The Simplest Solution to the Deepest Paradox of Deontic Logic

CLE e-Prints Vol. 8(6), 2008

Usually, a deontic paradox consists of a set of sentences in natural language which are, intuitively, logically independent and jointly consistent but, when formalized in standard deontic logic (SDL), the set derives contradictory obligations and/or has logical dependencies. In this paper, following the approach initiated in [8], two deontic systems based on Logics Formal Inconsistency are proposed: the first one is closer to SDL because contradictory obligations trivialize but contradictory sentences do not. The second one is a bimodal extension of system DmbC introduced in [8] by adding a modality for deontic inconsistency as a primitive, such that contradictory obligations do not trivialize. This approach overcomes deontic paradoxes such as Chisholm’s paradox by allowing a richer repertoire of connectives which avoids logical dependencies, and by avoiding logical collapse in the presence of contradictory obligations.

2008

1981

In a recent paper, Sven Danielsson argued that the 'original paradoxes' of deontic logic, in particular Ross's paradox and Prior's paradox of derived obligation, can be solved by restricting the modal inheritance rule. I argue that this does not solve the paradoxes.

Normative Multi-agent …, 2007

The paper discusses ten philosophical problems in deontic logic: how to formally represent norms, when a set of norms may be termed 'coherent', how to deal with normative conflicts, how contraryto-duty obligations can be appropriately modeled, how dyadic deontic operators may be redefined to relate to sets of norms instead of preference relations between possible worlds, how various concepts of permission can be accommodated, how meaning postulates and counts-as conditionals can be taken into account, and how sets of norms may be revised and merged. The problems are discussed from the viewpoint of input/output logic as developed by van der Torre & Makinson. We argue that norms, not ideality, should take the central position in deontic semantics, and that a semantics that represents norms, as input/output logic does, provides helpful tools for analyzing, clarifying and solving the problems of deontic logic.

The Logics of Formal Inconsistency (LFIs) are paraconsistent logics which internalize the notions of consistency and inconsistency by means of connectives. Based on that idea, in this paper we propose two deontic systems in which contradictory obligations are allowed, without trivializing the system. Thus, from conflicting obligations Oϕ and O¬ϕ contained in (or derived from) an information set, it can be derived that the sentence ϕ is deontically inconsistent. This avoids the logic collapse, and, on the other hand, this allows to "repair" or to refine the given information set. This approach can be used, for instance, for analyzing paradoxes based on contrary-toduty obligations. KEYWORDS: Logics of formal inconsistency, deontic logic, contrary-to-duty obligations.

Ratio Juris, 2002

A recent series of papers, sparked off by a note by Robert Walter (1996), has rekindled the debate over the possibility of creating a logic of normative concepts. The debate correctly centres on ways in which Jørgensen’s dilemma might be resolved (Jørgensen 1937–8), since a means of resolving that dilemma is the only apparently available way in which to establish that a logic of norms is possible. Two separate questions require answers: (i) what is the correct way in which to regard Jørgensen’s dilemma; and (ii) how should one face that dilemma? I shall argue that traditional responses to the first question are inadequate, and I shall then try to expose as flawed two recent attempts to resolve the dilemma. Finally, I shall relate my conclusions in the earlier part of the paper to the wider question of whether a logic of normative concepts is, after all, a possibility.

Journal of Logic, Language and Information

Centered around the analysis of the prescriptive portion of the Vedas, the Sanskrit philosophical school of Mīmāṃsā provides a treasure trove of normative investigations. We focus on the leading Mīmāṃsā authors Prabhākara, Kumārila and Maṇḍana, and discuss three modal logics that formalize their deontic theories. In the first part of this paper, we use logic to analyze, compare and clarify the various solutions to the śyena controversy, a two-thousand-year-old problem arising from seemingly conflicting commands in the Vedas. In the second part, the formalized Mīmāṃsā theories are analyzed and employed to provide alternative perspectives on well-known paradoxes from the contemporary field of deontic logic. Thus, we go from logic to Mīmāṃsā and back again.

Artificial Intelligence and Law, 2000

The book under review here, Defeasible Deontic Logic, consists of thirteen pa-pers and an introduction, dealing with the combination of the two themes deontic reasoning and defeasible reasoning. Many of the papers are quite technical and although some of the authors are ...

2019

This paper provides a proof that Tennant's logical system entails a paradox that is called Core logic paradox, in reference to the new name given by Tennant to his intuitionistic relevant logic.

A. Introduction. Two key concepts and three perspectives in deontic logic. Situation, agency and agent oriented deontic theories. B. Concept of norm and its structure revisited. Norms as atomic and molecular entities. C. Two approaches to deontic logic: deterministic, focusing on alethic \ deontic regularities, and indeterministic, viewing agentive choice and alternative lines of behavior. D. Conclusion. Three faces of deontic logic pursue different perspective of normative codes' analysis, reasoning about norms and agentive behavior with preferences \ priorities accordingly.