a corresponding intermediate syllogism is determined by a simple ...

Quantum computational logics provide a fertile common ground for a uni ed treatment of vagueness and uncertainty. In this paper we describe an approach to the logic of quantum computation that has been recently taken up and developed by the present authors. Special attention will be devoted to a generalisation of Chang's MV algebras (called quasi-MV algebra) which abstracts over the algebra who...

In this paper we study an outer measure on MV -algebras. In Section 1 the definition of MV -algebra and Mundici theorem are remind. In Section 2 there is defined an outer measure, measurable elements and there is proved Choquet lema for this structure. In conclusion some properties of measurable elements are resumed.

The focus of this paper is the class of perfect GMV-algebras, which includes all non-commutative analogues of perfect MV-algebras. As in the commutative case, we show that each perfect GMV-algebra possesses a single negation, it is generated by its infinitesimal elements, and can be realized as an interval in a lexicographical product of the lattice-ordered group of integers and an arbitrary la...

We present a preliminary study of applying the concepts of algebraic geometry over fields to the theory of MV-algebras. We proceed along lines similar to B. Plotkin and others where an algebraic geometry over groups is developed.

Here, we report a spontaneously formed nanolamellar BaTiO3–CoFe2O4 bicrystal. 11̄0 interfaces join the BaTiO3 and CoFe2O4 single crystalline periodically arranged lamellae that have a common 111 direction. The superlattice of approximately 2 nm wavelength is magnetoelectric with a frequency dependent coupling coefficient of 20 mV/Oe cm at 100 Hz. The BaTiO3 component is a ferroelectric relaxor w...

Multiple-valued logics are non-classical logics. They are similar to classical logic because they accept the principle of truth-functionality, namely, the truth of a compound sentence is determined by the truth values of its component sentences (and so remains unaffected when one of its component sentences is replaced by another sentence with the same truth value). But they differ from classica...

We derive a new four-dimensional partial differential equation with the isospectral Lax representation by shrinking symmetry algebra of reduced quasi-classical self-dual Yang–Mills and applying technique twisted extensions to obtained Lie algebra. Then we find recursion operator for symmetries construct Bäcklund transformation between this Martínez Alonso–Shabat equation. Finally, integrable hi...