A different approach to deontic logic: Deontic logic viewed as a variant of dynamic logic
type: Item
instance of: scholarly article
title: A different approach to deontic logic: Deontic logic viewed as a variant of dynamic logic
zbMATH Open document ID: 0695.03009
published in: Notre Dame Journal of Formal Logic
publication date: 1988-01-01T00:00:00Z
review text: 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…
Mathematics Subject Classification ID: 03B60
Mathematics Subject Classification ID: 03B45
zbMATH DE Number: 4137748
zbMATH Keywords: deontic logic
zbMATH Keywords: dynamic logic
zbMATH Keywords: trouble
zbMATH Keywords: passage of time
zbMATH Keywords: Kripke style accessibility relations
zbMATH Keywords: act negation
zbMATH Keywords: logic of action
author: John-Jules Meyer
reviewed by: David Makinson
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093637776
OpenAlex ID: W2021916230
DOI: 10.1305/NDJFL/1093637776
description: scientific article; zbMATH DE number 4137748