Guillaume Aucher

Dynamic context logic

Building on a simple modal logic of context, the paper presents a dynamic logic characterizing operations of contraction and expansion on theories. We investigate the mathematical properties of the logic, and show how it can capture some aspects of the dynamics of normative systems once they are viewed as logical theories.

Privacy policies with modal logic: the dynamic turn

Privacy policies are often defined in terms of permitted messages. Instead, in this paper we derive dynamically the permitted messages from static privacy policies defined in terms of permitted and obligatory knowledge. With this new approach, we do not have to specify the permissions and prohibitions of all message combinations explicitly. To specify and reason about such privacy policies, we extend a multi-modal logic introduced by Cuppens and Demolombe with update operators modeling the dynamics of both knowledge and privacy policies. We show also how to determine the obligatory messages, how to express epistemic norms, and how to check whether a situation is compliant with respect to a privacy policy. We axiomatize and prove the decidability of our logic.

DEL-sequents for regression and epistemic planning

Dynamic Epistemic Logic (DEL) deals with the representation and the study in a multi-agent setting of knowledge and belief change. It can express in a uniform way epistemic statements about: (i) what is true about an initial situation, (ii) what is true about an event occurring in this situation, (iii) what is true about the resulting situation after the event has occurred. We axiomatise within the DEL framework what we can infer about (ii) given (i) and (iii) and what we can infer about (i) given (ii) and (iii). Given three formulas , and describing respectively (i), (ii) and (iii), we also show how to build two formulas and which capture respectively all the information which can be inferred about (ii) from and , and all the information which can be inferred about (i) from and . We show how our results extend to modal logics other than . Finally, we generalise the classical language of dynamic epistemic logic, where one can reason only with complete specifications of events, in order to account also for incomplete description of events. In the companion paper (Aucher, 2011), we axiomatise what we can infer about (iii) given (i) and (ii), and show how to build a formula which captures all the information which can be inferred about (iii) from and .

Generalized DEL-Sequents

Let us consider a sequence of formulas providing partial information about an initial situation, about a set of events occurring sequentially in this situation, and about the resulting situation after the occurrence of each event. From this whole sequence, we want to infer more information, either about the initial situation, or about one of the events, or about the resulting situation after one of the events. Within the framework of Dynamic Epistemic Logic (DEL), we show that these different kinds of problems are all reducible to the problem of inferring what holds in the final situation after the occurrence of all the events. We then provide a tableau method deciding whether this kind of inference is valid. We implement it in LotrecScheme and show that these inference problems are NEXPTIME-complete. We extend our results to the cases where the accessibility relation is serial and reflexive and illustrate them with the coordinated attack problem.

BMS revisited

The insight of the BMS logical framework (proposed by Baltag, Moss and Solecki) is to represent how an event is perceived by several agents very similarly to the way one represents how a static situation is perceived by them: by means of a Kripke model. There are however some differences between the definitions of an epistemic model (representing the static situation) and an event model. In this paper we restore the symmetry. The resulting logical framework allows, unlike any other one, to express statements about ongoing events and to model the fact that our perception of events (and not only of the static situation) can also be updated due to other events. We axiomatize it and prove its decidability. Finally, we show that it embeds the BMS one if we add common belief operators.

Exploring the power of converse events

D ynamic epistemic logic as viewed by Baltag, Moss and Solecki (BMS) and propositional dynamic logic (PDL) offer different semantics of events. On the one hand, BMS adds dynamics to epistemic logic by introducing so-called event models as syntactic objects into the language. On the other hand, PDL has instead transition relations between possible worlds. This last approach allows to easily introduce converse events. In this paper we add epistemics to this, and call the resulting logic epistemic dynamic logic (EDL). We show that BMS can be translated into EDL thanks to this use of the converse operator : it enables us to translate the structure of the event model directly within a particular axiomatization of EDL, without having to refer to a particular epistemic event model in the language (as done in BMS).We show that EDL is more expressive and general than BMS and we characterize semantically and syntactically in EDL this embedding of BMS.

A dynamic logic for privacy compliance

Knowledge based privacy policies are more declarative than traditional action based ones, because they specify only what is permitted or forbidden to know, and leave the derivation of the permitted actions to a security monitor. This inference problem is already non trivial with a static privacy policy, and becomes challenging when privacy policies can change over time. We therefore introduce a dynamic modal logic that permits not only to reason about permitted and forbidden knowledge to derive the permitted actions, but also to represent explicitly the declarative privacy policies together with their dynamics. The logic can be used to check both regulatory and behavioral compliance, respectively by checking that the permissions and obligations set up by the security monitor of an organization are not in conflict with the privacy policies, and by checking that these obligations are indeed enforced.

Tableau Method and NEXPTIME-Completeness of DEL-Sequents

Dynamic Epistemic Logic (DEL) deals with the representation of situations in a multi-agent and dynamic setting. It can express in a uniform way statements about:(i)what is true about an initial situation (ii)what is true about an event occurring in this situation (iii)what is true about the resulting situation after the event has occurred. After proving that what we can infer about (ii) given (i) and (iii) and what we can infer about (i) given (ii) and (iii) are both reducible to what we can infer about (iii) given (i) and (ii), we provide a tableau method deciding whether such an inference is valid. We implement it in LOTRECscheme and show that this decision problem is NEXPTIME-complete. This contributes to the proof theory and the study of the computational complexity of DEL which have rather been neglected so far.

Prescriptive and descriptive obligations in dynamic epistemic deontic logic

Normative sentences can be used to change or to describe the normative system, known as prescriptive and descriptive obligations respectively. In applications of deontic logic it is important to distinguish these two uses of normative sentences. In this paper we show how they can be distinguished and analysed in a Dynamic Epistemic Deontic Logic.

Private announcement and belief expansion

AGM belief revision theory and the BMS framework of dynamic epistemic logic both deal with the formalization of belief change, the former in a single-agent setting and the latter in a multi-agent setting. In this article, we study the relation between these two formalisms.To be fair,we restrict our attention to the AGM operation of expansion since the original BMS framework does not allow for belief revision. The generalization of the AGM operation of revision to the multi-agent setting is dealt with in the companion paper [Aucher (2010, Logic Journal of the IGPL, 18, 530–558)]. Besides, because AGM theory follows the internal approach, instead of the original BMS framework we define and deal with its internal version. This allows us to show that the AGM operation of expansion can naturally be viewed in the multi-agent setting of the BMS framework as the operation of private announcement, which goes against the claims of [van Ditmarsch, van der Hoek and Kooi (2004, Advances in Modal Logic, 335–346)]. In parallel, we also provide conditions under which seriality of accessibility relations is preserved during an update, in the BMS framework as well as its internal version: it is a preliminary step towards the introduction of revision mechanisms into these frameworks.