In this work we provide an analysis of some issues arising with geometrical representations of a family of deontic and potestative relations that can be classified as Hohfeldian modalities, traditionally illustrated on two diagrams, the Hohfeldian squares. Our main target is the lack of symmetry to be found in various formal accounts by drawing analogies with the square of opposition for alethic modalities. We argue that one should rather rely on an analogy with the alethic hexagon of opposition and exploit (...) the notions of contingency and absoluteness in order to restore the symmetry of Hohfeldian modalities in accordance to the diagrams presented by Hohfeld. Interestingly, the investigation unveils three potestative squares defined at different levels of granularity (force, outcome and change) and allows us to further elaborate on the connections between deontic and potestative relations. (shrink)

The conditional,if an agent did something, then the agent could have done otherwise, is analyzed usingstit theory, which is a logic of seeing to it that based on agents making choices in the context of branching time. The truth of the conditional is found to be a subtle matter that depends on how it is interpreted (e.g., on what otherwise refers to, and on the difference between could and might) and also on whether or not there are busy choosers that (...) can make infinitely many choices in a finite span of time. (shrink)

Deontic logic as a way of formally reasoning about norms, an important area in AI and law, has traditionally concerned itself about formalising provisions of general statutes. Despite the long history of deontic logic, given the wide scope of the logic, it is difficult, if not impossible, to formalise all these notions in a single formalism, and there are still ongoing debates on appropriate semantics for deontic modalities in different contexts. In this paper, we restrict our attention to contracts between (...) interactive parties, which are both general enough to be an interesting object of study but specific enough so as to narrow down the debates regarding the meaning of modalities, and present a formalism for reasoning about them. (shrink)

The volume analyses and develops David Makinson’s efforts to make classical logic useful outside its most obvious application areas. The book contains chapters that analyse, appraise, or reshape Makinson’s work and chapters that develop themes emerging from his contributions. These are grouped into major areas to which Makinsons has made highly influential contributions and the volume in its entirety is divided into four sections, each devoted to a particular area of logic: belief change, uncertain reasoning, normative systems and the resources (...) of classical logic. Among the contributions included in the volume, one chapter focuses on the “inferential preferential method”, i.e. the combined use of classical logic and mechanisms of preference and choice and provides examples from Makinson’s work in non-monotonic and defeasible reasoning and belief revision. One chapter offers a short autobiography by Makinson which details his discovery of modern logic, his travels across continents and reveals his intellectual encounters and inspirations. The chapter also contains an unusually explicit statement on his views on the role of logic in philosophy. (shrink)

We shall introduce a set of fundamental legal concepts, providing a definition of each of them. This set will include, besides the usual deontic modalities (obligation, prohibition and permission), the following notions: obligative rights (rights related to other’s obligations), permissive rights, erga-omnes rights, normative conditionals, liability rights, different kinds of legal powers, potestative rights (rights to produce legal results), result-declarations (acts intended to produce legal determinations), and sources of the law.

This paper discusses the place of philosophical naturalism in the philosophy of law, with special reference to Scandinavian Realism. Hägerström originated a non-cognitivist analysis of certain fundamental legal concepts, but he also proposed an error theory. The two approaches are incompatible, but were not always clearly distinguished. Among his followers, Olivecrona and Ross gradually abandoned the latter, at least from the late 1940s. Many accounts of their views are unclear, because the presence of these two kinds of analysis, their incompatibility, (...) and the gradual abandonment of one, has often been overlooked. A corollary of the discussion is that there are some important corrigenda in the entry “Naturalism in legal philosophy” in the Stanford Encyclopedia of Philosophy. (shrink)

Hohfeld’s analysis on the different types of rights and duties is highly influential in analytical legal theory, and it is considered as a fundamental theory in AI&Law and normative multi-agent systems. Yet a century later, the formalization of this theory remains, in various ways, unresolved. In this paper I provide a formal analysis of how the working of a system containing Hohfeldian rights and duties can be delineated. This formalization starts from using the same tools as the classical ones by (...) Kanger and Lindahl used, but instead of focusing on the algebraic features of rights and duties, it aims at providing a comprehensive analysis of what these rights and duties actually are and how they behave and at saying something substantial on Power too—maintaining all along the Hohfeldian intentions that these rights and duties are sui generis and inherently relational. (shrink)

This paper investigates the semantic treatment of conditional obligation, explicit permission (often called positive permission), and prohibition based on models with agents and branched time. In such models branches (rather than moments) are taken as basic, and the branching provides a way to represent the indeterminism which is normally presupposed by talk of free will, responsibility, action and ability. Careful treatment of the relation between ability and responsibility avoids many common problems with accounts of conditional obligation. Recognition of the generality (...) often involved in conditional obligations makes possible a sensitive way of expressing some kinds of general prohibitions, which in turn makes it possible to account for the special role of explicit permission. (shrink)

We discuss similarities and residual differences, within the general semantic framework of minimality, between defeasible inference, belief revision, counterfactual conditionals, updating — and also conditional obligation in deontic logic. Our purpose is not to establish new results, but to bring together existing material to form a clear overall picture.

I present a variant of with time, called, interpreted in standard Kripke semantics. On the syntactic level, is nothing but the extension of atemporal individual by: the future tense and past tense operators, and the operator of group agency for the grand coalition. A sound and complete axiomatisation for is given. Moreover, it is shown that supports reasoning about interesting normative concepts such as the concepts of achievement obligation and commitment.

The concept of legal power is important in the law since, with regard to actions having legal effect, the “exercise of legal power” delimits those actions for which manifestation of intention to achieve a legal effect is essential for the effect to ensue. The paper proposes a definition that captures this feature of legal power and marks it off from “direct effect,” as well as from permissibility and practical ability to achieve the legal effect. This analysis of power is limited (...) to the “immediate” legal power of a physical person characterized by the power-holder achieving a legal result by the power-holder's own behaviour. It is argued that in the literature on power the concept of legal power is frequently construed in such a way that it becomes either too broad or too narrow. (shrink)

The paper tackles the problem of the relation between rights and obligations. Two examples of situations in which such a relation occurs are discussed. One concerns the abortion regulations in Polish law, the other one—a clash between freedom of expression and freedom of enterprise occurring in the context of discrimination. The examples are analysed and formalised using labelled transition systems in the \ framework. Rights are introduced to the system as procedures allowing for their fulfilment. Obligations are based on the (...) requirement of cooperation in the realisation of the goals of the agent that has a right. If the right of an agent cannot be fulfilled without an action of another agent, then that action is obligatory for that agent. If there are many potential contributors who are individually allowed to refuse, then the last of them is obliged to help when all the others have already refused. By means of formalisation this account of the relation under consideration is precisely expressed and shown consistent. (shrink)

Two areas of importance for agents and multiagent systems are investigated: design of agent programming languages, and design of agent communication languages. The paper contributes in the above mentioned areas by demonstrating improved or novel applications for deontic logic and normative reasoning. Examples are taken from computer-supported cooperative work, and electronic commerce.

We extend the monotonic and regular modal logics to the multi-modal cue, and give semantical characterization w.r.t. a semantics of minimal frames. For this we introduce a calculus over neighbourhoods and we obtain simpler conditions than those from the literature.

This paper provides a computational framework, based on defeasible logic, to capture some aspects of institutional agency. Our background is Kanger-Lindahl-Pörn account of organised interaction, which describes this interaction within a multi-modal logical setting. This work focuses in particular on the notions of counts-as link and on those of attempt and of personal and direct action to realise states of affairs. We show how standard defeasible logic (DL) can be extended to represent these concepts: the resulting system preserves some basic (...) properties commonly attributed to them. In addition, the framework enjoys nice computational properties, as it turns out that the extension of any theory can be computed in time linear to the size of the theory itself. (shrink)

This paper arose out of the 2017 international conference on AI and law doctoral consortium. There were five students who presented their Ph.D. work, and each of them has contributed a section to this paper. The paper offers a view of what topics are currently engaging students, and shows the diversity of their interests and influences.

We propose a new formalization of legal competences, and in particular for the Hohfeldian categories of power and immunity, through a deontic reinterpretation of dynamic epistemic logic. We argue that this logic explicitly captures the norm-changing character of legal competences while providing a sophisticated reduction of the latter to static normative positions. The logic is completely axiomatizable, and we apply it to a concrete case in German contract law to illustrate that it can capture the distinction between legal ability and (...) legal permissibility. (shrink)

Practical methods are introduced for the construction of definitions, both for philosophical purposes and for uses in other disciplines. The structural and contentual requirements on definitions are clarified. It is emphasized that the development of a definition should begin with careful choice of a primary definiendum, followed by the selection of appropriate variables for the definition. Two methods are proposed for the construction of the definiens, the case list method and the method of successive improvements. Four classes of concepts are (...) discussed that are particularly difficult to define: vague concepts, value-laden concepts, controversial concepts, and inconsistent concepts. (shrink)

Modern belief revision theory is based to a large extent on partial meet contraction that was introduced in the seminal article by Carlos Alchourrón, Peter Gärdenfors, and David Makinson that appeared in 1985. In the same year, Alchourrón and Makinson published a significantly different approach to the same problem, called safe contraction. Since then, safe contraction has received much less attention than partial meet contraction. The present paper summarizes the current state of knowledge on safe contraction, provides some new results (...) and offers a list of unsolved problems that are in need of investigation. (shrink)

This paper aims to explore two objections raised against Bulygin’s second approach to the definition of the nature of legal power-conferring rules. According to the first objection, such an account is vague about what is defined by legal power-conferring rules qua constitutive rules. I maintain that this vagueness is rooted in the lack of a suitable definition of legal power. I shall be arguing for the reduction of the complexity of the definientia by defining legal power as a species of (...) competence. According to the second objection, this non-reductive approach cannot explain the normativity of this kind of rules. Against this approach, it argues that legal powerconferring rules perform a deontic and a definitional function as constitutive rules of legal practice. (shrink)