Tense operators in fuzzy logic

Chajda, Ivan; Paseka, Jan

doi:10.1016/j.fss.2014.09.007

Cited by 9 publications

(5 citation statements)

References 16 publications

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“…In the next theorem we verify that the tense operators P , F , H and G as defined in Section 2 satisfy the composition laws in accordance with known sources, see e.g. [4,7] or [11].…”

Section: Properties Of Tense Operatorsmentioning

confidence: 76%

“…As mentioned in our previous section, our logic based on a finite orthomodular poset is equipped with logical connectives and → forming an adjoint pair. The aim of this section is to show that our tense operators satisfy properties considered in classical or non-classical tense logics as collected in [7] although they are defined in an inexact way. Before formulating of our results, let us illuminate our concepts by the following example.…”

Section: Properties Of Tense Operatorsmentioning

confidence: 99%

“…For our purposes in this paper we will consider only so-called serial relations (see [7]), i.e. relations R such that for each s ∈ T there exist some r, t ∈ T with r R s and s R t.…”

Section: Introductionmentioning

confidence: 99%

“…Namely, we want to show that our couple (P , G) of tense operators forms a dynamic pair on the given orthomodular poset A = (A, ≤, , 0, 1), i.e. the following axioms (P1) -(P3) hold (see [7]):…”

Section: Introductionmentioning

confidence: 99%

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Tense Logic Based on Finite Orthomodular Posets

Chajda

Länger

2023

Int J Theor Phys

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It is widely accepted that the logic of quantum mechanics is based on orthomodular posets. However, such a logic is not dynamic in the sense that it does not incorporate time dimension. To fill this gap, we introduce certain tense operators on such a logic in an inexact way, but still satisfying requirements asked on tense operators in the classical logic based on Boolean algebras or in various non-classical logics. Our construction of tense operators works perfectly when the orthomodular poset in question is finite. We investigate the behaviour of these tense operators, e.g. we show that some of them form a dynamic pair. Moreover, we prove that if the tense operators preserve one of the inexact connectives conjunction or implication as defined by the authors recently in another paper, then they also preserve the other one. Finally, we show how to construct the binary relation of time preference on a given time set provided the tense operators are given, up to equivalence induced by natural quasi-orders.

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“…In the next theorem we verify that the tense operators P , F , H and G as defined in Section 2 satisfy the composition laws in accordance with known sources, see e.g. [4,7] or [11].…”

Section: Properties Of Tense Operatorsmentioning

confidence: 76%

Section: Properties Of Tense Operatorsmentioning

confidence: 99%

“…For our purposes in this paper we will consider only so-called serial relations (see [7]), i.e. relations R such that for each s ∈ T there exist some r, t ∈ T with r R s and s R t.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tense Logic Based on Finite Orthomodular Posets

Chajda

Länger

2023

Int J Theor Phys

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“…Relationships between FI-algebra and BCK-algebra [13,14], MV-algebras [15], Rough set algebras [16,17], and were partly investigated, and FI-algebras were axiomatized [18]. In the recent work, the relationship between these FI-algebras and several famous fuzzy algebras were systematically discussed [3,[19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Some New Properties of <i>W<sub>d</sub></i>-fuzzy Implication Algebras

Fang-an¹

2021

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Implication is an important logical connective in practically every propositional logic. In 1987, the so-called Fuzzy implication algebras were introduced by Wu Wangming, then various interesting properties of FI-algebras and some subalgebra of Fuzzy implication algebra, such as regular FI-algebras, commutative FI-algebras, W d -FI-algebras, and other kinds of FIalgebras were reported. The main aim of this article is to study W d -fuzzy implication algebras which are subalgebra of fuzzy implication algebras. We showed that W d -fuzzy implication algebras are regular fuzzy implication algebras, but the inverse is not true. The relations between W d -fuzzy implication algebras and other fuzzy algebras are discussed. Properties and axiomatic systems for W d -fuzzy implication algebras are investigated. Furthermore, a few new results on W d -fuzzy implication algebras has been added.

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