A different approach to deontic logic: Deontic logic viewed as a variant of dynamic logic
This paper proposes a new setting for deontic logic, i.e. the logic of obligation, permission and prohibition. The essential idea is to reduce deontic logic to a form of so-called dynamic logic, with the addition of a propositional constant for ``trouble'' in the style of A. R. Anderson. Thus, for example, ``it is forbidden to do \(\alpha\) in state \(\sigma\) '', written \(\sigma \vDash F\alpha\), is reduced to ``performance of \(\alpha\) in state \(\sigma\) always leads to trouble'', written in the notation of dynamic logic as \(\sigma \vDash [\alpha]V\), where V is the ``trouble'' constant. A central feature of the author's approach is that actions are strictly separated from propositions, with only the former subject to deontic appraisal, which renders iterated deontic modalities such as FF\(\alpha\) meaningless, since the prohibition operation F applies only to actions and always yields a proposition. This protects the approach from several of the paradoxes that have arisen for deontic logics in which all the work is done by propositions. By the same token, the role of the ``trouble'' constant as representing the outcome of an action rather than as the consequent of a conditional proposition also enables the author to avoid anomalies associated with the use of that constant in a purely propositional fashion. Another important feature of the author's approach in this paper is that it explicitly takes into account the passage of time. This had already been done by a few previous accounts, notably that of \textit{J. A. van Eck} in his thesis and subsequent paper [``A system of temporally relative modal and deontic predicate logic and its philosophical applications'', Logique Anal., Nouv. Sér. 25, 249-290, 339-381 (1982; Zbl 0549.03004)], but in a rather different manner. Both van Eck and the author use Kripke style accessibility relations, but those of van Eck are between worlds \underbar{within} each time slice, whilst those of Meyer are between a world \underbar{before} a certain action is performed and a world \underbar{after} it is performed. To facilitate comprehension, the author uses the main text of the paper to give an ``informally rigorous'' exposition of the ideas, and reserves the formal presentation for an appendix. The informal exposition is in general very clear, except unfortunately for the key concept of act negation. The author promises to give an informal semantics for this operation, but reneges on the promise, giving only a list of equational constraints on its interaction with other operations, and warning that ``we do not require \({\bar \alpha}\) to be a set-complement of \(\alpha\) in the sense that \(\alpha\) \(\cup {\bar \alpha}=Act\) or anything of this kind''. This warning should not be misunderstood. For in the presentation of the formal semantics in the appendix (which makes extremely dense reading) set-theoretic complementation does indeed play a part in the definition of act negation; the point is that it is a subtle use embedded in a rather complex construction. The constructions of this paper have been refined by th author in some respects in subsequent papers, namely: ``Using programming concepts in deontic reasoning'' [in: \textit{R. Bartsch} et al. (eds.), Semantics and contextual expression, 117-145 (Foris Publications, Dordrecht/Riverton, 1989)] and \textit{F. P. M. Dignum} and the author: ``Negations of transactions and their use in the specification of dynamic and deontic integrity constraints'' [in: \textit{M. Z. Kwiatkowska} et al. (eds.), Semantics for concurrency, 61-80 (Springer-Verlag, Berlin/London, 1990)]. Overall, it can be said that this paper opens the way to a better understanding of what is involved in deontic reasoning, by getting it out of its traditionally purely propositional framework and embedding it in a logic of action.
scientific article; zbMATH DE number 4137748