We present the logic BL_Chang, 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 BL_Chang-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.

The variety generated by all the ordinal sums of perfect MV-Chains / M. Bianchi. - In: STUDIA LOGICA. - ISSN 0039-3215. - 101:1(2013 Feb), pp. 11-29. [10.1007/s11225-012-9371-5]

The variety generated by all the ordinal sums of perfect MV-Chains

M. Bianchi
Primo
2013

Abstract

We present the logic BL_Chang, 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 BL_Chang-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.
many-valued logics; BL-algebras; perfect MV-algebras; Łukasiewicz logic; basic logic; Wajsberg hoops
Settore MAT/01 - Logica Matematica
Settore MAT/02 - Algebra
Settore INF/01 - Informatica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/216626
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