ABSTRACT
Our focus now narrows to partially ordered value structures that are equipped with an absolute zero value and sum and negative operators (Sections 3.1–3.4). These are not the familiar numerical concepts of zero, sum, and negative, but generalizations of them that are applicable not just to numbers but to many other kinds of values. To visualize and model these concepts, we adopt procedures for constructing sums and negatives in Hasse diagrams and use them to detect fallacies (Sections 3.5–3.8). From the sum and negative operators, we then define a concept of subtraction (Section 3.9). Some of the chapter’s main results are summarized in the form of addition and subtraction tables (Section 3.10), and a final section (3.11) shows how these operations can be used to generate bounds that enable us indirectly to compare incomparable values.
