A Paraconsistentist Approach to Chisholm's Paradox

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.

2020

Different notions of the consistency of obligations collapse in standard deontic logic.In justification logics, which feature explicit reasons for obligations, the situation isdifferent. Their strength depends on a constant specification and on the availableset of operations for combining different reasons. We present different consistencyprinciples in justification logic and compare their logical strength. Further, we proposea novel semantics for which justification logics with the explicit version of axiom D,jd,are complete for arbitrary constant specifications. We then discuss the philosophicalimplications with regard to some deontic paradoxes.

J. Marcos, D. Batens, and WA Carnielli, organizers, …

The logics of formal inconsistency (LFIs) are logics that allow to explicitly formalize the concepts of consistency and inconsistency by means of formulas of their language. Contradictoriness, on the other hand, can always be expressed in any logic, provided its la nguage includes a symbol for negation. Besides being able to represent the distinction between contradiction and inconsistency, LFIs are non-explosive logics, in the sense that a contradiction does not entail arbitrary statements, but yet are gently explosive, in the sense that, adjoining the additional requirement of consistency, then contradictoriness does cause explosion. Several logics can be seen as LFIs, among them the great majority of paraconsistent logics developed under the Brazilian tradition, as well as the sytems developed under the Polish tradition. We present here their semantical interpretations by way of possible-translations semantics, stressing their significance and applications to human reasoning and machine reasoning. We also give tableaux systems for some important LFIs: bC, Ci and LFI1.

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.

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.

2008

IOS Press eBooks, 2021

Inspired by Kelsen's view that norms establish causal-like connections between facts and sanctions, we develop a deontic logic in which a proposition is obligatory iff its complement causes a violation. We provide a logic for normative causality, define non-contextual and contextual notions of illicit and duty, and show that the logic of such duties is well-behaved and solves the main deontic paradoxes.

We present a refinement of Anderson’s reduction of deontic logic to modal logic with only alethic modalities. The refined proposal contextualizes the Andersonian sanction constant s by replacing it with a unary sanction operator S that is dependent on the concrete normative requirement that is violated. A formula SB is then for instance interpreted as “B causes a sanction” or as “B provides a reason for (the applicability of) a sanction”. Due to its modified sanction operator, the resulting logic DSL invalidates some instances of the inheritance principle. This gives rise to new interesting features. For instance, DSL consistently allows for the presence of conflicting obligations. Moreover, it provides novel insights in various central ‘paradoxes’ in deontic logic such as the Ross paradox, the paradox of the good Samaritan, and Forrester’s ‘gentle murderer’ paradox.

(For correct references compare the uploaded file) Lou Goble proposed in his [6] logics which are able to deal with deontic conflicts by restricting the inheritance principle. In [3] he developed this systems further in order to treat conditional obligations. One of the central problems for dyadic deontic logics is to properly treat the restricted applicability of the principle “strengthening the antecedent”. In most cases of moral reasoning we want to derive from an obligation A under condition B, that A is also obliged under condition B and C. However, there are important counterexamples. Goble proposed a weakened rational monotonicity principle to tackle this problem. This solution is suboptimal as it is for some examples counter-intuitive or even leads to explosion. The paper identifies also other problems of Goble’s systems. An adaptive logic framework is proposed which is able to tackle these problems. For the adaptive logics there is no need for further explicit additions of permission statements to the premise set which was for Goble’s logics a consequence of restricting inheritance. The addition of such statements was ad hoc and in need to be done externally by the user. The proof dynamics of the adaptive logic takes care of this as a part of the reasoning process which is explicated by the proof. Furthermore, for non-conflicting premise sets the adaptive logics are equivalent to Goble’s dyadic version of standard deontic logic.

Lecture Notes in Computer Science, 1995

There is a fundamental difference between a conditional obligation being violated by a fact, and a conditional obligation being overridden by another conditional obligation. In this paper we analyze this difference in the multi preference semantics of our defeasible deontic logic DEFDIODE. The semantics contains one preference relation for ideality, which can be used to formalize deontic paradoxes like the Chisholm and Forrester paradoxes, and another preference relation for normality, which can be used to formalize exceptions. The interference of the two preference orderings generates new questions about preferential semantics.