Documentation
Learn how to use LexMathematica to create algebraic legal contracts with mathematical precision.
How to Use the Builder
Define Parties
Add at least two parties to your contract. For a loan agreement, this typically includes a Lender and a Borrower. Each party is assigned an algebraic symbol (P₁, P₂, etc.).
Set Loan Parameters
Configure the core details: who pays whom, the amount, due date, and optional loan duration. The system automatically generates both human-readable prose and algebraic notation in real-time.
Select Axioms (Optional)
Add foundational legal principles (maxims) that govern your contract. Examples include Consensus (mutual agreement) and Fraud (prohibition of misrepresentation).
Review & Export
Verify all parameters are filled correctly. Download your contract as a professional PDF (dual-column layout) or as a .algex file containing just the algebraic expression.
Symbol Conventions Guide
| Prefix | Category | Examples |
|---|---|---|
O_ | Obligations | O_pay, O_lease, O_obligation, O_sale |
R_ | Rights | R_right, R_receive, R_own, R_remedy |
C_ | Conditions | C_condition, C_duration, C_if |
E_ | Entities | E_person, E_company |
V_ | Values | V_value, V_amount |
Op_ | Operators | Op_breach, Op_and |
M_ | Maxims (Axioms) | M_fraud, M_consensus |
Example Contract
Natural Language
LOAN AGREEMENT
The Borrower (John Smith) agrees to pay the Lender (Jane Doe) the sum of $10,000.00, due on December 31, 2026. The loan term begins March 15, 2026 and ends December 31, 2026.
This agreement is governed by the following principles: Consensus.
This agreement is entered into voluntarily by both parties and constitutes a binding legal obligation.
Algebraic Form
# Party Definitions
P₁ = E_person("John Smith")
P₂ = E_person("Jane Doe")
# Contract Equation
C = (P₁, P₂) ∧
O_pay(P₁, P₂, 10000, 2026-12-31) ∧
C_duration(2026-03-15, 2026-12-31) ∧
M_consensus
Mathematical Notation Guide
| Symbol | Name | Meaning |
|---|---|---|
∧ | AND (Conjunction) | Both conditions must be true |
→ | Implies | If A then B |
¬ | NOT (Negation) | The opposite of a condition |
∨ | OR (Disjunction) | At least one condition must be true |
P₁, P₂ | Party symbols | References to contract parties |
f(x, y) | Function notation | Term with parameters |
Frequently Asked Questions
Is this tool a substitute for legal advice?
No. LexMathematica is an experimental educational tool. The algebraic representations are for clarity and learning purposes only. Always consult a qualified attorney for legal matters.
Are the algebraic contracts legally binding?
The prose (human-readable) version of the contract remains the legally binding document. The algebraic form is a complementary representation that provides mathematical precision and clarity.
What types of contracts can I create?
Currently, Phase 1 focuses exclusively on Loan Agreements. Future phases will expand to include other contract types.
Where do the term definitions come from?
All 20 terms in our library are sourced from Black's Law Dictionary, 12th Edition (2024), the most authoritative legal dictionary in use today.
Is my contract data saved?
Contract drafts are stored in your browser session. We recommend downloading your completed contracts as PDF or .algex files for permanent storage.