Re: Dick Lipton & Ken Regan • (1) • (2)

(4)

Figure 4 shows the eight terms of the tacit extension as arcs, arrows, or directed edges in the venn diagram of the original proposition Each term of the tacit extension corresponds to an arc that starts from the cell where is true and ends in one of the eight cells of the venn diagram.

For ease of reference, here is the expansion of from the previous post:

Two examples suffice to convey the general idea of the extended venn diagram:

• The term is shown as a looped arc starting in the cell where is true and returning back to it. The differential factor corresponds to the fact that the arc crosses no logical feature boundaries from its source to its target.
• The term is shown as an arc going from the cell where is true to the cell where is true. The differential factor corresponds to the fact that the arc crosses all three logical feature boundaries from its source to its target.

To be continued …

Resources

• Differential Logic : Introduction
• Differential Propositional Calculus
• Differential Logic and Dynamic Systems