HpsUL is not the logic of pseudo-uninorms and their residua
- 4 July 2009
- journal article
- research article
- Published by Oxford University Press (OUP) in Logic Journal of the IGPL
- Vol. 17 (4) , 413-419
- https://doi.org/10.1093/jigpal/jzp023
Abstract
This paper presents several results on the non-commutative fuzzy logic HpsUL, a Hilbert system whose corresponding algebraic semantics is the variety of bounded representable residuated lattices. In particular, we prove that HpsUL is not complete with respect to algebras based on the real unit interval, which answers the question posed by Metcalfe, Olivetti and Gabbay and shows that HpsUL is not the logic of pseudo-uninorms and their residua. MSC2000: 03B52, 03G10.Keywords
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