Category Archives: Computational Complexity

Differential Propositions • Tangent Spaces The tangent space to at one of its points sometimes written takes the form   Strictly speaking, the name cotangent space is probably more correct for this construction but since we take up spaces and … Continue reading →

Differential Propositions • Qualitative Analogues of Differential Equations The differential extension of a universe of discourse is constructed by extending its initial alphabet to include a set of symbols for differential features, or basic changes capable of occurring in   … Continue reading →

Fire over water: The image of the condition before transition. Thus the superior man is careful In the differentiation of things, So that each finds its place. — I Ching ䷿ Hexagram 64 Differential Extension of Propositional Calculus This much … Continue reading →

Re: Differential Propositional Calculus • Discussion 1 Re: Reinaldo Cristo • Comment 1 RC: We can say that emptiness came first, as it is the basis of the invention of mathematics, our perception, and numerical base 2.  Do you agree … Continue reading →

Differential Extensions Table 11 summarizes the notations needed to describe the first order differential extensions of propositional calculi in a systematic manner. Resources Logic Syllabus Differential Propositional Calculus • Part 1 • Part 2 Differential Logic and Dynamic Systems Differential Extension … Continue reading →

Differential Extensions An initial universe of discourse supplies the groundwork for any number of further extensions, beginning with the first order differential extension   The construction of can be described in the following stages. The initial alphabet is extended by … Continue reading →

Special Classes of Propositions (concl.) Last and literally least in extent, we examine the family of singular propositions in a 3‑dimensional universe of discourse. In our model of propositions as mappings from a universe of discourse to a set of … Continue reading →

Special Classes of Propositions (cont.) Next we take up the family of positive propositions and follow the same plan as before, tracing the rule of their formation in the case of a 3‑dimensional universe of discourse. Positive Propositions The positive … Continue reading →

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 →