Toward a formal language for unsharp properties

Giuntini, Roberto; Greuling, Heinz

doi:10.1007/bf01889307

Cited by 183 publications

(86 citation statements)

References 12 publications

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“…Another equivalent structure was introduced by Giuntini and Greuling in [9]. We refer to [6] for more information on effect algebras and related topics.…”

Section: Definitions and Basic Relationshipsmentioning

confidence: 99%

Extensions of Witness Mappings

Jenča

2011

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Abstract. We deal with the problem of coexistence in interval effect algebras using the notion of a witness mapping. Suppose that we are given an interval effect algebra E, a coexistent subset S of E, a witness mapping β for S, and an element t ∈ E \ S. We study the question whether there is a witness mapping βt for S ∪ {t} such that βt is an extension of β. In the main result, we prove that such an extension exists if and only if there is a mapping et from finite subsets of S to E satisfying certain conditions. The main result is then applied several times to prove claims of the type "If t has a such-and-such relationship to S and β, then βt exists".

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“…Another equivalent structure was introduced by Giuntini and Greuling in [9]. We refer to [6] for more information on effect algebras and related topics.…”

Section: Definitions and Basic Relationshipsmentioning

confidence: 99%

Extensions of Witness Mappings

Jenča

2011

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“…In their papers [15] and [16], Kôpka and Chovanec introduced an essentially equivalent structure called D-poset. Another equivalent structure, called weak orthoalgebras was introduced by Giuntini and Greuling in [9]. We refer to the monograph [7] for more information on effect algebras and similar algebraic structures.…”

Section: Definitions and Basic Relationshipsmentioning

confidence: 99%

The category of MV-pairs

Nola

Holčapek

Jenča³

2009

Logic Journal of IGPL

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Abstract. An MV-pair is a pair (B, G), where B is a Boolean algebra and G is a subgroup of the automorphism group of B satisfying certain condition. Recently it was proved by one of the authors that for an MV-pair (B, G), ∼ G is an effect-algebraic congruence and B/ ∼ G is an MV-algebra. Moreover, every MV-algebra M can be represented by an MV-pair in this way.In this paper we show that one can define a suitable category of MV-pairs in such a way that there exist a faithful functor from the category of MV-algebras to the aforementioned category and a functor in the reversed direction.

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“…For more details we refer the reader to [7], [8], [13]- [17], [20]- [23] and the references given there. We review only a few properties without proof.…”

Section: Basic Definitionsmentioning

confidence: 99%