Results on equality algebras

In this paper, by considering the notion of equality algebra, which is introduced by Jenei in [18], as a possible algebraic semantic for fuzzy type theory, we study and show that there are relations among equality algebras and some of other logical algebras such as residuated lattice, MTL-algebra, B...

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Published inInformation sciences Vol. 381; pp. 270 - 282
Main Authors Zebardast, F., Borzooei, R.A., Aaly Kologani, M.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.03.2017
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Abstract In this paper, by considering the notion of equality algebra, which is introduced by Jenei in [18], as a possible algebraic semantic for fuzzy type theory, we study and show that there are relations among equality algebras and some of other logical algebras such as residuated lattice, MTL-algebra, BL-algebra, MV-algebra, Hertz-algebra, Heyting-algebra, Boolean-algebra, EQ-algebra and hoop-algebra. The aim of this paper is to find that under which conditions, equality algebras are equivalent to these logical algebras.
AbstractList In this paper, by considering the notion of equality algebra, which is introduced by Jenei in [18], as a possible algebraic semantic for fuzzy type theory, we study and show that there are relations among equality algebras and some of other logical algebras such as residuated lattice, MTL-algebra, BL-algebra, MV-algebra, Hertz-algebra, Heyting-algebra, Boolean-algebra, EQ-algebra and hoop-algebra. The aim of this paper is to find that under which conditions, equality algebras are equivalent to these logical algebras.
Author Zebardast, F.
Borzooei, R.A.
Aaly Kologani, M.
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Keywords BL-algebra
Hoop-algebra
Hertz-algebra
Equality algebra
Residuated lattice
Boolean-algebra
Heyting-algebra
MTL-algebra
03G25
EQ-algebra
MV-algebra
Language English
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  ident: 10.1016/j.ins.2016.11.027_bib0015
  article-title: Monoidal t-norm based logic, towards a logic for left-continuous t-norms
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/S0165-0114(01)00098-7
  contributor:
    fullname: Esteva
– volume: 53
  start-page: 561
  year: 2014
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  article-title: On pseudo-equality algebras
  publication-title: Arch. Math. Logic
  doi: 10.1007/s00153-014-0380-0
  contributor:
    fullname: Ciungu
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Snippet In this paper, by considering the notion of equality algebra, which is introduced by Jenei in [18], as a possible algebraic semantic for fuzzy type theory, we...
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StartPage 270
SubjectTerms Algebra
BL-algebra
Boolean-algebra
EQ-algebra
Equality algebra
Equivalence
Fuzzy logic
Hertz-algebra
Heyting-algebra
Hoop-algebra
Lattices
MTL-algebra
MV-algebra
Residuated lattice
Semantics
Title Results on equality algebras
URI https://dx.doi.org/10.1016/j.ins.2016.11.027
https://search.proquest.com/docview/1879990657
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