Structure of commutative cancellative integral residuated lattices on (0, 1] |
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Authors: | Rostislav Horčík |
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Affiliation: | (1) Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07 Prague 8, Czech Republic;(2) Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 166 27 Prague 6, Czech Republic |
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Abstract: | ΠMTL-algebras were introduced as an algebraic counterpart of the cancellative extension of monoidal t-norm based logic. It was shown that they form a variety generated by ΠMTL-chains on the real interval [0, 1]. In this paper the structure of these generators is investigated. The results illuminate the structure of cancellative integral commutative residuated chains, because every such algebra belongs to the quasivariety generated by the zero-free subreducts on (0, 1] of all ΠMTL-chains on [0, 1]. The work of the author was partly supported by the grant No. A100300503 of the Grant Agency of the Academy of Sciences of the Czech Republic and partly by the Institutional Research Plan AV0Z10300504. |
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Keywords: | Primary: 06F05 Secondary: 03G25 |
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