
doi: 10.1007/bf00248639
Novel conditions of relevance are defined for conditionals in order to weed out some of the deontic paradoxes, such as Ross's paradox. Semantically, first-degree positive relevant entailment is defined in terms of fulfilment conditions, which are sets of sets of literals (atomic sentences or their negations). The construction has much in common with \textit{B. C. van Fraassen's} treatment of facts and truthmaker sets [J. Philos. 66, 477-487 (1969)]. The resulting logic of positive relevant entailment resembles \textit{W. T. Parry's} system of analytic implication [Erg. Math. Kolloqu. 4, 5-6 (1933; JFM 59.0862.08)], with interesting divergences. The author varies his semantic definition and the fulfilment conditions to rule out negative relevance, yielding two further first-degree entailment relations. Three corresponding types of obligation are then defined as entailment by a set of basic norms. Ross's paradox is blocked, but free choice of alternatives for fulfilling norms is upheld.
deontic logic, first-degree positive relevant entailment, obligation, Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics), deontic paradoxes, Ross paradox, Other nonclassical logic, conditions of relevance for conditionals
deontic logic, first-degree positive relevant entailment, obligation, Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics), deontic paradoxes, Ross paradox, Other nonclassical logic, conditions of relevance for conditionals
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