A Paraconsistent Multi-agent Framework for Dealing with Normative Conflicts

Abstract

Abstract. In a multi-agent deontic setting, normative conflicts can take a variety of different logical forms. In this paper, we present a very general characterization of such conflicts, including both intra-and inter-agent normative conflicts, conflicts between groups of agents, conflicts between obligations and permissions, and conflicts between contradictory norms. In order to account for the consistent possibility of this wide variety of conflict-types, we present a paraconsistent deontic logic, i.e. a logic that invalidates the classical principle of non-contradiction. Next, we strengthen this logic within the adaptive logics framework for defeasible reasoning. The resulting inconsistency-adaptive deontic logic interprets a given set of norms 'as consistently as possible'.

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

“…[7,29,39,41]). It improves on earlier work presented in [6]. We compare the logics PMDL r and PMDL m to both logics of action and adaptive deontic logics in Section 6.…”

“…(5) and (6) illustrate that ML's agency operators do not allow for the inclusion of 'free riders' in their actions: for each action ◻ J A, each member of the group J is essential to J's bringing about A.…”

“…More specifically, it continues the task set out in [6] of constructing a multi-agent adaptive deontic logic capable of tolerating normative conflicts. The system PMDL x improves on the semantics defined in [6] in various ways.…”

“…In a non-agentive setting, paraconsistent deontic logics were presented in [6,7,11,34]. Notwithstanding their representation of agents, the logics presented here are closely related to the system DP r from [7].…”

“…In stit logic, operators for agency are closed under 'weakening' by the addition of further agents: If J ⊂ K ⊆ ∅ I, then if J sees to it that A, then K sees to it that A. As illustrated in (5) and (6), this kind of weakening is invalid in the logics defined here. Consequently, a statement like (66) is ML-,MDL-,PMDL-, and PMDL x -consistent, while its stit analogue would cause explosion:…”