Fundamenta Informaticae

We define a deontic logic of regular action as a characterization within a modal μ-calculus of action. First a semantics of deontic notions for regular action is given in terms of conditions on modal action structures. Then modal μ-calculus formulas characterizing these conditions are constructed by closely following the structure of deterministic finite automatons for regular action.

In this paper we address the problem of organized collective agency, and propose a deontic/action modal logic for that purpose. We argue that once we want to attribute obligations (permissions or other deontic notions) to a set of agents, we need to consider a new agent - that we called institutionalized agent, and specify how he interacts with the external world: how the obligations flow from the institutionalized agent to the real agents that support him, and how the actions of the latter count as actions of the former. But an agent may act in many qualities (roles), and it is essential to know in which quality an agent has acted, or intends to act, for three main reasons: to know the effects of the act, its deontic qualification, and authentication issues. Thus, we extend the ``sees to it'' action operator with an explicit index that states the quality (role) in which the agent has acted. We also show how to associate obligations to roles, and illustrate how this can be used to express the desired flow of obligations.

In the field of information systems the term ``constraint'' is applied to statements of various kinds. Here we start from the analysis of a simple example to characterise the different kinds of constraints. It is shown that constraints may be necessary truths or deontic constraints. Moreover, deontic constraints are classified into three different types: deontic constraints about the world, deontic constraints about the representation of the world (self-completeness), and deontic constraints about the links between the world and its representation (validity and completeness). We describe a modal logical framework to define the different types of constraints, to characterise their violations, and to show how to repair their violations. Two different general forms of deontic constraints are considered, namely O(�→ψ) and �→O�, and it is shown that, except for deontic constraints about the world, the latter is more appropriate. Special issues related to the definition of quantifiers in the context of modal operators are also considered.

This paper presents an attempt to adapt, in the context of deontic reasoning, a logic defined by Boutilier for reasoning with conditional preferences. The first motivation for this work is that deontic logic can be given a semantics in terms of ordered worlds like in this kind of logic: the preference relation among worlds aims at ordering worlds from the most ideal ones to the least ideal ones. The second motivation is that Boutilier introduced a model of an agent's ability by distinguishing between controllable, influenceable and uninfluenceable propositions. And we noticed that this partition can be related to the notions introduced by Carmo and Jones for reasoning with Contrary-To-Duties. This present work shows an extension of Boutilier's work in order to use his logic for reasoning with Contrary-To-Duties. An exhaustive study of a benchmark example of CTDs leads us to show that the results obtained with this extension coincide exactly with those obtained by Carmo and Jones.

Though deontic logic is regarded as the logic of normative reasoning, norms – as entities lacking truth values – are usually represented neither in its language nor its semantics. Limiting ourselves to unconditional imperatives, we propose a concept for their semantic representation and show that existing systems of monadic and dyadic deontic logic can be reconstructed accordingly.

The paper revisits a class of model structures introduced by the author in 1974, with particular attention to the system SCon, which axiomatizes the universal class. SCon, which independently deserves notice as an algebraically plausible weakest modal system, is self-dual; that is, its □ and ◊ have the same logic. The paper gives a semantic analysis of the system on model structures capable of an axiological interpretation, presenting a number of determination- and correspondence-theoretic results. Some intriguing consequences of self-duality for the axiological interpretation of natural frames are discussed.

We first analyse the future-orientated account of conditional obligation as put forth by David Makinson. We show that the introduction of the futurity dimension is not indispensable in the elimination of the identity principle. This leads us to a more general observation. Most systems of dyadic deontic logic either accept both the identity principle and the cumulativity condition, or exclude both. We then develop an account of defeasible conditional obligation based on the ``and next" operator, as a solution to this dilemma.

This paper investigates whether current nonmonotonic logics are suitable for formalising the defeasibility of legal reasoning. It does so by studying the role of burden of proof in legal argument, in particular how allocations of burden of proof determine the required strength of counterarguments. It is argued that the two currently available modelling approaches both have some shortcomings. On the one hand, techniques for modelling burden of proof in nonmonotonic logics do not allow for shifts of the burden of proof from one party to the other. On the other hand, current procedural models of legal argument are too rigid, in that every counterargument induces a shift of proof burdens; this fails to respect that in legal reasoning burden shifts only occur in some cases. It is then shown how current dialectical models of defeasible reasoning can be adapted to overcome these shortcomings.

The theory of normative positions attempts to apply a combination of deontic logic and a logic of action/agency to the formalisation of the `Hohfeldian concepts' (duty, right, power, privilege, etc.) and other complex normative relations between agents. This paper is concerned with the practical applicability of the theory to such tasks as formalising the content of an existing set of regulations, designing a new set of regulations, or refining aspects of a computer system specification, with particular attention to the usefulness of the action component as a representational device. Points are made by reference to a simple example concerning rules in a car park. The second part of the paper covers three simple extensions: the representation of `permitted to bring about', a treatment of interpersonal control relations, and the ability to distinguish between being permitted to bring about a new state of affairs and being permitted to sustain a state of affairs that already exists.