The schematics presented in ReasonLines were developed for my Numerically Exceptive Logic: A Reduction of the Classical Syllogism (American University Series, Peter Lang, New York, 1991); that work proposes that traditional, categorical logic is implicitly numerical and demonstrates how it expands to cover any quantity whatever when this is made explicit.

However it turns out that these schematics which were initially devised to illustrate the expanded logic can also provide an intuitive and easy entrance into the traditional logic itself—and from there a seamless entrance to the expanded logic. ReasonLines is especially designed to make this material appropriate for precollege classroom use.

A tutorial* is provided in the Help page for teachers who might want to consider it, as well as for others who might want to master it on their own.

*Special thanks is due Gloria Howell Reeves for her help with this section.