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Legal Content Topology

Topology is the mathematical study of properties of objects that are preserved through continuous deformations, such as stretching, twisting, compressing, and folding, without closing holes, opening holes, tearing, gluing, or passing through itself. For example, a circle is topologically equivalent to an ellipse (deformed by stretching), and a sphere is equivalent to an ellipsoid or a cube.

Two topologies that can generate different objects.

A topological space is a set equipped with a structure, called a “topology,” that allows the definition of continuous deformation of subspaces and, more generally, all types of continuity. A good definition of topology is expressed in the following mathematical joke: “Q: What is a topologist? A: Someone who cannot distinguish between a donut and a coffee cup.

The term “topology” also refers to a mathematical idea; informally, a topology describes how the elements of a set are spatially related to one another.

For legal engineering, we use this “informal” concept of topology to group different Templates according to their general properties and attributes.

For example, a defense petition has certain abstract topological properties regardless of the theme (cause of action) defended, the counterarguments or theses used, whether it was prepared for a judicial or administrative process, or whether the defense includes preliminary arguments, etc.

Understanding the topology of a Document Template allows the legal engineer to decompose the elements of its content into different layers of semantic content (input forms on one side and text, parameters, and variables on the other). This decomposition enables the reuse of these elements in various mapping, construction, and instantiation scenarios for a legal document, understanding what can be “stretched” or extended, “twisted” or modified, without violating the general properties of the document—its topology.

It is possible to describe and consider different topologies for BI dashboards, organization, flows, and case layouts, and, of course, Documents. Although the Looplex platform incorporates topology and structures across all these elements, this article focuses specifically on Document Topology, which deals more directly with content.

In Looplex’s semantic reference model, we consider three dimensions or topological properties of content:

For example:
(a) In defining the structure of a Legal Data Model, such as the qualification of a person, which includes name, domicile or headquarters, occupation or activity, identification document, etc., we might think of a star graph (star network) or a series of connected graphs.
(b) In mapping the interview and defining the construction nodes of a document, we observe that they resemble a tree-structured network (tree-structured network), with path dependency defined according to the construction.
(c) Elements of a Case or Dashboard views may be partially or fully connected (partially or fully connected network).
(d) A document negotiation and review flow can be seen as a ring of iterations cycling until the document is finalized (ring network).

Understanding the correct topology for each engineering use case ensures engineers avoid constructing documents with recursive loops. For example, a contract Template should not include clauses and their respective construction nodes interfering with each other recursively or bidirectionally. Instead, they should interact unidirectionally or hierarchically, based on a parent-child or predecessor-successor logic.

In other words, legal logic documents in Looplex must be organized as a series of DFA (deterministic finite automaton), as certain logical “violations” would render them NFA (nondeterministic finite automaton), which poses problems for processing intelligent documents.

Similarly, understanding the topology of a Document allows the use of pre-built Layouts for parts of the Template, customizing only what is truly different in that use case.