What is The Mathematics of Natural Language?

The Mathematics of Natural Language is a formal procedure for extracting business rules from subject matter experts that starts with the creation of simple sentences and then answering a set of straightforward questions. The result is a set of fully normalized fact types that accurately state the involved business rules. This allows the subject matter experts to be accountable for the completed design.

The Mathematics of Natural Language procedure directly extracts knowledge from the subject matter experts without the analyst being the intermediate repository. Many times subject matter experts and/or their managers have stated that they did not know the MNL analyst was an expert in their subject area (radar, project management, etc.). They were not! The MNL procedure provides a mirror that directly reflects the subject matter experts’ knowledge back to them.

Greenfield Design

This is when The Mathematics of Natural Language is used at the start of a modeling project to define the business rules. Input materials come from any existing documentation and directly from subject matter experts. Experts challenge each other by disagreeing on answers to questions. Once the correct answers are determined the modeling effort continues until no more sentences are needed to describe the current subject area.

Verification and Validation

Design reviews are a major project milestone. The modeling team describes what the model contains and the subject matter experts and management listen and then make decisions about future efforts. The problem is that the reviewers cannot ‘read’ the model and the developers do not know where the model violates business rules. This results in repeating cycles of code development and model changes. The later the business rule violations are identified delays delivery targets and increases project cost.

Creating sentences from the model and having subject matter experts answer questions directed by The Mathematics of Natural Language procedure can identify business rule errors before development begins. Accountability for business rules can now be assigned to the subject matter experts and accountability for the implementation of the business rules can be assigned to the development team.

Legacy Data

Existing data contains corporate knowledge. The Mathematics of Natural Language procedures can be used to extract business rules from legacy data. Any dependencies that exist in the data can be determined. The procedure depends on true sentence instances, so bad data can complicate the effort. Some business rules can also be extracted from the data structure. The combination of these two efforts yields a preliminary set of business rules. Subject Matter Experts (some historical – if available – and some current) can then review and validate the rules. Identified bad data is removed from the data set as the new application is developed.


Experienced analysts are used to creating models from their existing external or corporate knowledge and obtaining additional knowledge from the current set of subject matter experts. This knowledge and their ability to express this knowledge, usually in a tool, is important to the ultimate success of the resulting design. The Mathematics of Natural Language extracts knowledge directly from the subject matter experts and does not depend as much on subject knowledge accumulated by experienced analysts.

The basic Mathematics of Natural Language course spans a full week. The course is for both experienced and novice analysts. For experienced analysts, unlearning may require extra effort and take some time.

The first three days are theory and practice against the theory. The fourth day is the “Challenge the MNL Expert” day where the participants bring in a part of a model (nothing proprietary or classified) and work with subject matter experts from the home office for an hour or so on a portion of the model to either verify and/or correct the model.

An example: A senior analyst brought in a model of petroleum pipelines between Texas and California. The mixing station where products are switched from one type to another had six variables in a defined key. After asking the subject matter expert the MNL questions it was established that there was an overlapping key in addition to the defined key. The expert analyst said he would have never determined that key. The subject matter expert stated that the result of violating that key would be the mixing of a large volume of product and the shutting down of the pipeline while it was cleaned up. The analyst was glad that was not experienced after installation.

The last day is devoted to review, testing, and possibly more model verification.

The Mathematics of Natural Language training can be through a public course or internally at a corporate site.