The aim of this paper is to introduce a system of dynamic deontic logic in which the main problems related to the de finition of deontic concepts, especially those emerging from a standard analysis of permission in terms of possibility of doing an action without incurring in a violation of the law, are solved. The basic idea is to introduce two crucial distinctions allowing us to differentiate (i) what is ideal with respect to a given code, which fixes the types (...) of action that are abstractly prescribed, and what is ideal with respect to the specific situation in which the agent acts, and (ii) the transitions associated with actions and the results of actions, which can obtain even without the action being performed. (shrink)

Philosophers like G.H. von Wright and D. Makinson have pointed to serious challenges regarding the foundations of deontic logic. In this paper, I suggest that to deal successfully with these challenges a reconsideration of the research program of the discipline is useful. Some problems that have troubled this particular field of logical study for decades may disappear or appear more tractable if we view them from the perspective of a language game introduced by D. Lewis involving three characters: the Master, (...) the Slave and the Kibitzer. The adoption of this perspective opens a natural approach to a new layout of the domain of deontic studies. I propose dividing deontic logic into six sub-areas which are distinguished by their focus on the different idioms typical of the individual players, by conceiving the language game as either being static or as dynamic and by the aims of the logical inquiry. What kind of insights the proposed perspective provides is illustrated by an analysis of the so-called Ross paradox—a problem that has troubled deontic logic since its origins and, though it was many times pronounced solved, still keeps coming back ‘alive and kicking’. (shrink)

The semantics for a deontic action logic based on Boolean algebra is extended with an interpretation of action expressions in terms of sets of alternative actions, intended as a way to model choice. This results in a non-classical interpretation of action expressions, while sentences not in the scope of deontic operators are kept classical. A deontic structure based on Simons’ supercover semantics is used to interpret permission and obligation. It is argued that these constructions provide ways to handle various problems (...) related to free choice permission. The main result is a sound and complete axiomatization of the semantics. (shrink)

The paper offers a logical characterisation of multi-step actions in the context of deontic notions of obligation, permission and prohibition. Deontic notions for sequentially composed actions are founded on deontic notions for one-step actions. The present work includes a formal study of situations where execution of a multi-step action has been unsuccessful and provides normative analysis of such actions.

In this paper we present a tableau system for deontic logics with the operator of explicit permission. By means of this system the decidability of the considered logics can be proved. We will sketch how these logics are semantically defined by means of relating semantics and how they provide a simple solution to the free choice permission problem. In short, these logics employ relating implication and a certain propositional constant. These two are in turn used to define deontic operators similarly (...) as in Andersonian-Kangerian reduction, which uses different intensional implications and constants. (shrink)

In this paper, we apply relating semantics to the widely discussed problem of free choice between permitted actions or situations in normative systems. Leaving aside contexts in which the free choice principle is obviously unacceptable or uncontroversially valid, we concentrate on free choice for explicit permissions. In order to construct a formal representation of explicit permissions, we introduce a special constant, $\texttt {permit}$, which is analogous to the constant $\texttt {violation}$ used in the Andersonian–Kangerian approach to deontic logic with respect (...) to prohibition and obligation. Consequently, we define a permission operator on the basis of the $\texttt {permit}$ constant and a relation of legitimization. The general idea is that $P \varphi $ is true if and only if $\texttt {permit}$ is true, which means that a permission is actually issued and $\varphi $ is legitimized by $\texttt {permit}$. The intuitive notion of legitimization is formally represented by an operator of relating implication: a non-classical implication that is semantically defined by adding a constraint to the classical meaning of implication to the effect that arguments are related by a special relation. The properties of this relation are based on an informal, intuitive meaning of legitimization and determine the properties of the permission operator. We show that the resulting permission operator possesses the free choice property and avoids certain unwanted consequences that follow from alternative approaches. (shrink)

This paper proposes a framework for formalising intuitions about the behaviour of imperative commands. It seeks to capture notions of satisfaction and coherence. Rules are proposed to express key aspects of the general logical behaviour of imperative constructions. A key objective is for the framework to allow patterns of behaviour to be described while avoiding making any commitments about how commands, and their satisfaction criteria, are to be interpreted. We consider the status of some conundrums of imperative logic in the (...) context of this proposal. (shrink)

The starting point of this work is the gap between two distinct traditions in information engineering: knowledge representation and data - driven modelling. The first tradition emphasizes logic as a tool for representing beliefs held by an agent. The second tradition claims that the main source of knowledge is made of observed data, and generally does not use logic as a modelling tool. However, the emergence of fuzzy logic has blurred the boundaries between these two traditions by putting forward fuzzy (...) rules as a Janus-faced tool that may represent knowledge, as well as approximate non-linear functions representing data. This paper lays bare logical foundations of data - driven reasoning whereby a set of formulas is understood as a set of observed facts rather than a set of beliefs. Several representation frameworks are considered from this point of view: classical logic, possibility theory, belief functions, epistemic logic, fuzzy rule-based systems. Mamdani's fuzzy rules are recovered as belonging to the data - driven view. In possibility theory a third set-function, different from possibility and necessity plays a key role in the data - driven view, and corresponds to a particular modality in epistemic logic. A bi-modal logic system is presented which handles both beliefs and observations, and for which a completeness theorem is given. Lastly, our results may shed new light in deontic logic and allow for a distinction between explicit and implicit permission that standard deontic modal logics do not often emphasize. (shrink)

It is well known that systems of action deontic logic emerging from a standard analysis of permission in terms of possibility of doing an action without incurring in a violation of the law are subject to paradoxes. In general, paradoxes are acknowledged as such if we have intuitions telling us that things should be different. The aim of this paper is to introduce a paradox-free deontic action system by (i) identifying the basic intuitions leading to the emergence of the paradoxes (...) and (ii) exploiting these intuitions in order to develop a consistent deontic framework, where it can be shown why some phenomena seem to be paradoxical and why they are not so if interpreted in a correct way. (shrink)