An adaptive logic framework for conditional obligations and deontic dilemmas

Abstract

Lou Goble proposed powerful conditional deontic logics (CDPM) that are able to deal with deontic conflicts by means of restricting the inheritance principle. 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 it is desirable 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. For instance, to make optimal use of the restricted inheritance principle, in many cases the user has to manually add certain statements to the premises.An adaptive logic framework based on CDPM is proposed which is able to tackle these problems. It allows for certain rules to be applied as much as possible. In this way counter-intuitive consequences as well as explosion can be prohibited and no user interference is required. Furthermore, for non-conflicting premise sets the adaptive logics are equivalent to Goble's dyadic version of standard deontic logic.

Non-monotonic reasoning with normative conflicts in multi-agent deontic logic

“…This paper fits within the larger project of adaptive deontic logics devised for consistently accommodating normative conflicts (see e.g. [7,29,39,41]). It improves on earlier work presented in [6].…”

“…In [40] factual detachment is defeasibly applied to O(A B) and B in order to derive the non-conditional obligation OA. Similarly, in [39] strengthening the antecedent is applied to O(A B) defeasibly in order to derive O(A B ∧ C).…”

“…For some other adaptive deontic logics that can consistently accommodate instances of normative conflicts, see [7,29,39,41]. For an introduction to the framework of adaptive logics, see [3].…”

Computational Logic in Multi-Agent Systems

“…There too, SDL gives rise to explosion in view of formulas of the form OA ∧ O¬A, OA ∧ P¬A, etc. And there too, authors have suggested weakening the logic in order to tolerate normative conflicts; for some examples, see [12,21,25,28,31,32]. A good oversight can be found in [13].…”

A deontic logic framework allowing for factual detachment

“…Prominent examples are inconsistency ALs (e.g., [4]) or applications to abduction (e.g., [22]) and induction (e.g., [2]). Recent research has shown a growing interest in ALs that tackle various problems with deontic logics (see [6,23,31,29]). …”