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Syntactic characterizations of classes of first-order structures in mathematical fuzzy logic

Authors
  • Badia, Guillermo1, 2
  • Costa, Vicent3
  • Dellunde, Pilar3, 4, 5
  • Noguera, Carles6
  • 1 Johannes Kepler University Linz, Department of Knowledge-Based Mathematical Systems, Linz, Austria , Linz (Austria)
  • 2 University of Queensland, School of Historical and Philosophical Inquiry, Brisbane, Australia , Brisbane (Australia)
  • 3 Universitat Autónoma de Barcelona, Department of Philosophy, Bellaterra, Catalonia, Spain , Bellaterra (Spain)
  • 4 Artificial Intelligence Research Institute (IIIA – CSIC), Bellaterra, Catalonia, Spain , Bellaterra (Spain)
  • 5 Barcelona Graduate School of Mathematics, Barcelona, Catalonia, Spain , Barcelona (Spain)
  • 6 Czech Academy of Sciences, Institute of Information Theory and Automation, Prague, Czech Republic , Prague (Czechia)
Type
Published Article
Journal
Soft Computing
Publisher
Springer-Verlag
Publication Date
Feb 22, 2019
Volume
23
Issue
7
Pages
2177–2186
Identifiers
DOI: 10.1007/s00500-019-03850-6
Source
Springer Nature
Keywords
License
Green

Abstract

This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal–existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.

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