Alchourrón and Bulygin on deontic logic and the logic of norm-propositions: axiomatization and representability results

Lennart Åqvist


The paper deals with the problem of axiomatizing three formal systems of Deontic Logic / Normative Logic in a sense derived from Alchourrón & Bulygin (1973) and Alchourrón (1969). First of all we consider a version DL of their Deontic Logic (= Logic of Norms), secondly a version NL of their Normative Logic (= Logic of Norm-Propositions), to which they add a number of definitions generating certain normative operators “proper”. Thirdly, we deal with a third system NOBL constructed with a view to isolating the normative fragment of NL which arises as a result of adding those definitions to NL. The main outcome of this paper is then a representability result to the effect that the set of sentences provable in NOBL is exactly the set of the sentences which are provable in NL on the basis of those definitions. The distinction Logic of Norms vs. Logic of Norm-Propositions is explained and discussed rather informally both in the introduction and in the concluding section of the present paper.

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