Category Archives: Gradient Descent

Special Classes of Propositions (cont.) Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general.  We can do this by recruiting our visual … Continue reading →

Special Classes of Propositions The full set of propositions contains a number of smaller classes deserving of special attention. A basic proposition in the universe of discourse is one of the propositions in the set   There are of course … Continue reading →

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 shows the rules of inference responsible for giving the differential quality its meaning in practice. cc: FB | Differential Logic • Laws of Form • Mathstodon • Academia.edu cc: Conceptual Graphs • Cybernetics • Structural Modeling … Continue reading →

Casual Introduction (cont.) Figure 3 extends the basis of description for the space to a set of two qualities and the corresponding terms of description to an alphabet of two symbols Any propositional calculus over two basic propositions allows for … 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. This new quality, is an example of a differential quality, since its … 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   So far, nothing … 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 →