Unification in Łukasiewicz Logic with a Finite Number of Variables

We prove that the unification type of Łukasiewicz logic with a finite number of variables is either infinitary or nullary. To achieve this result we use Ghilardi’s categorical characterisation of unification types in terms of projective objects, the categorical duality between finitely presented MV-...

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Autores principales: Abbadini, Marco, Di Stefano, Federica, Spada, Luca
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7274729/
http://dx.doi.org/10.1007/978-3-030-50153-2_46
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author Abbadini, Marco
Di Stefano, Federica
Spada, Luca
author_facet Abbadini, Marco
Di Stefano, Federica
Spada, Luca
author_sort Abbadini, Marco
collection PubMed
description We prove that the unification type of Łukasiewicz logic with a finite number of variables is either infinitary or nullary. To achieve this result we use Ghilardi’s categorical characterisation of unification types in terms of projective objects, the categorical duality between finitely presented MV-algebras and rational polyhedra, and a homotopy-theoretic argument.
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spelling pubmed-72747292020-06-08 Unification in Łukasiewicz Logic with a Finite Number of Variables Abbadini, Marco Di Stefano, Federica Spada, Luca Information Processing and Management of Uncertainty in Knowledge-Based Systems Article We prove that the unification type of Łukasiewicz logic with a finite number of variables is either infinitary or nullary. To achieve this result we use Ghilardi’s categorical characterisation of unification types in terms of projective objects, the categorical duality between finitely presented MV-algebras and rational polyhedra, and a homotopy-theoretic argument. 2020-05-16 /pmc/articles/PMC7274729/ http://dx.doi.org/10.1007/978-3-030-50153-2_46 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Abbadini, Marco
Di Stefano, Federica
Spada, Luca
Unification in Łukasiewicz Logic with a Finite Number of Variables
title Unification in Łukasiewicz Logic with a Finite Number of Variables
title_full Unification in Łukasiewicz Logic with a Finite Number of Variables
title_fullStr Unification in Łukasiewicz Logic with a Finite Number of Variables
title_full_unstemmed Unification in Łukasiewicz Logic with a Finite Number of Variables
title_short Unification in Łukasiewicz Logic with a Finite Number of Variables
title_sort unification in łukasiewicz logic with a finite number of variables
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7274729/
http://dx.doi.org/10.1007/978-3-030-50153-2_46
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