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)

Input/output logics are abstract structures designed to represent conditional obligations and goals. In this paper we use them to study conditional permission. This perspective provides a clear separation of the familiar notion of negative permission from the more elusive one of positive permission. Moreover, it reveals that there are at least two kinds of positive permission. Although indistinguishable in the unconditional case, they are quite different in conditional contexts. One of them, which we call static positive permission, guides the citizen (...) and law enforcement authorities in the assessment of specific actions under current norms, and it behaves like a weakened obligation. Another, which we call dynamic positive permission, guides the legislator. It describes the limits on the prohibitions that may be introduced into a code, and under suitable conditions behaves like a strengthened negative permission. (shrink)

In a range of contexts, one comes across processes resembling inference, but where input propositions are not in general included among outputs, and the operation is not in any way reversible. Examples arise in contexts of conditional obligations, goals, ideals, preferences, actions, and beliefs. Our purpose is to develop a theory of such input/output operations. Four are singled out: simple-minded, basic (making intelligent use of disjunctive inputs), simple-minded reusable (in which outputs may be recycled as inputs), and basic reusable. They (...) are defined semantically and characterised by derivation rules, as well as in terms of relabeling procedures and modal operators. Their behaviour is studied on both semantic and syntactic levels. (shrink)

In this paper we present a Gentzen system for reasoning with contrary-to-duty obligations. The intuition behind the system is that a contrary-to-duty is a special kind of normative exception. The logical machinery to formalise this idea is taken from substructural logics and it is based on the definition of a new non-classical connective capturing the notion of reparational obligation. Then the system is tested against well-known contrary-to-duty paradoxes.

In this paper we propose an extension of Defeasible Logic to represent and compute different concepts of defeasible permission. In particular, we discuss some types of explicit permissive norms that work as exceptions to opposite obligations or encode permissive rights. Moreover, we show how strong permissions can be represented both with, and without introducing a new consequence relation for inferring conclusions from explicit permissive norms. Finally, we illustrate how a preference operator applicable to contrary-to-duty obligations can be combined with a (...) new operator representing ordered sequences of strong permissions. The logical system is studied from a computational standpoint and is shown to have linear computational complexity. (shrink)

In this paper we show how defeasible logic could formally account for the non-monotonic properties involved in motivational attitudes like intention and obligation. Usually, normal modal operators are used to represent such attitudes wherein classical logical consequence and the rule of necessitation comes into play, i.e., ⊢A/⊢ □A, that is from ⊢A derive ⊢ □A. This means that such formalisms are affected by the Logical Omniscience problem. We show that policy-based intentions exhibit non-monotonic behaviour which could be captured through a (...) non-monotonic system like defeasible logic. To this end we outline a defeasible logic of intention that specifies how modalities can be introduced and manipulated in a non-monotonic setting without giving rise to the problem of logical omniscience. In a similar way we show how to add deontic modalities defeasibly and how to integrate them with other motivational attitudes like beliefs and goals. Finally we show that the basic aspect of the BOID architecture is captured by this extended framework. (shrink)