Back-and-forth systems for fuzzy first-order models

Pilar Dellunde, Àngel García-Cerdaña, Carles Noguera

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)


© 2018 Elsevier B.V. This paper continues the study of model theory for fuzzy logics by addressing the fundamental issue of classifying models according to their first-order theory. Three different definitions of elementary equivalence for fuzzy first-order models are introduced and separated by suitable counterexamples. We propose several back-and-forth conditions, based both on classical two-sorted structures and on non-classical structures, that are useful to obtain elementary equivalence in particular cases as we illustrate with several examples.
Original languageEnglish
Pages (from-to)83-98
JournalFuzzy Sets and Systems
Publication statusPublished - 15 Aug 2018


  • Back-and-forth systems
  • Elementary equivalence
  • First-order fuzzy logics
  • Mathematical fuzzy logic
  • Model theory
  • Non-classical logics


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