A Short Note on the Chisholm Paradox

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.

Annals of Mathematics and Artificial Intelligence, 1993

A variant of Belnap's stit-semantics due to Horty and yon Kutschera is used to develop a semantics of obligation. A partial completeness result is stated. The semantics is then used to discuss conditional obligation as well as two paradoxes of deontic logic. The paper argues for the importance of an analysis of agency for deontic logic. I.

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.

2008

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.

Abstract. This paper looks at deontic logic as resulting from both a betterness ordering on states (ie, a 'deontic preference') and a priority ordering on properties (ie, a 'law'explicitly representing a standard of behavior). The correspondence between these two orderings offers a rich perspective from which to look at deontic scenarios and puzzles, and in particular at contrary-to-duties.

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.

Handbook of Deontic Logic and Normative Systems, 2021

This chapter is a light-weighted overview of significant contributions to legal logic insofar as they involve deontic reasoning and related methods. A special emphasis is given to defeasible reasoning, which has been the major topic for legal reasoning in the last decades. The chapter is divided into three parts and the layout is as follows. Part 1 provides an introductory outline. In particular, we briefly recall an issue that was discussed in the context of deontic logic and that has been as well a hot research theme in legal reasoning, i.e., the very possibility of the use of logic in the law. Part 2 reconstructs the contribution of the literature about some classic topics or methods in deontic logic as relevant for the law: normative positions, the concept of permission, contrary-to-duty reasoning, input/output logic, algebras for normative systems, norm change, defeasibility in law. Part 3 is the largest one and offers, from our previous work, a unifying formal framework, based on Defeasible Logic, re-addressing some of the topics that we have already discussed in Part 2: legal hierarchies and dynamics, institutional agency and normative positions, and deontic aspects of legal interpretation.

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.

2017

The main aim of this paper is to study the notion of conditional right by means of constructive type theory (CTT) which provides the means to develop a system of contentual inferences rather than of syntactic derivations. Moreover, in line with Armgardt, we will first study the general notion of dependence as triggered by hypotheticals and then the logical structure of dependence specific to conditional right. I will develop this idea in a dialogical framework where the distinction between play-object and strategy-object leads to the further distinction between two basic kinds of pieces of evidence and where meanings is constituted by the interaction of obligations and entitlements. The present paper is based on Rahman (2015). However, though the underlying CTT-analysis is the same, the dialogical reconstruction makes use of a new way of linking dialogical logic and CTT. Introduction: