An algorithmic theory of Private Law: Possible applications of the Fourth Industrial Revolution to the legal field

An algorithmic theory of Private Law

INTRODUCTION

1- Algorithms as legal rules 

2- Definition of cyberspace 

3- The fourth Industrial Revolution 

FIRST SECTION: THE SUBJECTIVE RIGHT

4- Subjective rights within cyberspace 

a) Subject 

a.1.) The digital identity 

a.2) Co-ownership trees 

a.3) Power of disposal 

b) Object 

b.1) Tokens 

b.1.1) Fungible tokens 

b.1.2) Non fungible tokens ( NFTs ) 

c) Powers 

d) Representation of digital assets as states of an automaton

d.1.) The concept of a state machine 

d.2.) Databases as state machines 

SECOND SECTION: OBJECTIVE LAW

5- Digital objective law as a collection of algorithms

a) Algorithms 

b) Legal rules

c) Normative algorithms

d) Types of normative algorithms

Secundum legem algorithms

Praeter legem algorithms

6- Independent algorithmic legal systems

a) A short introduction to distributed protocol technology (DLT) and blockchain

a.1) Distributed protocols

a.2) Blockchain

b) The definition of an algorithmic legal system 

c) The principles of the algorithmic legal system 

c.1) Redundancy principle 

c.2) Decentralization principle 

c.3) Principle of anonymity 

c.4) Principle of constitutive registration 

c.5) Principle of celerity 

c.6) Chain-of-title principle 

c.7) Principle of unseizability 

c.8) Principle of formal publicity 

THIRD SECTION: LEGAL USES OF FINITE-STATE AUTOMATA

7.- Digital money 

8.- Legal registries

9.- Real rights ( iura in re ) 

9.1.- Definition of real rights 

9.2.- Land registries 

9.3.- A new type of Land Registry, of algorithmic nature 

9.3.a)- Centralized system 

9.3.b)- Decentralized system 

9.4.- The principles of algorithmic real estate publicity

a) Title by registration 

b) Formal consent and abstraction

c) Chain of title 

d) Validation 

e) Legality 

f) Formal publicity 

g) Priority 

h) Application principle 

9.5.- Transactions in the Registry

9.5.1.- Request by external users

a) Application for the transfer of a right

b) Land application and creation of the ownership right

c) Application for the creation of a right of enjoyment

d) Application for the creation of a mortgage

e) Application for a cautionary note 

g) Additional note

9.5.2.- Cryptographic validation of signatures 

9.5.3.- Validation of the transaction and issue of the record

a) Transmission of rights 

b) Creation of the ownership right

c) Creation of rights of enjoyment

d) Creation of mortgages

e) Cautionary note

f) Cancellation

9.6.- The plot and its modifications 

a) Plot application

b) Plot fusion

c) Plot aggregation 

d) Plot division 

 e) Plot segregation

FINAL CONSIDERATIONS

12.- The incipient algorithmization of Law

TECHNICAL APPENDIX

A.1. Finite state automata

A.2. An example of asymmetric cryptography: the RSA system 

A.3. Validation of electronic signatures: General outline of the procedure of the European standard ETSI EN 319 102-1 

A.4. Ethereum’s structure 

References

Copyright

INTRODUCTION

1- Algorithms as legal rules

Can an automaton reason like a human being? This question, which has troubled mankind for millenia, only began to be systematically studied in the 20th century. Although precedents can be found in Ramon Llull’s Ars Magna or in Gottfried Leibniz ’s calculus ratiocinator, it was David Hilbert who in a 1928 lecture posed the so-called Entscheidungsproblem (decision problem): What are the limits of formal logic? Can we create an algorithm that determines in a general way the validity or invalidity of a given proposition of first-order logic? The debate that immediately followed was extraordinary fruitful, and we owe to it disciplines such as Alonzo Church’s lambda calculus, the automata theories of Turing and Post or Gödel’s two teorems.

This paper aims to explore to what extent the development of the Theory of Automata, that took place mainly from the 1930’s onwards, can affect the field of Private Law. Specifically, we intend to explore questions such as the following: Can legal rules be expressed algorithmically? Is it possible to create an algorithm that interprets legal rules and is capable of applying them to a specific case? Can and individual right reside in cyberspace?

Through this entire work we will be unraveling the different possibilities that cyberspace offers for the representation of rights. And to what extent it is possible for the said rights to be altered by the automatic application of an algorithm, without any human intervention whatsoever.

The first section of this book is devoted to digital law and identity. A subjective right residing in cyberspace in called a digital right. Each digital right is structured in two elements: The subject (also called the holder) and the object, which are the powers or possibilities of action that the right grants to its holder. Within cyberspace, subjects are recognized by means of digital identity procedures, which ensure that the declarations of will issued telematically are invested by the notes of integrity, confidentiality and non-repudiation. Such systems include asymmetric cryptography, two-factor authentication and biometric data. All of them will be briefly analyzed in the corresponding section.

In the digital field, subjective rights are embodied in the machine state of an electric automaton (e.g. a computer, a bank database, a blockchain). Transmission of rights is thus equivalent to transitions (state modifications) of such an automaton.

The second section of the book refers to objective law, which is the set of legal norms in force in a given territory. A legal norm is a general mandate of behaviour imposed on the members of a certain community, which has a modus ponens logical structure composed of two elements: Factual assumption and legal consequence. Within the digital sphere, some algorithms have undoubtedly the characterization of a legal norm, since they have a modus ponens structure and impose deterministic rules of behavior on certain classes of automata: those that represent digital rights. The functions that regulate the state transtitions of blockchains (and consequently, the transmission of cryptocurrencies) or those algorithms residing in the servers of public administrations are therefore considered legal norms.

Normative algorithms can be of two types: dependent or independent. The former come from state authorities and their main function is to execute certain legal regulations of that state. The latter reside exclusively on a distributed ledger, and their execution does not require the collaboration of any state authority. We introduce the notion of independent algorithmic legal system, which is the system of independent algorithms residing on a given blockchain. It has a pyramidal structure and carries out its activity under a series of basic principles that we analyze in the corresponding paragraphs.

The third section proposes to use the scheme outlined in the previous sections to incorporate real estate and corporate traffic into cyberspace.

Under this new model, ownership and other rights over real estate are represented by the machine state of an automaton called the Land Registry. Any alteration of these rights must take place through transactions requested by third parties via an HTTP request. The automaton must verify the validity of the requested transaction and, if it is correct, it will perform a state transition, equivalent to a modification of rights. The Land Registry database can be centralized or decentralized. In the latter case, data related to real state rights would be stored in the form of non-fungible tokens (NFTs) in a private Ethereum network.

In the commercial and corporate field, we believe that it is possible also to represent commercial companies, foundations and other legal entities by means of the machine state of an automaton that we should call the Registry of Legal Entities. The modification of circumstances of these legal entities must also be articulated through transactions and state transitions requested by third parties. The Registry can be organized in a centralized or decentralized manner, in the same terms as indicated in the previous paragraph.

Before beginning the first section, the reader will be given an introduction to the concepts of cyberspace, which is the realm where digital rights reside, and Fourth Industrial Revolution, which is the set of techniques that have emerged to articulate the growing interaction between cyberspace and the physical world.

2- Definition of cyberspace

Although the term cyberspace appeared, in a loose sense, in the novels Burning in Chrome (1982) and Neuromancer (1984) by science fiction writer William Gibson, the word acquired its current meaning as interconnected cybernetic space in the mid-1990s, with the emergence of the World Wide Web. In my view, cyberspace could be defined as the domain of virtual reality created by the electric activity of computing systems. Just as the human brain and its neurons support the mental world, thoughts and ideas, the electrical activity of computer circuits shapes a virtual world called cyberspace that evolves over time according to predetermined rules.

From the point of view of information content, cyberspace could be subdivided in three different domains: Data, emergent structures and algorithms (executable code). We will analyze each of these areas separately:

The first of these is composed of digital information (data) stored in electrical computers through multiple memory systems, like flip-flop circuits (SRAM, registers and CPU cache), capacitors (DRAM memory cards), hard disk cylinders or the flash memory of USB devices. In all these cases, the information is discrete, not continuous, and is stored by creating stable electromagnetic fields over time. In the case of memories operated by capacitors or flash memory, the electric charge stored in them creates an electrostatic field by virtue of Maxwell’s first equation (Gauss’s law for the electric field), which only disappears when the capacitor (or the flash memory) is discharged again. In flip-flop circuits, characteristic of the internal memory of precessors, it is the electrical current of the circuit that remains stable over time. The circuit is switched on and off externally by transistors (formerly, by relays or vacuum valves). In hard drives, on the other hand, information is recorded by magnetizing the material of its cylinders. In all these cases, electromagnetic fields encode binary signals (off, on), which can be used to store natural numbers in base 2 and, in general, to perform logical-mathematical operations. It should be emphasized at this point that all the information stored in cyberspace is of a discrete nature. Although electrical computers that operated with continuous variables appeared at the beginning of the 20th century, the fact is that the presence of noise extraordinarily reduced their computational capacity. Therefore, in the 1930s, Claude Shannon and Konrad Zuse proposed the abandonment of analog computing and the adoption of a new model of discrete, digital computation based in binary arithmetic, boolean algebra and circuit switching. Their system, universally adopted from the 1950s onwards, proposed that mathematical operations should be performed by circuits controlled by other circuits through switches (relays, vacuum tubes, transistors), and always on discrete variables. It should be noted that the absence of continuous variables is, perhaps, the most important feature that currently distinguish cyberspace from physical space. Thus, in the realm of the visible Universe, the laws of the four fundamental forces of Physics are expressed in a continuous way, by means of differential equations, such as Schrödinger’s, Maxwell’s or Dirac’s ones. It is true that the description of theUniverse also involves discrete elements (e.g. atomic energy levels) related fundamentally with the field of Quantum Mechanics, but in the macroscopic realm, space and time are continuous and the laws governing the mechanics of bodies are differential in nature. In contrast, in cyberspace computation