Obligation as Optimal Goal Satisfaction

Abstract

Formalising deontic concepts, such as obligation, prohibition and permission, is normally carried out in a modal logic with a possible world semantics, in which some worlds are better than others. The main focus in these logics is on inferring logical consequences, for example inferring that the obligation O q is a logical consequence of the obligations O p and O (p → q). In this paper we propose a nonmodal approach in which obligations are preferred ways of satisfying goals expressed in first-order logic. To say that p is obligatory, but may be violated, resulting in a less than ideal situation s, means that the task is to satisfy the goal p ∨ s, and that models in which p is true are preferred to models in which s is true. Whereas, in modal logic, the preference relation between possible worlds is part of the semantics of the logic, in this non-modal approach, the preference relation between first-order models is external to the logic. Although our main focus is on satisfying goals, we also formulate a notion of logical consequence, which is comparable to the notion of logical consequence in modal deontic logic. In this formalisation, an obligation O p is a logical consequence of goals G, when p is true in all best models of G. We show how this non-modal approach to the treatment of deontic concepts deals with problems of contrary-to-duty obligations and normative conflicts, and argue that the approach is useful for many other applications, including abductive explanations, defeasible reasoning, combinatorial optimisation, and reactive systems of the production system variety.

Connecting Rule-Based and Case-Based Representations of Soft-Constraint Norms

“…Solutions to a constraint hierarchy are intuitively valuations that satisfy all of the hard constraints and no other valuations that better satisfy the soft constraints (for formal definitions, see [1,3]). We define an obligatory consequence based on the solutions to a constraint hierarchy according to the concept of obligation [4], as follows.…”

Dischargeable Obligations in the 𝒮CIFF Framework

“…A notable application of Abductive Logic Programming to normative reasoning is Kowalski and Satoh's Normative ALP Frameworks [38]. Normative ALP Frameworks are abductive logic programs with a preference relation defined as a partial order over models; a formula is obligatory in a Normative ALP if it is true in all its optimal (i.e., such that no other model is preferred) models.…”