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Proof theory, semantics and algebra for normative systems. (English) Zbl 1444.03076

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.

MSC:

03B45 Modal logic (including the logic of norms)
03G25 Other algebras related to logic
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