The formal definition of causality raises non trivial issues in the case of several agents acting together. Several action operators are defined in the semantics of a multi modal logic. The approach which is proposed is an extension to several agents of the "bringing it about” operators. A joint action operator is defined which holds the property of non monotonicity with respect to sets of agents. It is refined in a restricted joint operator for cases where several sets of agents cause in- dependently a state of affairs and it is extended to sets of agents who are acting indirectly. The formal definitions are evaluated with respect to several typical case studies and a detailed comparison with other approaches based on the STIT operators is presented.

Abstract normative systems allow to reason with norms even when their content is not detailed. In this paper, we propose a our preliminary results to visualize abstract normative systems, in such a way that we are able to reason with institutional facts, obligations and per- missions. Moreover, we detect meaningful patterns emerging from the proposed visualization, and we show how these patterns can be used to define commonly used reusable solutions.

Deontic logic has extensively been used to reason about what a player (or coalition) should do when confronted with several choices at its disposal while being aware of its opponents' possibilities. So far this line of research, inspired by Horty's utilitarian account of obligations, has been focused on interpreting coalitional oughts as rational choices, going on to characterizing game-theoretical solution concepts, such as Nash equilibria. With the present contribution we would like to extend the scope of this account to include contractual aspects of coalitional choices, arguing that deontic logic can be used as a comprehensive reasoning tool for the normative aspects of game theory.

Defeasible Deontic Logic is a simple and computationally efficient approach for the representation of normative reasoning. Traditionally defeasible logics are defined proof theoretically based on the proof conditions for the logic. While several logic programming, operational and argumentation semantics have been provided for defeasible logics, possible world semantics for (modal) defeasible logics remained elusive. In this paper we address this issue.

Parametrized logic programs, for which a syntax and natural declarative semantics have been recently defined, are very expressive logic programs under the stable model semantics (also usually called answer set programs) in which complex formulas of a given parameter logic are allowed to appear in the body and head of rules. The choice of the parameter logic depends largely on the domain of the problem to be modeled. In this paper we show how input-output logic can be embedded into parametrized logic programs, by choosing deontic logic as the parameter logic. This embedding not only shows how to recast input-out logic in this extension of answer set programming, but also sheds light on how to extend input-output logic with some interesting non-monotonic features.

In this paper I show that one cannot faithfully represent contrary-to-duty obligations in logics with sanction semantics. In order to do so I first provide a number of desiderata that a logic should satisfy in order to represent contrary-to-duty obligations using sanction semantics. I then show that no logic satisfying all desiderata can faithfully represent contrary-to-duty obligations. Finally I show that when dropping any one of the desiderata there is a logic that satisfies all others and can represent some contrary-to-duty obligations faithfully.

We consider a generalised Chisholm set of contrary to duty obligations (CTD) of the form Oq₀ and for i=0,..., n we have the CTD is q_i→Oq_i+1 and ¬q_i→O ¬q_i+1 and the facts ±q_j for some j∈ J ⊆{0,1,..., n+1}. Note that for the case of n = 1 and fact ¬q₀ we have the Chisholm paradox. We also allow for temporal sequencing of the q_i in the form that q_i + 1 may come temporally before or after q_i . We offer a representation of this problem in a variation of standard deontic logic that we call TSDL, with the standard temporal operator ◊ , the deontic obligation operator O, and the past operator Y for “yesterday”. This formalism is free of the above paradoxes. We provide an axiomatization and show it to be complete. The logic formalism enjoys the finite tree model property and hence is decidable.

The aim of this work is to provide a logical analysis of moral agency. Although this concept has been extensively studied in social philosophy and in social sciences, it has been far less studied in the field of deontic logic and multi-agent systems (MASs). We discuss different aspects of moral agency such as the distinction between desires and moral values and the concept of moral agent. All these concepts are formalized in a variant of STIT logic with explicit actions.

This paper proposes a new simulation approach for investigating phenomena such as norm emergence and internalization in large groups of learning agents. We define a probabilistic defeasible logic instantiating Dung's argumentation framework. Rules of this logic are attached to probabilities and describe the agents' minds and behaviour. We thus adopt the paradigm of reinforcement learning over this probability distribution to allow agents to adapt to their environment.

This paper studies the following interpretation of obligations: A person i ought to do A in a situation S just in case everything else i may (and can) do in S is consistent with A. In such a case A can be called the weakest permission that i has in S. We show that, under this interpretation, obligation and permission are not dual notions, and that it gives rise to an interesting interplay between deontic and alethic notions. We also discuss the logics adequacy w.r.t. the paradoxes of (classic) deontic logic and provide a sound and complete axiomatization for it. We finally show that practical, rational recommendations in games provide a natural, concrete application of such an understanding of obligations and permissions.

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.

In this article, we propose a Dynamic Logic of Propositional Control DL-PC in which the concept of `seeing to it that' (abbreviated stit) as studied by Belnap, Horty and others can be expressed; more precisely, we capture the concept of the so-called Chellas stit theory and the deliberatibe stit theory, as opposed to Belnap's original achievement stit. In this logic, the sentence `group G sees to it that φ' is defined in terms of dynamic operators: it is paraphrased as `group G is going to execute an action now such that whatever actions the agents outside G can execute at the same time, φ is true afterwards'. We also prove that the satisfiability problem is decidable. In the second part of the article we extend DL-PC with operators modeling normative concepts, resulting in a logic DL-PC<sup>Leg</sup>. In particular, we define the concepts of `legally seeing to it that' and `illegally seeing to it that'. We prove that the decidability result for DL-PC transfers to DL-PC^Leg.

We start our investigations from the deontic action model defined in multi-situation settings. Then we discuss the validity of formulas constructed in a language with a finite number of basic actions, parallel and sequential compositions of actions, a free choice operator and the standard deontic operators of obligation, strong permission and prohibition. The main achievements of the paper are definitions of metalogical counterparts of deontic operators and interpretation function of actions taking into account their terminating and non-terminating executions.

Norm change is one of the main challenges for normative reasoning. This discussion paper presents some novel informal and semi-formal ideas regarding the nature and formalization of norm change. First, we contrast the second-order nature of norm change with the first-order nature of obligation change. Second, we discuss how to change the normative system to avoid future obligations in the input/output logic framework, which explicitly distinguishes norms from obligations. Third, we present a semantical two dimensional view on change. Fourth, we illustrate norm change using automata changing automata. Fifth, we compare norm change with analogous mechanisms in non-normative contexts.