Besides pure declarative arguments, whose premises and conclusions are declaratives, and pure imperative arguments, whose premises and conclusions are imperatives, there are mixed-premise arguments, whose premises include both imperatives and declaratives, and cross-species arguments, whose premises are declaratives and whose conclusions are imperatives or vice versa. I propose a general definition of argument validity: an argument is valid exactly if, necessarily, every fact that sustains its premises also sustains its conclusion, where a fact sustains an imperative exactly if it favors (...) the satisfaction over the violation proposition of the imperative, and a fact sustains a declarative exactly if, necessarily, the declarative is true if the fact exists. I argue that this definition yields as special cases the standard definition of validity for pure declarative arguments and my previously defended definition of validity for pure imperative arguments, and that it yields intuitively acceptable results for mixed-premise and cross-species arguments. (shrink)

The paper is motivated by the need of accounting for the practical syllogism as a piece of defeasible reasoning. To meet the need, the paper first refers to ranking theory as an account of defeasible descriptive reasoning. It then argues that two kinds of ought need to be distinguished, purely normative and fact-regarding obligations. It continues arguing that both kinds of ought can be iteratively revised and should hence be represented by ranking functions, too, just as iteratively revisable beliefs. Its (...) central proposal will then be that the fact-regarding normative ranking function must be conceived as the sum of a purely normative ranking function and an epistemic ranking function. The distinctions defends this proposal with a comparative discussion of some critical examples and some other distinctions made in the literature. It gives a more rigorous justification of this proposal. Finally, it starts developing the logic of purely normative and of fact-regarding normative defeasible reasoning, points to the difficulties of completing the logic of the fact-regarding side, but reaches the initial aim of accounting for the defeasible nature of the practical syllogism. (shrink)

In this paper, we develop a formalisation of the main ideas of the work of Van de Poel on responsibility. Using the basic concepts through which the meanings of responsibility are defined, we construct a logic which enables to express sentences like “individual i is accountable for φ”, “individual i is blameworthy for φ” and “individual i has the obligation to see to it that φ”. This formalization clarifies the definitions of responsibility given by Van de Poel and highlights their (...) differences and similarities. It also helps to assess the consistency of the formalisation of responsibility, not only by showing that definitions are not inconsistent, but also by providing a formal demonstration of the relation between three main meanings of responsibility. The formal account can be used to derive new properties of the concepts. With the help of the formalisation, we detect the occurrence of the problem of many hands by defining a logical framework for reasoning about collective and individual responsibility. This logic extends the Coalition Epistemic Dynamic Logic by adding a notion of group knowledge, agent ability and knowing how to its semantics. (shrink)

The DAPRECO knowledge base is the main outcome of the interdisciplinary project bearing the same name. It is a repository of rules written in LegalRuleML, an XML formalism designed to be a standard for representing the semantic and logical content of legal documents. The rules represent the provisions of the General Data Protection Regulation, the new Regulation that is significantly affecting the digital market in the European Union and beyond. The DAPRECO knowledge base builds upon the Privacy Ontology, which provides (...) a model for the legal concepts involved in the GDPR, by adding a further layer of constraints in the form of if-then rules, referring either to standard first order logic implications or to deontic statements. If-then rules are formalized in reified Input/Output logic and then codified in LegalRuleML. Reified Input/Output logic is an application of standard Input/Output logic for legal reasoning, in which Input/Output logic is combined with the reification-based approach in Hobbs and Gordon. The DAPRECO knowledge base is then a case study for reified Input/Output logic, and it shows that the formalism indeed appears to be a good candidate to effectively formalize, via uniform and simple representations, complex linguistic/deontic phenomena that may be found in legal texts. To date, the DAPRECO knowledge base is the biggest knowledge base in LegalRuleML and Input/Output logic freely available online. (shrink)

The phenomenon of defeasibility has long been a central theme in legal literature. This essay aims to shed new light on that phenomenon by clarifying some fundamental conceptual issues. First, the most widespread definition of legal defeasibility is examined and criticized. The essay shows that such a definition is poorly constructed, inaccurate and generates many problems. Indeed, the definition hides the close relationship between legal defeasibility and legal interpretation. Second, this essay argues that no new definition is needed. I will (...) show that from an interpretative standpoint, there is nothing special about legal defeasibility. Contrary to what some authors maintain, no unique or privileged source of legal defeasibility exists, nor are there privileged arguments to justify it. Specifically, legal defeasibility refers to interpretative outcomes deriving from interpretative arguments that, on the one hand, are very different from one another, and, on the other, are often employed to justify different interpretative outcomes. In the legal field, the problems related to defeasibility have little in common with the problems that this label covers in other areas—such as logic or epistemology—and they are nothing but the well-known problems related to legal interpretation. In conclusion, this paper argues that as far as legal argumentation is concerned, the notion of legal defeasibility lacks explanatory power, and it should be abandoned. (shrink)

One of the popular albeit controversial ideas in the last century of moral philosophy is that what we ought to do is explained by our reasons. And one of the central features of reasons that accounts for their popularity among normative theorists is that they can conflict. But I argue that the fact that reasons conflict actually also poses two closely related problems for this popular idea in moral philosophy. The first problem is a generalization of a problem in deontic (...) logic concerning the existence of conflicting obligations. The second problem arises from a tension between the fact that reasons can conflict and a model of how reasons explain ‘ought’s that has been widely accepted. Having presented each of these problems, I develop a unified solution to them that is informed by results in both ethics and deontic logic. An important implication of this solution is that we must distinguish between derivative and nonderivative reasons and revise our conception how it is that reasons explain ‘ought’s. (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)

Over the course of more than two millennia the philosophical school of Mīmāṃsā has thoroughly analyzed normative statements. In this paper we approach a formalization of the deontic system which is applied but never explicitly discussed in Mīmāṃsā to resolve conflicts between deontic statements by giving preference to the more specific ones. We first extend with prohibitions and recommendations the non-normal deontic logic extracted in Ciabattoni et al. from Mīmāṃsā texts, obtaining a multimodal dyadic version of the deontic logic \. (...) Sequent calculus is then used to close a set of prima-facie injunctions under a restricted form of monotonicity, using specificity to avoid conflicts. We establish decidability and complexity results, and investigate the potential use of the resulting system for Mīmāṃsā philosophy and, more generally, for the formal interpretation of normative statements. (shrink)

According to the author, moral systems deal with our unconditional ultimate values. An ethical theory fixes the rules which allow us to distinguish good grounds and valid arguments in moral matters. The general attitude is decidedly antinaturalistic. Since value statements do not describe (perceptible) states of affairs they cannot have a truth value. Being ultimate, moral values give rise to commands which have to be obeyed most urgently, i.e., before any requirements of pudence.The author proposes his own hierarchy of values (...) which is supposed to correspond to the convictions of most normal people. The justification of a norm can only be given internally, i.e., relative to the accepted system of values. To the external question concerning the system as a whole there can be no absolute answer. Moral systems must influence the real human communicites; with respect to concrete situations within which an individual will have to take decisions a so-called system of defeasible deontic logic will be needed. The general conception is close to ``Pflichtethik'''' resting on the principle ``noblesse oblige''''. (shrink)

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. In this paper we propose a non-modal 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. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

A new deontic logic, Action Type Deontic Logic, is presented. To motivate this logic, a number of benchmark cases are shown, representing inferences a deontic logic should validate. Some of the benchmark cases are singled out for further comments and some formal approaches to deontic reasoning are evaluated with respect to the benchmark cases. After that follows an informal introduction to the ideas behind the formal semantics, focussing on the distinction between action types and action tokens. Then the syntax and (...) semantics of Action Type Deontic Logic is presented and it is shown to meet the benchmarks. Finally, possibilities for further research are indicated. In the appendix, decidability of the satisfiability of formulas is proved via a technique known from monadic First Order Logic. (shrink)

Normative systems have been advocated as an effective tool to regulate interaction in multi-agent systems. The use of deontic operators and the ability to represent defeasible information are known to be two fundamental ingredients to represent and reason about normative systems. In this paper, after introducing a framework that combines standard deontic logic and non-monotonic logic programming, deontic logic programs (DLP), we tackle the fundamental problem of equivalence between normative systems using a deontic extension of David Pearce’s Equilibrium Logic and (...) its monotonic basis, the logic of Here-and-There. We also show how deontic logic programs can be used to represent and reason about normative systems, and establish a strong connection with input-output logic. (shrink)

In the present work we illustrate how two sorts of defeasible reasoning that are fundamental in the normative domain, that is, reasoning about exceptions and reasoning about violations, can be simulated via monotonic propositional theories based on a bimodal language with primitive operators representing knowledge and obligation. The proposed theoretical framework paves the way to using native theorem provers for multimodal logic, such as MleanCoP, in order to automate normative reasoning.

Overview of fundamental work in deontic logic.