Revisiting Ultraproducts in Fuzzy Predicate Logics

Abstract-In this paper we examine different possibilities of defining reduced products and ultraproducts in fuzzy predicate logics. We present analogues to the Łos Theorem for these notions and discuss the advantages and drawbacks of each definition introduced. Following the work in [9], we show that these constructions are adequate for working in a reduced semantics

Revisiting ultraproducts in fuzzy predicate logics

In this paper we examine different possibilities of defining reduced products and ultraproducts in fuzzy predicate logics. We present analogues to the Łoś theorem for these notions and discuss the advantages and drawbacks of each definition introduced

A Lindström theorem in many-valued modal logic over a finite MTL-chain

We consider a modal language over crisp frames and formulas evaluated on a finite MTL-chain (a linearly ordered commutative integral residuated lattice). We first show that the basic modal abstract logic with constants for the values of the MTL-chain is the maximal abstract logic satisfying Compactness, the Tarski Union Property and strong invariance for bisimulations. Finally, we improve this result by replacing the Tarski Union Property by a relativization property. © 2019 Elsevier B.V.We are grateful to two anonymous referees and the editor of this journal for their numerous and helpful comments. Their help greatly improved the paper. Guillermo Badia is supported by the project I 1923-N25 of the Austrian Science Fund (FWF). Grigory Olkhovikov is supported by Deutsche Forschungsgemeinschaft (DFG), project WA 936/11-1

A Lindström Theorem in Many-Valued Modal Logic over a Finite MTL-chain

We consider a modal language over crisp frames and formulas evaluated on a finite MTL-chain (a linearly ordered commutative integral residuated lattice). We first show that the basic modal abstract logic with constants for the values of the MTL-chain is the maximal abstract logic satisfying Compactness, the Tarski Union Property and strong invariance for bisimulations. Finally, we improve this result by replacing the Tarski Union Property by a relativization property

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

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 example

Revisiting ultraproducts in fuzzy predicate logics

In this paper we examine different possibilities of defining reduced products and ultraproducts in fuzzy predicate logics. We present analogues to the Łoś theorem for these notions and discuss the advantages and drawbacks of each definition introduced. © 2012 Old City Publishing, Inc.Research partially funded by the projects CSD2007-0022, TIN2009-14704-C03-03, FFI2008-03126- E/FILO and by the grant 2009-SGR-1434.Peer Reviewe