{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T19:15:32Z","timestamp":1784920532615,"version":"3.55.0"},"reference-count":16,"publisher":"Emerald","issue":"10","license":[{"start":{"date-parts":[[2012,10,12]],"date-time":"2012-10-12T00:00:00Z","timestamp":1350000000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,10,12]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>Deontical impure systems are systems whose object set is formed by an s\u2010impure set, whose elements are <jats:italic>perceptuales significances<\/jats:italic> (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\u2010way directions and at least one of its relations has deontical properties such as permission, prohibition, obligation and faculty.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>The paper looks at the mathematical and logical development of human society structure.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>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 to the system, in as much to the modality faculty its neurocerebral system, because it allows him to make decisions. Transactions of energy, money, merchandise, population, etc. would be the equivalent one to the sanguineous system. These economic transactions and inferential relations, depend, as well, of the existence of a legislative body with their obligations, prohibitions and permissions that regulate them. A Social System \u03a3 may be considered like an alysidal set with an only alysidal element. The authors consider two theories: Enlarged theory and Reduced theory.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>This paper is a continuation of two previous papers \u2013 Part I published in Kybernetes, Vol. 41 No. 1\/2 and Part II published in Vol. 41 No. 5\/6 \u2013 and develops the theory of deontical impure systems.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684921211276800","type":"journal-article","created":{"date-parts":[[2013,3,25]],"date-time":"2013-03-25T14:02:52Z","timestamp":1364220172000},"page":"1638-1649","source":"Crossref","is-referenced-by-count":21,"title":["An introduction to alysidal algebra (III)"],"prefix":"10.1108","volume":"41","author":[{"given":"J.","family":"Nescolarde\u2010Selva","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.L.","family":"Us\u00f3\u2010Dom\u00e9nech","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"140","reference":[{"key":"key2022031120423913100_b1","doi-asserted-by":"crossref","unstructured":"Lloret\u2010Climent, M., Villacampa, Y. and Us\u00f3, J.L. 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