REASONING ABOUT EPISTEMIC RIGHTS

This thesis contributes to two underexplored aspects of deontic logic: the interaction between deontic and epistemic concepts, and the logical analysis of rights. The general research question is to formalize and reason about epistemic rights (the right to know) using logical techniques. As a theoretical background, we rely on the theory of normative positions. Applying this theory to epistemic rights allows us to distinguish four different meanings of the term ``the right to know'': the privilege, the claim, the power, and the immunity to know. In practice, the right to know may refer to any of the four meanings or their combinations. This thesis develops logical frameworks to reason about the different meanings of the right to know, except for the immunity to know.

In the theory of normative positions, rights (and duties) are understood as possible normative relations between pairs of agents. To illustrate the different meanings of the right to know, consider two agents $x$ and $y$. When we say that $x$ has the privilege to know $\phi$ against $y$, this means that $x$ has no duty (toward $y$) not to know $\phi$, or equivalently, $x$ is permitted to know $\phi$ against $y$. Thus, the notion of privilege to know corresponds to epistemic permission. Chapter 2 presents a family of logics to reason about epistemic permission and obligation. In doing so, we address two challenges: \r{A}qvist's paradox of epistemic obligation and the relation between epistemic obligation and factuality. This is achieved by employing two-dimensional semantics instead of standard Kripke semantics. We completely axiomatize the resulting logics and show that their satisfiability problems are all PSPACE-complete, no more complex than that of standard deontic logic. Finally, we discuss the possibility of expressing the notion of knowledge-based obligation in the extensions of our framework.

Chapter 3 focuses on the claim-right to know. Intuitively, ``$x$ has the claim-right to know $\phi$ against $y$'' means that $y$ has a duty toward $x$ (to see to it) that $x$ knows $\phi$. In the context of information exchange (communication), this is simply understood as that $y$ has the duty to inform $x$ that $\phi$. We consider the problem of formalizing the obligatory and permitted announcements in the context of information security, such as privacy policy compliance. In such a context, the main change is to reason about the receiver's knowledge. The two logics (LPOA and DLPOA) developed in Chapter 3 addressed this challenge, and, furthermore, we distinguish different notions of permitted and obligatory announcements. The main technical contribution in Chapter 3 is the sound and complete axiomatizations of LPOA and DLPOA. We also discussed the extension to the multiagent case.

Chapter 4 analyzes the power-right to know. In a two-agent setting, $x$'s power right to know $\phi$ against $y$ means that $x$ has the power to impose a duty on $y$ to inform $x$ of $\phi$. In practice, to impose such a duty on the counterparty, the right-holder just makes a request to obtain the information $\phi$ or, alternatively, asks the question whether $\phi$. This is described in the GDPR as the right of access. The logic LRK developed in Chapter 4 can be used to reason about the power to know, the obligatory announcements, and the dynamics of questions and public announcements. The logic LRK has been completely axiomatized.

Chapter 5 presents applications of the logical frameworks developed in this thesis in AI and computer science, using four GDPR-related examples (including two real legal cases). Finally, Chapter 6 reviews the results of the thesis and identifies 10 directions for future research.