A multi-valued version of CTL (mv-CTL), where both the propositions and the accessibility relation are multi-valued taking values in a nite quasi-boolean algebra, is considered. A general translation from mv-CTL to CTL model checking is deened. An application of the translation is shown for the most commonly used quasi-boolean algebras.

Working jointly in the equivalent categories of MV-algebras and lattice-ordered abelian groups with strong order unit (for short, unital l-groups), we prove that isomorphism is a sufficient condition for a separating subalgebra A of a finitely presented algebra F to coincide with F . The separation and isomorphism conditions do not individually imply A = F . Various related problems, like the s...

The poset product construction is used to derive embedding theorems for several classes of generalized basic logic algebras (GBL-algebras). In particular it is shown that every n-potent GBL-algebra is embedded in a poset product of finite n-potent MV-chains, and every normal GBL-algebra is embedded in a poset product of totally ordered GMV-algebras. Representable normal GBLalgebras have poset p...

In this paper we shall describe a very natural extension of MV-algebras, the divisible MV-algebras (DMV). Such algebraic structures will be used to give a formal description of rules of fuzzy control.

Weak pseudo BL-algebras (WPBL-algebras) are non-commutative fuzzy structures which arise from pseudot-norms (i.e. the non-commutative versions of triangular norms). In this paper, we study the pairs of weak negations on WPBL-algebras, extending the case of weak negations on Esteva–Godo MTL-algebras. A geometrical characterization of the pairs of weak negations in bounded chains is provided. Our...

We prove that on the finitely generated free MV-algebras the only automorphism-invariant truth averaging process that detects pseudotrue propositions is the integral with respect to Lebesgue measure.

We introduce the tense LMn-algebras and the tense MV algebras as algebraic structures for some tense many-valued logics. A representation theorem for tense LMn-algebras is proved and the polynomially equivalence between tense LM3-algebras (resp. tense LM4-algebras) and tense MV3-algebras (resp. tense MV4-algebras) is established. We study the pairs of dually-conjugated operations on MV -algebra...

This work presents measurements of the electrical resistivity srd, Seebeck coefficient, and thermal conductivity skd of icosahedral Al70Pd22.5sRe1−xMnxd7.5 quasicrystals from 10 to 300 K. A series of quasicrystals was prepared with x=0, 0.1, 0.2, 0.3, 0.5, 0.6, 0.8, and 1.0 to systematically study the effect of substitution. The electrical resistivity increases as the temperature decreases, sug...

Quasi-MV algebras are generalisations of MV algebras arising in quantum computational logic. Although a reasonably complete description of the lattice of subvarieties of quasi-MV algebras has already been provided, the problem of extending this description to the setting of quasivarieties has so far remained open. Given its apparent logical repercussions, we tackle the issue in the present pape...

The algebraic theory of quasi-MV algebras, generalizations of MV algebras arising in quantum computation, is by now rather well-developed. Although it is possible to define several interesting logics from these structures, so far this aspect has not been investigated. The present article aims at filling this gap.