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A Representation Theorem for Finite Gödel Algebras with Operators

  • Tommaso FlaminioEmail author
  • Lluis Godo
  • Ricardo O. Rodríguez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11541)

Abstract

In this paper we introduce and study finite Gödel algebras with operators (GAOs for short) and their dual frames. Taking into account that the category of finite Gödel algebras with homomorphisms is dually equivalent to the category of finite forests with order-preserving open maps, the dual relational frames of GAOs are forest frames: finite forests endowed with two binary (crisp) relations satisfying suitable properties. Our main result is a Jónsson-Tarski like representation theorem for these structures. In particular we show that every finite Gödel algebra with operators determines a unique forest frame whose set of subforests, endowed with suitably defined algebraic and modal operators, is a GAO isomorphic to the original one.

Keywords

Finite Gödel algebras Modal operators Finite forests Representation theorem 

Notes

Acknowledgments

The authors acknowledge partial support by the SYSMICS project (EU H2020-MSCA-RISE-2015 Project 689176). Further, Flaminio acknowledges partial support by the Spanish Ramon y Cajal research program RYC-2016-19799; Flaminio and Godo by the Spanish FEDER/MINECO project TIN2015- 71799-C2-1-P; Rodriguez, by the projects UBA-CyT: 20020150100002BA and PIP 112-2015-0100412 CO.

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Copyright information

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

Authors and Affiliations

  • Tommaso Flaminio
    • 1
    Email author
  • Lluis Godo
    • 1
  • Ricardo O. Rodríguez
    • 2
  1. 1.Artificial Intelligence Research Institute (IIIA - CSIC)BellaterraSpain
  2. 2.FCEyN, Departamento de Computación, CONICET-UBA, Inst. de Invest. en Cs. de la ComputaciónUBABuenos AiresArgentina

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