Skip to main content
SpringerLink
Log in

A note to the definition of the ŁΠ-algebras

  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The ŁΠ-algebras are interesting algebraic structures. They were introduced by Esteva, Godo, and Montagna. These algebras are closely related to the well-known MV-algebras and Π-algebras. They have two sets of operations and reduct to one set is an MV-algebra and to the other one is a Π-algebra.

Other important reducts of ŁΠ-algebras are so-called PŁ-algebras (an MV-algebras enriched with product connective) and Π∼-algebras (Π-algebras with additional involutive negation).

The definition of ŁΠ-algebras is based on its MV-algabraic reduct and the additional identities. In this paper we present how to base this definition on the other reducts we mention above. We present minimal sets of conditions which has to be added to the defining conditions of those reducts in order to obtain ŁΠ-algebras.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  • Cintula P (2001) An alternative approach to the Ł Π logic. Neural Network World 11: 561–572

  • Esteva F, Godo L, Hájek P, Montagna F (2003) Hoops and fuzzy logic. J Logic Comput. (13): 531–555

  • Esteva F, Godo L, Montagna F (2001) The Ł Π and Ł Π logics: two complete fuzzy systems joining Łukasiewicz and product logics. Arch Math Logic 1(40): 39–67

    Google Scholar 

  • Esteva F, Godo L, Hájek P, Navara M (2000) Residuated fuzzy logics with an involutive negation. Arch Math Logic 2(39): 103–124

    Google Scholar 

  • Hájek P (1998) Metamathematics of fuzzy logic. Kluwer, Dordrecht

  • Horčík R, Cintula P (2004) Product Łukasiewicz logic. Arch Math Logic 4(43): 477–503

    Google Scholar 

  • Montagna F (2000) An algebraic approach to propositional fuzzy logic. J Logic Lang Inf 9: 91–124

    Google Scholar 

  • Montagna F, Panti G (2001) Adding structure to MV-algebras. J Pure Appl Algebra 3(164): 365–387

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague

    Petr Cintula

  2. Department of Math., Faculty of nuclear sciences and physical engineering, Czech Technical University, Prague

    Petr Cintula

Authors
  1. Petr Cintula
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Petr Cintula.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cintula, P. A note to the definition of the ŁΠ-algebras. Soft Comput 9, 575–578 (2005). https://doi.org/10.1007/s00500-004-0400-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-004-0400-9

Search

Navigation