Denisa Diaconescu

Lexicographic MV-algebras and lexicographic states

Abstract In this paper we introduce lexicographic MV-algebras and prove that they are the counterpart of unital abelian lattice-ordered groups defined via lexicographic products. The Di Nola–Lettieri categorical equivalence between perfect MV-algebras and abelian lattice-ordered groups is extended to lexicographic MV-algebras. We also investigate lexicographic states of lexicographic MV-algebras. These are additive and normalized maps from any lexicographic MV-algebra into an ad hoc defined MV-subalgebra of a non-principal ultraproduct [ ⁎ 0 , 1 ] of the real unit interval [ 0 , 1 ] . For lexicographic states we prove a representation theorem which can be regarded as the measure-theoretical analog of the representation theorem for lexicographic MV-algebras. We also provide necessary and sufficient conditions for a lexicographic state to be faithful.

The Riesz Hull of a Semisimple MV-Algebra

Abstract MV-algebras and Riesz MV-algebras are categorically equivalent to abelian lattice-ordered groups with strong unit and, respectively, with Riesz spaces (vector-lattices) with strong unit. A standard construction in the literature of lattice-ordered groups is the vector-lattice hull of an archimedean latticeordered group. Following a similar approach, in this paper we define the Riesz hull of a semisimple MV-algebra.

Refinement-Preserving translation from event-b to register-voice interactive systems

The state-based formal method Event-B relies on the concept of correct stepwise development, ensured by discharging corresponding proof obligations. The register-voice interactive systems (rv-IS) formalism is a recent approach for developing software systems using both structural state-based as well as interaction-based composition operators. One of the most interesting feature of the rv-IS formalism is the structuring of the components interactions. In order to study whether a more structured (rv-IS inspired) interaction approach can significantly ease the proof obligation effort needed for correct development in Event-B, we need to devise a way of integrating these formalisms. In this paper we propose a refinement-based translation from Event-B to rv-IS, exemplified with a file transfer protocol modelled in both formalisms.

Mutually Exclusive Nuances of Truth in Moisil Logic

Moisil logic, having as algebraic counterpart \L ukasiewicz-Moisil algebras, provide an alternative way to reason about vague information based on the following principle: a many-valued event is characterized by a family of Boolean events. However, using the original definition of \L ukasiewicz-Moisil algebra, the principle does not apply for subalgebras. In this paper we identify an alternative and equivalent definition for the

Refinement of Structured Interactive Systems

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A real-valued modal logic

-valued \L ukasiewicz-Moisil algebras, in which the determination principle is also saved for arbitrary subalgebras, which are characterized by a Boolean algebra and a family of Boolean ideals. As a consequence, we prove a duality result for the

Non-commutative Product Logic and Probability of Fuzzy Events

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Forcing operators on MTL-algebras

-valued \L ukasiewicz-Moisil algebras, starting from the dual space of their Boolean center. This leads us to a duality for MV

Towards game semantics for nuanced logics

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On Standard Completeness for Non-commutative Many-Valued Logics

-algebras, since are equivalent to a subclass of