Filosofiska Notiser Årgång 6, Nr 1, 2019

This is a special issue on deontic logic.

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This paper presents axiomatic systems equivalent to Bengt Hansson's semantically defined dyadic deontic logics, DSDL1, DSDL2 and DSDL3. Each axiomatic system is demonstrated to be sound and complete with respect to the particular classes of models Hansson defined, and in that way to be equivalent to his logics. I also include another similar member of the family I call DSDL2.5 and provide an axiomatic system for it. These systems are further found to be decidable, and, although DSDL3 is compact, the three weaker ones are shown not to be.

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In this paper a retrospective is given on the development of deontic dynamic logic. It first reviews the basic system PDeL as introduced in 1988, with emphasis on conceptual issues and technical choices and properties. It then continues with later developments and applications by ourselves and related work by others. Thus we will see how contrary-to-duties and free choice permissions are treated, and how violations can be handled more expressively, including a way of dealing with red/green states and transitions.

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The Theory of Joining Systems, abbreviated TJS, is a general theory of representing for example legal and other normative systems as formal structures. It uses algebraic tools and a fundamental idea in this algebraic approach is the representation of a conditional norm as an ordered pair of concepts. Another fundamental idea is that the components in such a pair are concepts of different sorts. Conditional norms are thus links from for example descriptive to normative concepts and the result is the joining of two conceptual systems. However, there are often at least three kinds of concepts involved in many normative systems, viz. descriptive, normative and intermediate concepts. Intermediate concepts such as ‘being the owner’ and ‘being a citizen’ have descriptive grounds and normative consequences and can be said to be located intermediately between the system of grounds and the system of consequences. Intermediate concepts function as bridges (links, joinings) between concepts of different sorts. The aim of this paper is to further develop TJS and widen the range of application of the theory. It will be shown that the idea of norms as ordered pairs is flexible enough to handle nested implications and hypothetical consequences. Minimal joinings, which are important in TJS, are shown to be closely related to formal concepts in Formal Concept Analysis. TJS was developed for concepts of a special kind, namely conditions. In this paper a new model of TJS is developed, where the concepts are attributes and aspects, and the role of intermediate concepts in this model is discussed.

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This position paper aims to explore some preliminary suggestions to develop a theory of deontic modalities under a generic understanding. I suggest, for instance, that a sentence such as ‘Everyone ought to pay taxes’ is true just in case the generic (deontically relevant) individual pays taxes. Different degrees of genericity are explored, without assuming too much about a specific theory of genericity. I argue that such an analysis captures our intuitions about exceptions and the general character of deontic claims better than classical approaches based on possibleworld semantics and than defeasibility-based approaches, while remaining within a broadly deductive framework.

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I specify a very large class of logics with monadic and dyadic modal operators, primarily (but not exclusively) intended to represent monadic and dyadic agency in the tradition of Kanger, Pörn, Elgesem, etc. I explore logics both for pure monadic agency, pure dyadic agency, and mixed monadic-dyadic agency. Employing neighborhood semantic frames, but with an extra parameter governed by a modest algebraic structure, I prove determination theorems for all the consistent logics of those specified. I briefly present some motivation and rationales for some of the principles, but the main focus is on the framework and key meta-theorems.

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Makinson and van der Torre introduced a number of input/output (I/O) logics to reason about conditional norms. The key idea is to make obligations relative to a given set of conditional norms. The meaning of the normative concepts is, then, given in terms of a set of procedures yielding outputs for inputs. Using the same methodology, Stolpe has developed some more I/O logics to include systems in which the rule of weakening of the output (or principle of inheritance) is replaced by a rule of closure under logical equivalence. We extend Stolpe’s account in two directions. First, we show how to make it support reasoning by cases–a common form of reasoning. Second, we show how to inject a new (as we call it, aggregative) form of cumulative transitivity, which we think is more suitable for normative reasoning. The main outcomes of the paper are soundness and completeness theorems for the proposed systems with respect to their intended semantics.

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The purpose of this paper is to develop a set of quantified temporal alethic boulesic deontic systems. Every system in this class consists of five parts: a 'quantified' part, a temporal part, a modal part (an alethic part), a boulesic part and a deontic part. Separately, all these parts, except the boulesic part, have been studied extensively, but there are no systems in the literature that combine them all. So, all systems in this paper are new. The 'quantified part' consists of relational predicate logic with identity, where the quantifiers are, in effect, a kind of possibilist quantifiers that vary over every object in the domain. The alethic part includes two types of modal operators, for absolute and historical necessity and possibility. By 'boulesic logic', I mean the logic of the will; it treats 'willing' ('consenting', 'rejecting', 'indifference' and 'non-indifference') as a kind of modal operator. Deontic logic is the logic of norms; it deals with such concepts as ought, permitted and forbidden. I will investigate some possible relationships between these different parts, and consider various principles that include more than one type of logical expression. Every system is described both semantically and proof theoretically. I use a kind of T x W semantics to describe the systems semantically, and semantic tableaux to describe them proof theoretically. I prove that every tableau system in the paper is sound and complete with respect to its semantics. Finally, I consider some examples of valid and invalid sentences and arguments, show how one can use semantic tableaux to prove their validity or invalidity, and try to illustrate the philosophical usefulness of the systems developed in the paper.

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