To read this content please select one of the options below:

An introduction to alysidal algebra (IV)

Jose-Luis Usó-Domenech (Universidad Jaume I, Castellón, Spain)
Josué Antonio Nescolarde-Selva (University of Alicante, Alicante, Spain)

Kybernetes

ISSN: 0368-492X

Article publication date: 2 September 2013

75

Abstract

Purpose

Deontical impure systems are systems whose object set is formed by an s-impure set, whose elements are perceptuales significances (relative beings) of material and/or energetic objects (absolute beings) and whose relational set is freeways of relations, formed by sheaves of relations going in two-way directions and at least one of its relations has deontical properties such as permission, prohibition, obligation and faculty. The paper aims to discuss these issues.

Design/methodology/approach

Mathematical and logical development of human society ethical and normative structure.

Findings

Existence of relations with positive imperative modality (obligation) would constitute the skeleton of the system. Negative imperative modality (prohibition) would be the immunological system of protection of the system. Modality permission the muscular system, that gives the necessary flexibility. Four theorems have been formulated based on Gödel's theorem demonstrating the inconsistency or incompleteness of DISs. For each constructed systemic conception can happen to it one of the two following things: either some allowed responses 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.

Keywords

Acknowledgements

To Dr Daniel Berend.

Citation

Usó-Domenech, J.-L. and Antonio Nescolarde-Selva, J. (2013), "An introduction to alysidal algebra (IV)", Kybernetes, Vol. 42 No. 8, pp. 1235-1247. https://doi.org/10.1108/K-09-2012-0054

Publisher

:

Emerald Group Publishing Limited

Copyright © 2013, Emerald Group Publishing Limited

Related articles