Normatively determined propositions

In V. Giardino, S. Linker, S. Burns, F. Bellucci, J. M. Boucheix & P. Viana (eds.), Diagrammatic Representation and Inference. Diagrams 2022. Springer. pp. 78-85 (2022)
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Abstract

In the present work we provide a logical analysis of normatively determined and non-determined propositions. The normative status of these propositions depends on their relation with another proposition, here named reference proposition. Using a formal language that includes a monadic operator of obligation, we define eight dyadic operators that represent various notions of “being normatively (non-)determined”; then, we group them into two families, each forming an Aristotelian square of opposition. Finally, we show how the two resulting squares can be combined to form an Aristotelian cube of opposition.

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