🤖 AI

Understanding Privacy by Formalizing It

This paper proposes a formalization of the right to privacy as an epistemic right within the theory of normative positions, utilizing multi-modal logic to systematically specify various privacy theories and principles to guide algorithmic and AI development.

Original authors: Réka Markovich, Truls Pedersen, Marija Slavkovik

Published 2026-06-23

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Réka Markovich, Truls Pedersen, Marija Slavkovik

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Problem: Privacy is Too Vague

Imagine you are trying to build a robot that is supposed to be "polite." If you tell the robot, "Be polite," it will be confused. Does that mean it shouldn't interrupt? Should it say "please"? Should it not look at you? Without a specific definition, the robot can't know what to do.

The authors argue that privacy is exactly like that vague instruction. In our modern world, where Artificial Intelligence (AI) and computers process data faster than humans can think, we need to tell the machines exactly what "privacy" means. Currently, people argue about privacy using different definitions, and because these definitions aren't mathematically precise, we can't build algorithms to check if privacy is being violated.

The goal of this paper is to take the messy, fuzzy concept of privacy and turn it into a strict mathematical recipe (using logic) so computers can understand it.

The Toolkit: A "Legal Lego" Set

To build this recipe, the authors use a special type of logic called Multi-modal Logic. Think of this as a set of "Legal Legos" that allows them to snap together different types of rules.

They rely on a framework called the Theory of Normative Positions (based on the work of a legal scholar named Hohfeld). Imagine a game of chess. In chess, you don't just have "pieces"; you have specific powers and restrictions:

Claim-Right: You have a right to do something, and someone else has a duty to let you. (e.g., "I have a right to my castle; you have a duty not to enter.")
Privilege (Freedom): You are free to do something, and no one can stop you. (e.g., "I am free to walk on my own land.")
Power: You have the ability to change the rules for someone else. (e.g., "I can sell my land, which changes your ability to enter it.")
Immunity: You are protected from having the rules changed by others. (e.g., "No one can sell my land without my permission.")

The authors use these "Legos" to build different versions of privacy.

The Different "Flavors" of Privacy

The paper looks at how different famous thinkers have defined privacy and translates them into their logic language. Here are the main "flavors" they analyzed:

1. The "Do Not Disturb" Sign (Right to be Left Alone)

The Idea: Privacy means no one should know your secrets.
The Logic: This is translated as a rule where the state (the government) has a duty to make sure that for every person, there is a rule that no one else can know a specific piece of information about them.
The Catch: The authors realize that in the real world, we can't always be "alone." Sometimes, a doctor must know your health data, or a server must know your location to send you a package. So, the logic has to be flexible enough to say, "Okay, the doctor knows, but the doctor cannot tell the insurance company."

2. The "Control Knob" (Right to Control Access)

The Idea: Privacy isn't about being invisible; it's about being the boss of your own data. You decide who sees what.
The Logic: This is modeled as a "Power." You have the power to grant or deny access. Even if someone can see your data (like a waiter seeing your order), you have the right to control whether they can share that information with others.
Analogy: Imagine you are in a room with a glass wall. You can't stop people from seeing you (they can see), but you have a remote control. If you press a button, the glass turns opaque. If you don't, it stays clear. The logic defines who holds that remote.

3. The "Context Switch" (Contextual Integrity)

The Idea: It's okay to share your HIV status with a dating app, but not with your boss. Privacy depends on the situation.
The Logic: The authors try to write rules that say, "Information is private unless it is shared for a specific purpose in a specific context." If the data jumps from the "dating context" to the "job interview context," the logic flags it as a violation.

4. The "Transparency Mirror" (Right to Know)

The Idea: Sometimes, privacy isn't about hiding; it's about knowing who is looking at you.
The Logic: This is a rule that says, "If someone accesses your data, you have a right to know that they did." It's like having a security camera that not only records the thief but also sends you a text message saying, "Someone just looked at your diary."

Why Does This Matter?

The authors aren't trying to solve every privacy problem right now. Instead, they are building the blueprint.

Before this paper: We have different people saying, "Privacy is X," "Privacy is Y," and "Privacy is Z." They are arguing past each other because they are using different definitions.
After this paper: We can take Definition X and Definition Y and run them through the same mathematical logic machine. The machine can tell us: "These two definitions are actually the same," or "These two definitions contradict each other."

The Bottom Line

This paper is a foundational step. It says, "We cannot build a fair AI system for privacy until we can write the rules of privacy in a language that computers can read without getting confused."

They have created a "dictionary" and a "grammar" for privacy rights. By turning abstract ideas like "freedom from scrutiny" into strict logical formulas (like Oa→b...), they hope to eventually allow computers to automatically check if a new technology or law is actually respecting privacy, or if it is secretly breaking the rules.

In short: They are turning the concept of "Privacy" from a fuzzy feeling into a precise set of instructions that a computer can follow.

Technical Summary: Understanding Privacy By Formalizing It

Problem Statement
The paper addresses the challenge of translating the concept of privacy into a format suitable for algorithmic analysis and implementation, particularly within the context of Artificial Intelligence (AI) and digitization. While there is a broad consensus on the need to protect privacy, the concept itself lacks a unified definition and is subject to diverse interpretations in law, social science, and computer science. Current AI capabilities, such as pattern recognition in data, can erode privacy by inferring information not explicitly shared, yet existing regulatory frameworks often rely on vague or conflicting conceptualizations. The authors argue that to impose meaningful algorithmic restrictions or self-regulatory mechanisms, the right to privacy must be formally specified. Without such precision, it is impossible to compare different privacy conceptualizations or determine if they refer to the same underlying ideas.

Methodology
The authors employ a formal logical approach to characterize different theories of privacy. The methodology consists of three main components:

Theoretical Framework: The paper utilizes the Theory of Normative Positions, rooted in W.N. Hohfeld's analysis of rights. This framework distinguishes between four atomic types of rights and their correlatives: claim-rights (and duties), privileges (and no-claims), powers (and liabilities), and immunities (and disabilities). The authors extend this to multital rights (rights held against everyone) and molecular rights (complex combinations of atomic positions). They specifically focus on epistemic rights, defined as rights concerning the distribution and accessibility of epistemic goods (knowledge/information).
Logical Formalism: A multi-modal logic is constructed to represent these rights. The language $L$ $L$ extends propositional logic with four modalities:
- Agency ( $E_a$ ): "Agent $a$ sees to it that..." (modeled via neighborhood semantics).
- Directed Obligation ( $O_{a \to b}$ ): "Agent $a$ has a duty towards $b$ that..." (standard deontic logic, axiom D).
- Epistemic Knowledge ( $K_a$ ): "Agent $a$ knows that..." (standard S5 knowledge logic).
- Alethic Necessity ( $\Box$ ): "It is necessary that..." (S5).
  The logic avoids strong assumptions about action (using weak action logic) to allow for broad interpretation of "actions" while maintaining standard properties for knowledge and necessity.
Formalization Process: The authors map specific privacy definitions and theories onto this logical language. They translate concepts such as "the right to be left alone," "control over information," and "contextual integrity" into formulas involving combinations of the modalities above.

Key Contributions and Results
The paper provides initial formal representations of several prominent privacy approaches, demonstrating how they translate into distinct normative positions:

Right to be Left Alone / Control: The authors formalize the "right to be let alone" (Warren and Brandeis) and Westin's "control" definition. They distinguish between:
- Ought-to-be formulas (e.g., $O\Diamond E_a \neg K_b \phi$ ) which state a desired state of affairs.
- Ought-to-do formulas involving specific agents (e.g., the state $s$ imposing a duty on a company $c$ to enable agent $a$ to prevent $b$ from knowing $\phi$ ).
- They formalize multital freedoms (the absence of an obligation to disclose) and immunities (the inability of others to change this freedom), showing how privacy can be a complex molecular right rather than a single atomic claim.
Contextual Integrity and Unattainable Privacy: Addressing Nissenbaum's critique that absolute control is impossible, the paper formalizes scenarios where access is inevitable. In these cases, privacy is redefined as the right to control further dissemination or the right to prevent those who necessarily know the information from scrutinizing or commenting on it (e.g., $E_a O_{b \to a} \neg E_b K_a \phi$ ).
Transparency: The paper formalizes the "right to transparency" (knowing whether others have access) using a "knowing whether" operator to avoid logical paradoxes, ensuring the duty-bearer must inform the right-holder about access status.
Enforcement: The authors include formalizations for the power to enforce rights. They model the transition from a violation of a privacy duty to a new claim-right against the judiciary to enforce the original duty or provide compensation.

Significance and Claims
The paper claims its primary contribution is the use of logic specifications as both a goal and a method to clarify the distinctions between different concepts of privacy. By formalizing these concepts within the Theory of Normative Positions, the authors aim to:

Make privacy specifications accessible for algorithmic analysis, enabling the construction of algorithms that can detect privacy violations.
Provide a common ground for comparing different privacy conceptualizations (e.g., in law vs. computer science) to determine if they are equivalent or distinct.
Lay the groundwork for implementable specifications of privacy rights, serving as a basis for "policy-as-code" and "law-as-code" initiatives in AI and Multi-Agent Systems (MAS).

The authors explicitly state that they do not provide meta-logical results (such as completeness or decidability proofs) but rather focus on the formal conceptual analysis of how different privacy theories map to normative positions. They acknowledge that this is an initial step, with future work planned to address the defeasibility of these rights and to test these formalisms using frameworks like LogiKEy.