Triangle algebras: A formal logic approach to interval-valued residuated lattices
To obtain a triangle algebra, the authors extend the definition of a residuated lattice with a new constant \(u\) (uncertainty) and two new unary connectives \(v\) (necessity) and \(\mu \) (possibility). The authors show that triangle algebras serve as an equational representation of interval-valued residuated lattices (IVRLs). Also, they present triangle logic, a system of many-valued logic capturing the tautologies of IVRLs. Triangle algebras are used to cast the essence of using closed intervals of bounded lattices \(L\) as truth values into a set of appropriate logical axioms.
scientific article; zbMATH DE number 5599383
scientific article