On some properties of quasi-MV algebras and $$\sqrt{^{\prime}}$$ quasi-MV algebras. Part II

Bou, Fèlix; Paoli, Francesco; Ledda, Antonio; Freytes, Héctor

doi:10.1007/s00500-007-0185-8

Cited by 24 publications

(34 citation statements)

References 16 publications

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“…Among the additional results proved for √ quasi-MV algebras in [3,6,11], we mention the following: finite model property, congruence extension property, amalgamation property, failure of several algebraic properties (including congruence modularity, subtractivity and point regularity), a characterization of free algebras, a characterization of quasi-MV term reducts and subreducts of √ quasi-MV algebras.…”

Section: Theorem 11 For Everymentioning

confidence: 99%

“…It is worth noticing 4 A variety of algebras is the class of all algebraic structures of a given signature satisfying a given set of identities. 5 We remark that a variety of term reducts of algebras in √ qMV, whose language includes just ⊕, , 0 and 1, namely quasi-MV algebras, has been deeply investigated in [3,9,11]. that F is a variety, whose equational basis in √ qMV is given by the single equation 0 ≈ 1, while CAR is a quasivariety which is not a variety [6].…”

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confidence: 99%

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Towards Quantum Computational Logics

Ledda

Sergioli

2010

Int J Theor Phys

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Quantum computational logics have recently stirred increasing attention (Cattaneo et al. in Math. Slovaca 54:87-108, 2004; Ledda et al. in Stud. Log. 82(2):245-270, 2006; Giuntini et al. in Stud. Log. 87 (1): 2007). In this paper we outline their motivations and report on the state of the art of the approach to the logic of quantum computation that has been recently taken up and developed by our research group.

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Section: Theorem 11 For Everymentioning

confidence: 99%

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confidence: 99%

Towards Quantum Computational Logics

Ledda

Sergioli

2010

Int J Theor Phys

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“…It is shown in [8] that no variety of quasi-MV algebras has any congruence identity (in the language of lattices) unless it is a variety of MV algebras. Therefore, the variety qMV is not congruence n-permutable for any n (by results in [27]); also, it fails to be subtractive.…”

Section: Quasi-mv Algebrasmentioning

confidence: 99%

Joins and subdirect products of varieties

Kowalski

Paoli

2011

Algebra Univers.

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We generalise in three different directions two well-known results in universal algebra. Grätzer, Lakser and P lonka proved that independent subvarieties V 1 , V 2 of a variety V are disjoint and such that their join V 1 ∨ V 2 (in the lattice of subvarieties of V) is their direct product V 1 × V 2 . Jónsson and Tsinakis provided a partial converse to this result: if V is congruence permutable and V 1 , V 2 are disjoint, then they are independent (and so V 1 ∨ V 2 = V 1 × V 2 ). We show that (i) if V is subtractive, then Jónsson's and Tsinakis' result holds under some minimal assumptions; (ii) if V satisfies some weakened permutability conditions, then disjointness implies a generalised notion of independence and V 1 ∨ V 2 is the subdirect product of V 1 and V 2 ; (iii) the same holds if V is congruence 3-permutable.

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“…5). In the interests of space, we will not recapitulate the basic notions of the theory of √ qMV algebras: for a comprehensive introduction, the reader could consult the self-contained papers [5,18,24]. Some acquaintance with the concepts, results, and notation introduced in these papers is presupposed in what follows.…”

Section: Introductionmentioning

confidence: 98%

“…The algebraic properties of qMV algebras and √ qMV algebras have been investigated in greater detail in subsequent papers (e.g. [5,20,24]). …”

Section: Introductionmentioning

confidence: 99%

Logics from $\sqrt{^{\prime}}$ Quasi-MV Algebras

et al. 2011

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The purpose of the present article is to extend the scope of some investigations about abstract logics arising quite naturally out of Quasi-MV algebras (for short, qMV algebras) also to √ qMV algebras. We will therefore introduce, mutually compare and (in some cases) axiomatise several logics arising out of the variety of √ qMV algebras and out of some important subclasses of such. Subsequently, we will investigate the same logics by resorting to the methods and techniques of abstract algebraic logic.

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On some properties of quasi-MV algebras and $$\sqrt{^{\prime}}$$ quasi-MV algebras. Part II

Cited by 24 publications

References 16 publications

Towards Quantum Computational Logics

Towards Quantum Computational Logics

Joins and subdirect products of varieties

Logics from $\sqrt{^{\prime}}$ Quasi-MV Algebras

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