The variety generated by all the ordinal sums of perfect MV-chains
Abstract
We present the logic BL_Chang, an axiomatic extension of BL (see P. Hájek - Metamathematics of fuzzy logic - 1998, Kluwer) 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2011
- DOI:
- 10.48550/arXiv.1103.5943
- arXiv:
- arXiv:1103.5943
- Bibcode:
- 2011arXiv1103.5943B
- Keywords:
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- Mathematics - Logic;
- 03B47;
- 03B50;
- 03C05;
- 06D35 (Primary) 06B20 (Secondary)
- E-Print:
- This is a revised version of the previous paper: the modifications concern essentially the presentation. The scientific content is substantially unchanged. The major variations are: Definition 2.7 has been improved. Section 3.1 has been made more compact. A new reference, [Bus04], has been added. There is some minor modification in Section 3.2