Skip to main content

Advertisement

Log in

Tense operators on frameable equality algebras

  • Foundation, algebraic, and analytical methods in soft computing
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

In this paper, we introduce the frameable equality algebras and use the concept of tense operators on them to define tense equality algebras. We investigate some algebraic properties of tense equality algebras and prove the representation theory for strict strong tense equality algebras. Then, we introduce the notions of (prime) tense deductive systems and tense congruences and obtain some structural theorems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bakhshi M (2017) Tense operators on non-commutative residuated lattices. Soft Comput 21:4257-4268

  • Borzooei RA, Zebardasta F, Aaly Kologani M (2017) Some types of filters in equality algebras. Categ Gen Algebra Struct Appl 7:33–55

    MathSciNet  MATH  Google Scholar 

  • Borzooei RA, Zarean M, Zahiri O (2018) Involutive equality algebras. Soft Comput 22(22):7505–7517

    Article  Google Scholar 

  • Botur M, Chajda I, Halaš R, Kolaři M (2011) Tense operators on basic algebras. Int J Theor Phys 50:3737–3749

    Article  MathSciNet  Google Scholar 

  • Burges J (1984) Basic tense logic. In: Gabbay DM, Günther F (eds) Handbook of philosophical logic, vol II. D. Reidel Publishing Company, Dordrecht, pp 89–139

    Chapter  Google Scholar 

  • Chajda I, Paseka J (2012) Dynamic effect algebras and their representations. Soft Comput 16:1733–1741

    Article  Google Scholar 

  • Chajda I, Paseka J (2013) Tense operators and dynamic De Morgan algebras. In: 2013 IEEE 43rd International symposium on multiple-valued logic, pp 219–224

  • Chirita C (2010) Tense \(\theta \)-valued Moisil propositional logic. Int J Comput Commun Control 5(5):642–653

    Article  Google Scholar 

  • Ciungu LC (2015) Internal states on equality algebras. Soft Comput 19:939–953

    Article  Google Scholar 

  • Diaconescu D, Georgescu G (2007) Tense operators on MV-algebras and Lukasiewicz-Moisil algebras. Fund Inf 81:379–408

    MATH  Google Scholar 

  • Dvurečenskij A, Zahiri O (2016) Pseudo equality algebras-revision. Soft Comput 20:2091–2101

    Article  Google Scholar 

  • Ghorbani S (2019) Monadic pseudo-equality algebras. Soft Comput 23(24):12937–12950

    Article  Google Scholar 

  • Ghorbani S (2020) Equality logic. Bull Sect Log 49(3):291–324

    Google Scholar 

  • Jenei S (2012) Equality algebras. Stud Log 100:1201–1209

    Google Scholar 

  • Jenei S, Kóródi L (2013) Pseudo equality algebras. Arch Math Log 52:469–481

    Article  Google Scholar 

  • Jenei S, Kóródi L (2011) On the variety of equality algebras. In: Fuzzy logic and technology, pp 153–155

  • Liu H (2018) Strong tensor non-commutative residuated lattices. IAENG Int J Appl Math 48(1):1–6

    MathSciNet  Google Scholar 

  • Novák V (2005) On fuzzy type theory. Fuzzy Sets Syst 149(2):235–273

    Article  MathSciNet  Google Scholar 

  • Zarean M, Borzooei RA, Zahiri O (2017) On state equality algebras. Quasi Group Relat Syst 25(2):211–220

    MathSciNet  MATH  Google Scholar 

  • Zebardast F, Borzooei RA, Kologani MA (2017) Results on equality algebras. Inf Sci 381:270–282

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shokoofeh Ghorbani.

Ethics declarations

Conflict of interest

The author declares that she has no conflict of interest.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghorbani, S. Tense operators on frameable equality algebras. Soft Comput 26, 203–213 (2022). https://doi.org/10.1007/s00500-021-06453-2

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-021-06453-2

Keywords

Navigation