Category Archives: Discrete Dynamics

Formal Development (cont.) Before moving on, let’s unpack some of the assumptions, conventions, and implications involved in the array of concepts and notations introduced above. A universe of discourse qualified by the logical features is a set plus the set of … Continue reading →

Formal Development The preceding discussion outlined the ideas leading to the differential extension of propositional logic.  The next task is to lay out the concepts and terminology needed to describe various orders of differential propositional calculi. Elementary Notions Logical description … Continue reading →

Cactus Calculus Table 6 outlines a syntax for propositional calculus based on two types of logical connectives, both of variable -ary scope. A bracketed sequence of propositional expressions is taken to mean exactly one of the propositions is false, in … Continue reading →

Casual Introduction (concl.) Table 5 exhibits the rules of inference responsible for giving the differential proposition its meaning in practice. If the feature is interpreted as applying to an object in the universe of discourse then the differential feature may … Continue reading →

Casual Introduction (cont.) In Figure 3 we saw how the basis of description for the universe of discourse could be extended to a set of two qualities while the corresponding terms of description could be extended to an alphabet of … Continue reading →

Casual Introduction (cont.) Figure 3 returns to the situation in Figure 1, but this time interpolates a new quality specifically tailored to account for the relation between Figure 1 and Figure 2. The new quality, is marked as a differential quality on account of … Continue reading →

Casual Introduction (cont.) Now consider the situation represented by the venn diagram in Figure 2. Figure 2 differs from Figure 1 solely in the circumstance that the object is outside the region while the object is inside the region Nothing says our encountering … Continue reading →

A differential propositional calculus is a propositional calculus extended by a set of terms for describing aspects of change and difference, for example, processes taking place in a universe of discourse or transformations mapping a source universe to a target … Continue reading →

The most fundamental concept in cybernetics is that of “difference”, either that two things are recognisably different or that one thing has changed with time. W. Ross Ashby • An Introduction to Cybernetics Differential logic is the component of logic … Continue reading →

A reader once told me “venn diagrams are obsolete” and of course we all know how unwieldy they become as our universes of discourse expand beyond four or five dimensions.  Indeed, one of the first lessons I learned when I … Continue reading →