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.
Dellunde, P., Garcia-Cerdana, A., Noguera, C. (2018). Back-and-forth systems for fuzzy first-order models. FUZZY SETS AND SYSTEMS, 345, 83-98 [10.1016/j.fss.2018.01.016].
Back-and-forth systems for fuzzy first-order models
Noguera C.
2018-01-01
Abstract
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.File | Dimensione | Formato | |
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https://hdl.handle.net/11365/1200198