The paradoxes of permission an action based solution

Abstract

The aim of this article is to construct a deontic logic in which the free choice postulate [11] would be consistent and all the implausible result mentioned in [5] will be blocked. To achieve this we first developed a new theory of action. Then we build a new deontic logic in which the deontic action operator and the deontic proposition operator are explicitly distinguished.1 Background and orientation Background discussionDeontic logic is a field of logic that lets one reason about deontic concepts, such as obligations and permissions. SDL (Standard Deontic Logic) is a modal logic established by von Wright [18] to reason about such concepts. This logic has had difficulties and limitations and became outdated with the emergence of the DSDL (Dyadic Standard Deontic Logic) in 1969 by Hansson [4]. Nevertheless, our original idea to create a logic of action in order to reason about permissions and obligations comes from the analysis of paradoxes encountered while reasoning in SDL (Section 3.2). Traditional SDL uses the KD possible world semantics. Its models have the form (S, R, o) where R ⊆ S 2 is the accessibility relation, o ∈ S is the actual world and we have that ∀x∃y(xRy) holds. Figure 1 is a typical situation in the semantics. (In this figure, an arrow from x to y indicates xRy, and the labels on the arrows will be referred later, readers should ignore them here).To evaluate a modal formula for example o ♦♦q, 1 one has to find two worlds a,b such that oRa ∧ aRb and b q. The point of view of SDL about this model is the following:1. View the model from above. The model (S, R, o) is static and we evaluate deontic formulas in it.2. The set of worlds I t = {x|tRx} is interpreted as a set of ideal worlds relative to t.

Completely and partially executable sequences of actions in deontic context

“…In the present paper we do not assume any form of determinism [the determinism may have the form of a functionality restriction (Castro and Maibaum 2009;Kulicki and Trypuz 2012) or the assumption of linearity of time which effects actions (Lorini and Herzig 2008)]. A similar model with no deterministic restrictions was used in Gabbay et al (2014).…”

Connecting Actions and States in Deontic Logic

“…We are interested in a deontic logic in which we can express norms of these two kinds. There are some works that tackle this problem such as [6,19] and recently [7], but we are not fully pleased with those solutions mostly because of the fact that they do not really separate the deontic properties of actions from the properties of states. An approach closer to ours is presented in [4,[13][14][15], where a two-sorted propositional language is used to deal separately with the properties of states and the properties of actions.…”