Soft Computing

, Volume 23, Issue 21, pp 10635–10648 | Cite as

On the free frontal implicative semilattice extension of a frontal Hilbert algebra

  • Ramon Jansana
  • Hernán J. San MartínEmail author


In this paper, we define a functor which is left adjoint to the forgetful functor from the category of frontal implicative semilattices to that of frontal Hilbert algebras.


Hilbert algebras Implicative semilattices Modal operators 



This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No. 689176. The first author was also partially supported by the research grant 2014 SGR 788 from the government of Catalonia and by the research projects MTM2016-74892-P from the government of Spain, which includes feder funds from the European Union and he also acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the “María de Maeztu” Programme for Units of Excellence in R&D (MDM-2014-0445). The second author was also supported by CONICET Project PIP 112-201501-00412.

Compliance with ethical standards

Conflict of interest

Both authors declare that they have no conflict of interest.

Ethical standard

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


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departament de FilosofiaUniversitat de BarcelonaBarcelonaSpain
  2. 2.Departamento de MatemáticaFacultad de Ciencias Exactas (UNLP), and CONICETLa PlataArgentina

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