Documentation

Numerical Constraints

Note: This documentation describes a feature of Blawx that is not yet working as intended. This documentation will be updated when that problem is resolved. In the meantime, please do not rely on the numerical constraint blocks.

In Blawx, the value of a number in an answer can be a specific value, or it can be a range of values. These ranges of values can be logically combined to generate new ranges of values. The method used for doing this is called numerical constraints.

The Numerical Constraint Block

The numerical constraint block is very much like the comparison block, except that it does not have a way to check for equality. It allows you to impose, as a requirement, that a variable is constrainted to be greater than, greater than or equal to, less than, or less than or equal to another numerical value.

This block works on integers and real numbers.

Taxation Without Representation

To show how numerical constraints can be used, we will create a codebase to find out whether people are ever subject to taxation without representation. We will start with an ontology in which there are people, and a person has four attributes:

  • age, which is a number
  • can vote, which is true or false
  • must pay tax, which is true or false
  • taxation without representation age, which is a number

The ontology looks like this:

Tax Without Rep Ontology

Now we will create rules using the numerical constraints block. The first will indicate that a person can vote if their age is at least 18.

Voting Age Rule

Next we will indicate that a person must pay tax if they are at least 18.

Must Pay Tax Rule

Lastly, we will say that a persons taxation without representation age is the age at which they must pay taxes, but are not entitled to vote.

TWR Rule

Now, we will tell Blawx to assume that people have ages, and ask Blawx what a person's taxation without representation age is.

TWR Query

The answer, we know, is the person must pay taxes and may not vote when they are at least 16 and not yet 18. The "not yet 18" comes from the negation of "can vote", and the "at least 16" comes from the "must pay taxes". Blawx can combine those two ranges of values into a new range, "at least 16 and less than 18".

And that is the answer that Blawx provides, indicating that a person can have a taxation without representation age that is at least 16 and less than 18.

TWR Answer