In his well-known paper \How computer should think" ((Be77b]) Belnap argues that four-valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the four-valued structure has among Ginsberg's well-known bilattices is similar to the role that the two-valued algebra has among Boolean algebras .

Classical Segal–Bargmann theory studies three Hilbert space unitary isomorphisms that describe the wave-particle duality and configuration space-phase space. In this work, we generalized these concepts to Clifford algebra-valued functions. We establish among of square-integrable functions on $$\mathbb {R}^n$$ with respect a Gaussian measure, monogenic {R}^{n+1}$$ another measure linear function...

In this paper, we present a study of various concepts pertaining to compactness properties of a lattice. Special cases include such notions as countably compactness, almost countably compactness, and countably paracompactness. Some investigations in these matters have been done in [2, 7, 14]. We go beyond these results and introduce new subsets of I(L) and their lattices to investigate. This wa...

We develop the notion of deformations using a valuation ring as ring of coefficients. This permits to consider in particular the classical Gerstenhaber deformations of associative or Lie algebras as infinitesimal deformations and to solve the equation of deformations in a polynomial frame. We consider also the deformations of the enveloping algebra of a rigid Lie algebra and we define valued de...

in  cite{gl}, b. gerla and i. leuc{s}tean introduced the notion of similarity on mv-algebra. a similarity mv-algebra is an mv-algebra endowed with a binary operation $s$ that verifies certain additional properties. also, chirtec{s} in cite{c}, study the notion of similarity on l ukasiewicz-moisil algebras. in particular, strong similarity l ukasiewicz-moisil algebras were defined. in this paper...

Let T be an invertible, ergodic, measure-preserving transformation of a separable, nonatomic probability space (X, (B, ra), and let U be the induced unitary operator acting in L(X, (B, m). Let Ct(T) be the Banach algebra generated by the multiplication algebra and the nonnegative powers of U. It is shown that, if 5 is another such transformation, then 5 and T are conjugate if, and only if, a(5)...

We develop a natural generalization of vector-valued frame theory, we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case and extends to higher multiplicity their dilation approach. We prove several results for operator-valued frames concerning duality, disjointeness, complementar...

This paper shows a new approach to low-power low-voltage CMOS MultipleValued (MVL) Ternary Logic, the “complete model”. This logic uses standard technology processes and requires only an extra power supply more than binary CMOS circuits. Using an original characterisation of CMOS multivalued dynamic gates, it is shown as the advantages obtained are better noise margins and a lower power consump...