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Studia Logica

, Volume 101, Issue 1, pp 11–29 | Cite as

The Variety Generated by all the Ordinal Sums of Perfect MV-Chains

  • Matteo Bianchi
Article

Abstract

We present the logic BLChang, an axiomatic extension of BL (see [23]) whose corresponding algebras form the smallest variety containing all the ordinal sums of perfect MV-chains. We will analyze this logic and the corresponding algebraic semantics in the propositional and in the first-order case. As we will see, moreover, the variety of BLChang-algebras will be strictly connected to the one generated by Chang’s MV-algebra (that is, the variety generated by all the perfect MV-algebras): we will also give some new results concerning these last structures and their logic.

Keywords

Many-valued logics BL-algebras Perfect MV-algebras Łukasiewicz logic Basic Logic Wajsberg hoops 

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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Dipartimento di Informatica e ComunicazioneUniversità degli Studi di MilanoMilanItaly

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