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L O ] 4 O ct 2 01 8 Residuation in non-associative MV-algebras ∗
| Content Provider | Semantic Scholar |
|---|---|
| Author | Chajda, Ivan Länger, Helmut |
| Copyright Year | 2018 |
| Abstract | It is well known that every MV-algebra can be converted into a residuated lattice satisfying divisibility and the double negation law. In our previous papers we introduced the concept of an NMV-algebra which is a non-associative modification of an MV-algebra. The natural question arises if an NMV-algebra can be converted into a residuated structure, too. Contrary to MV-algebras, NMV-algebras are not based on lattices but only on directed posets and the binary operation need not be associative and hence we cannot expect to obtain a residuated lattice but only an essentially weaker structure called a conditionally residuated poset. Considering several additional natural conditions we show that every NMV-algebra can be converted in such a structure. Also conversely, every such structure can be organized into an NMV-algebra. Further, we study a bit more stronger version of an algebra where the binary operation is even monotonous. We show that such an algebra can be organized into a residuated poset and, conversely, every residuated poset can be converted in this structure. AMS Subject Classification: 06D35, 03G10, 06A11 |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv-export-lb.library.cornell.edu/pdf/1810.02405 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
