PL EN


2011 | 46 | 17-27
Article title

MINIMAL SUBVARIETIES OF INVOLUTIVE RESIDUATED LATTICES

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EN
Abstracts
EN
It is known that classical logic CL is the single maximal consistent logic over intuitionistic logic Int, which is moreover the single one even over the substructural logic FLew. On the other hand, if we consider maximal consistent logics over a weaker logic, there may be uncountablymany of them. Since the subvariety lattice of a given variety V of residuated lattices is dually isomorphic to the lattice of logics over the corresponding substructural logic L(V), the number of maximal consistent logics is equal to the number of minimal subvarieties of the subvariety lattice of V. Tsinakis and Wille have shown that there exist uncountably many atoms in the subvariety lattice of the variety of involutive residuated lattices. In the present paper, we will show that while there exist uncountably many atoms in the subvariety lattice of the variety of bounded representable involutive residuated lattices with mingle axiom x2 is less than or equal to b x, only two atoms exist in the subvariety lattice of the variety of bounded representable involutive residuated lattices with the idempotency x = x2.
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Year
Issue
46
Pages
17-27
Physical description
Document type
ARTICLE
Contributors
  • Daisuke Souma, Collaborative Research Team for Verification and Specification, National Institute of Advanced Industrial Science and Technology, Nakoji 3-11-46, Amagasaki, Hyogo 661-0974, Japan
References
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Publication order reference
Identifiers
CEJSH db identifier
11PLAAAA10192
YADDA identifier
bwmeta1.element.20309e13-9889-3f2b-a4ce-3ffd14ade00b
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