... are not produced or else some forbidden responses are produced. Responses prohibited by the system are defined as nonwished effects. Originality/value – This paper is a continuation of the four previous papers and is developed the theory of deontical impure systems. Alysidal set Gnorpsic function Gödel...

..., as well, of the existence of a legislative body with their obligations, prohibitions and permissions that regulate them. A Social System Σ may be considered like an alysidal set with an only alysidal element. The authors consider two theories: Enlarged theory and Reduced theory. Originality/value...

... of Alysidal Algebra, which is important for the study of deontical impure systems. They are defined coupling functions and alysidal structures. It is defined as a special coupling function denominated gnorpsic function that can be used for algebraic operations between alysidal sets...

... and inferential relations, depend, as well, on the existence of a legislative body with their obligations, prohibitions and permissions that regulate them. Originality/value The concepts of alysidal set are introduced, whose elements are chains and coupling function between alysidal sets. Environment...