Unification in Łukasiewicz logic with a finite number of variables

Marco Abbadini

doi:10.1007/978-3-030-50153-2_46

Unification in Łukasiewicz logic with a finite number of variables

Marco Abbadini

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

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.

Original language	English
Title of host publication	Information Processing and Management of Uncertainty in Knowledge-Based Systems
Pages	622-633
Volume	1239
DOIs	https://doi.org/10.1007/978-3-030-50153-2_46
Publication status	Published - 2020

Keywords

Łukasiewicz logic
MV-algebras
Unification
Universal cover

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10.1007/978-3-030-50153-2_46

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title = "Unification in {\L}ukasiewicz logic with a finite number of variables",

abstract = "We prove that the unification type of {\L}ukasiewicz logic with a finite number of variables is either infinitary or nullary. To achieve this result we use Ghilardi{\textquoteright}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.",

keywords = "{\L}ukasiewicz logic, MV-algebras, Unification, Universal cover",

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PY - 2020

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N2 - 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.

AB - 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.

KW - Łukasiewicz logic

KW - MV-algebras

KW - Unification

KW - Universal cover

U2 - 10.1007/978-3-030-50153-2_46

DO - 10.1007/978-3-030-50153-2_46

M3 - Conference contribution

VL - 1239

SP - 622

EP - 633

BT - Information Processing and Management of Uncertainty in Knowledge-Based Systems

ER -

Unification in Łukasiewicz logic with a finite number of variables

Abstract

Keywords

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