Abstract
We consider a generalised Chisholm set of contrary to duty obligations (CTD) of the form
and for i = 0,…, n we have the CTD is
and the facts ±q j for some j ∈ J ⊆ {0,1,…, n + 1}. Note that for the case of n = 1 and fact ¬q 0 we have the Chisholm paradox.
We also allow for temporal sequencing of the q i in the form that q i + 1 may come temporally before or after q i .
We offer a representation of this problem in a variation of standard deontic logic that we call TSDL, with the standard temporal operator \(\lozenge\), the deontic obligation operator O, and the past operator Y for “yesterday”. This formalism is free of the above paradoxes. We provide an axiomatization and show it to be complete. The logic formalism enjoys the finite tree model property and hence is decidable.
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Gabbay, D. (2012). Temporal Deontic Logic for the Generalised Chisholm Set of Contrary to Duty Obligations. In: Ågotnes, T., Broersen, J., Elgesem, D. (eds) Deontic Logic in Computer Science. DEON 2012. Lecture Notes in Computer Science(), vol 7393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31570-1_7
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