Quantified deontic logic with definite descriptions (Q2735770)

In a previous paper [``Ought and extensionality'', Noûs 30, 330-355 (1996)] the author argued that the deontic operator of obligation, unlike its counterparts for necessity and belief, should intuitively be regarded as extensional with respect to individual terms when used in the context of classical first-order logic. However, as he also observed in a much earlier paper [``Opacity and the ought-to-be'', Noûs 7, 407-412 (1973)], if the classical first-order logic admits definite descriptions then such an extensionality conflicts with certain principles of standard deontic logic, namely the congruence and monotony rules for obligation with respect to logical consequence.NEWLINENEWLINENEWLINETo resolve this conflict, he turns to the usual possible-worlds semantics for first-order deontic logic, and transcribes to it a treatment of definite descriptions that was devised in the context of alethic modal logic by \textit{R. H. Thomason} [``Some completeness results for modal predicate calculi'', in: K. Lambert (ed.), Philosophical problems in logic: some recent developments, Dordrecht, Reidel, 56-76 (1970; Zbl 0188.32002)]. The idea is to index each interpretation function by a world, so that when examining a formula in one world, the interpretation can also use information from the world serving as its index. Such a treatment validates extensionality but leads to restrictions on certain deontic principles when their component formulae contain definite descriptions. An axiomatization of the resulting deontic system is given, and an appropriate completeness theorem proven.