Sun, Xin Proof theory, semantics and algebra for normative systems. (English) Zbl 1444.03076 J. Log. Comput. 28, No. 8, 1757-1779 (2018). Summary: This article reports a correspondence between input/output logic and the theory of joining-system, an algebraic approach to normative system. The results have the form: every norm \((a, x)\) is logically derivable from a set of norms \(G\) if and only if it is in the space of norms algebraically generated by \(G\). We present three versions of correspondence: input/output logic and Boolean joining-system, intuitionistic input/output logic and Heyting joining-system, quasi input/output logic and quasi joining-system. The algebraic approach offers a holistic perspective on normative systems. We use isomorphism and embedding of joining-system to discuss the similarity of normative systems. Cited in 1 Document MSC: 03B45 Modal logic (including the logic of norms) 03G25 Other algebras related to logic Keywords:normative system; input/output logic; joining-system; deontic logic PDFBibTeX XMLCite \textit{X. Sun}, J. Log. Comput. 28, No. 8, 1757--1779 (2018; Zbl 1444.03076) Full Text: DOI Link