Generalized state operators on residuated lattices
- 262 Downloads
We give a definition of a generalized state operator (g-state operator) \(\sigma \) on a residuated lattice X and a g-state residuated lattice \((X,\sigma )\), by which the class of all g-state residuated lattices is proved to be a variety, and consider properties of g-state residuated lattices. We prove some fundamental results about them, such as characterizations of \(\sigma \)-filters, extended \(\sigma \)-filters, homomorphism theorems for g-state residuated lattices. Moreover, we show that every g-state residuated lattice is a subdirect product of subdirectly irreducible g-state residuated lattices.
Keywords(Generalized) state filters Extended filters Residuated lattices
This study was funded by JSPS KAKENHI (Grant Number 15K00024).
Compliance with ethical standards
Conflicts of interest
The author declares that he has no conflict of interest.
- Kondo M, Watari O, Kawaguchi MF, Miyakoshi M (2007) A logic determined by commutative residuated lattices. EUSFLAT Conference, pp 45–48Google Scholar