On tense MV-algebras

Botur, Michal; Paseka, Jan

doi:10.1016/j.fss.2014.06.006

Cited by 13 publications

(6 citation statements)

References 16 publications

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“…Contrary to Boolean algebras where the representation problem through a time frame is solved completely, authors in [9] only mention that this problem for MV-algebras was not treated. Botur and Paseka were able to find a suitable time frame for given tense operators on a semisimple MV-algebra (see [1]), i.e., to solve the representation problem for semisimple MV-algebras.…”

Section: Introductionmentioning

confidence: 99%

“…It is well known [2] that this problem is easily solvable for Boolean algebras but it is not solvable e.g. for MV-algebras or effect algebras in general (see [1] and [4] for details). Hence, we are encouraged to find certain restrictions that are still in accordance with physical reality.…”

Section: Introductionmentioning

confidence: 99%

“…This means that we get a procedure how to construct a corresponding time frame to be in accordance with the canonical construction from [6]. Since any MV-algebra and any lattice effect algebra with q-tense operators is a q-effect algebra our approach covers the results from [1] and [4].…”

Section: Introductionmentioning

confidence: 99%

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Galois connections and tense operators on q-effect algebras

Chajda

Paseka

2016

Fuzzy Sets and Systems

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Please cite this article in press as: I. Chajda, J. Paseka, Galois connections and tense operators on q-effect algebras, Fuzzy Sets and Systems (2015), http://dx.Abstract. For effect algebras, the so-called tense operators were already introduced by Chajda and Paseka. They presented also a canonical construction of them using the notion of a time frame.Tense operators express the quantifiers "it is always going to be the case that" and "it has always been the case that" and hence enable us to express the dimension of time both in the logic of quantum mechanics and in the many-valued logic.A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a time frame such that each of these operators can be obtained by the canonical construction. To approximate physical real systems as best as possible, we introduce the notion of a q-effect algebra and we solve this problem for q-tense operators on q-representable q-Jauch-Piron q-effect algebras.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Galois connections and tense operators on q-effect algebras

Chajda

Paseka

2016

Fuzzy Sets and Systems

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“…In particular, in [8,9], Chiriţȃ, introduced tense θ-valued Łukasiewicz-Moisil algebras and proved an important representation theorem which allowed to show the completeness of the tense θ-valued Moisil logic (see [8]). In [11], the authors formulated an open problem about representation of tense MValgebras, this problem was solved in [21,3] for semisimple tense MV-algebras. Also, in [2], were studied tense basic algebras which are an interesting generalization of tense MV-algebras.…”

Section: Introductionmentioning

confidence: 99%

Discrete Duality for Tense Łukasiewicz–Moisil Algebras

Figallo

Pelaitay

2015

Fundamenta Informaticae

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“…In particular, in [8], Chiriţȃ, introduced tense θ-valued Lukasiewicz-Moisil algebras and proved a representation theorem which allowed to show the completeness of the tense θ-valued Moisil logic (see [7]). In [11], the authors formulated an open problem about representation of tense MV-algebras, this problem was solved in [26,3] for semisimple tense MV-algebras. Also, in [2], were studied tense basic algebras which are an interesting generalization of tense MV-algebras.…”

Section: Introductionmentioning

confidence: 99%

Tense Polyadic N × M-Valued Łukasiewicz–Moisil Algebras

Figallo

Pelaitay

2015

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In 2015, A.V. Figallo and G. Pelaitay introduced tense n×m-valued LukasiewiczMoisil algebras, as a common generalization of tense Boolean algebras and tense n-valued Lukasiewicz-Moisil algebras. Here we initiate an investigation into the class tpLMn×m of tense polyadic n × m-valued Lukasiewicz-Moisil algebras. These algebras constitute a generalization of tense polyadic Boolean algebras introduced by Georgescu in 1979, as well as the tense polyadic n-valued Lukasiewicz-Moisil algebras studied by Chiriţȃ in 2012. Our main result is a representation theorem for tense polyadic n × m-valued Lukasiewicz-Moisil algebras. IntroductionIn 1962, polyadic Boolean algebras were defined by Halmos as algebraic structures of classical predicate logic. One of the main results in the theory of polyadic Boolean algebras is Halmos representation theorem (see [22]). This result is the algebraic counterpart of Gödel's completeness theorem for predicate logic. This subject caused great interest and led several authors to deepen and generalized the algebras defined by Halmos, to such an extent that research is still being conducted in this direction.

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On tense MV-algebras

Cited by 13 publications

References 16 publications

Galois connections and tense operators on q-effect algebras

Galois connections and tense operators on q-effect algebras

Discrete Duality for Tense Łukasiewicz–Moisil Algebras

Tense Polyadic N × M-Valued Łukasiewicz–Moisil Algebras

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