In this brief note, we discuss efforts to develop a foundation in mathematics and logic for artificial intelligence (AI) applications used in legal drafting. Before reading further, you may ask: Why should I care about AI and legal drafting? The answer is that as we proceed into the 4th Industrial Revolution, the convergence of technologies, including mathematics, logic, AI, data science, and computer science, among others, is changing the way we practice law generally, and in particular the way we draft legal documents. We have a choice: We can embrace the new technologies and develop best practices, or we can watch others do so and risk being left behind and losing market share. For further discussion of this point, see “Using Artificial Intelligence Technology to Remain Competitive in a Fintech Environment,” published in the Journal of Equipment Lease Financing.
For True Artificial Intelligence in the Law, We Need a Firm Foundation in Mathematics
As a fundamental premise, we assume that we need a strong foundation in mathematics in order to build AI applications. After much research, I discovered that arguably the best mathematical model for a “mathematics of ideas” is a Boolean algebra, otherwise known as the algebra of sets.
A Boolean algebra includes a robust set of mathematical rules built upon the operations of union, intersection, and complementation. In fact, these operations establish a complete system of logic where union, intersection, and complementation correspond precisely to the logic operations of OR, AND, and NOT. We refer to this logic as the “Logic of Lattices.”
The results of my research are found in the book: Math Without Numbers: The Mathematics of Ideas - Vol.1 Foundations.
New Logic of the Law
A natural question to ask is: How does a “mathematics of ideas” relate to the study of logic as applied in the practice of law? Traditionally, lawyers have primarily used, knowingly or unknowing, the Categorical Syllogism of Classical Logic when framing legal arguments. See, Aldisert, Ruggero J., Logic for Lawyers – A Guide to Clear Legal Thinking, South Bend, IN, National Institute for Trial Advocacy 1997. The good news is that we can reconcile Classical Logic with the new Logic of Lattices. In fact, the Logic of Lattices subsumes Classical Logic and propositional logic, as well as predicate logic, and opens the door to the creation of a “New Logic of the Law” as described in the book: The New Logic of the Law Vol. 1: Building a Foundation for Artificial Intelligence in the Law.
Applying the New Logic of the Law to Legal Drafting
To illustrate the practical application of the “mathematics of ideas” and logic to the law, I wrote four brief articles where I convert various types of legal writing to a data format, where the ideas in the legal document are stored as fields of data in a Boolean Lattice:
- “Converting a Credit Agreement to a Data Format - Example: Definitions of Affiliate; Control; and Change of Control”
- “Converting a Lease Agreement to a Data Format - Example: Events of Default”
- “UCC: Classification of Collateral Under the Uniform Commercial Code”
- “Converting the Substantive Law to Data - Restatement of the Law Second, Contracts 2d: Sections 1 and 2”
Why Convert Contracts to Data?
Currently, most contract management software programs operate at the “clause” level. Converting contracts to data at the “idea” level (a “Data Contract”), creates a much greater level of detail or granularity. For example, we can create software programs that summarize, report on, and even provide preliminary advice at the idea level regarding the contents of contracts in a large portfolio. Practical uses include:
- Diligence relating to enforcement and litigation with respect to contracts in a large portfolio
- Diligence in M&A transactions involving large portfolios of contracts
- Regulatory compliance
- Amendments resulting from a change in law or policy
- Securitization diligence
Conclusion
We now have the foundation in mathematics and logic to build artificial intelligence software applications that mimic “how” we think. While computers cannot currently decide “what” to think, they can analyze large amounts of data faster than humans using the techniques of “how” we think.
For those attorneys who are not intimidated by mathematics and logic, a whole new world has opened for exploration. Opportunities abound for a new breed of lawyer that understands at least enough mathematics, logic, data science, and computer science to meet the technology experts half-way.