On the impact of sup-compositions in the resolution of multi-adjoint relation equations

Abstract

Multi-adjoint relation equations are defined by means of a sup-composition operator involving different conjunctions. Former works reveal that the resolution of a multi-adjoint relation equation is closely related to such conjunctions. This paper presents a first approach on the study of the influence of the selection of a sup-composition operator in different aspects of multi-adjoint relation equations, as their solvability or the extremal elements of their solution set. The obtained results are illustrated by an example concerning multi-adjoint logic programming. Last but not least, a procedure for reducing the computation of the solution set when only the sup-composition operator is modified is also introduced.