Hereditary clones of multiple valued logic algebra

Abstract

We discuss relationships between properties and operations over the set /spl Omega/ of MVL functions. Closed properties are those invariant under the classical closure operation. A new type of properties, called hereditary, is defined, as well as hereditary closure. We calculate the ratio of hereditary properties, describe the families of maximal hereditary clones, and give a formula for their enumeration. We show that there are exactly eleven such clones in ternary logic. For Boolean algebra the lattice of all hereditary classes is finite, and we describe it completely. Meanwhile, starting from the three valued case there are still a continuum number of clones.<>