Monthly Archives: November 2024

Transforms Expanded over Ordinary and Differential Variables A first view of how the shift operator acts on the set of sixteen functions was provided by Table A3 in the previous post, expanding the expressions of over the set of ordinary variables. … Continue reading →

Transforms Expanded over Ordinary and Differential Variables As promised last time, in the next several posts we’ll extend our scope to the full set of boolean functions on two variables and examine how the differential operators and act on that … Continue reading →

Propositional Forms on Two Variables Tables A1 and A2 showed two ways of organizing the sixteen boolean functions or propositional forms on two variables, as expressed in several notations.  In future discussions the two Tables will be described as the … Continue reading →

Propositional Forms on Two Variables Table A2 arranges the propositional forms on two variables according to another plan, sorting propositions with similar shapes into seven subclasses.  Thereby hangs many a tale, to be told in time. Resources Logic Syllabus Survey … Continue reading →

Propositional Forms on Two Variables To broaden our experience with simple examples, let’s examine the sixteen functions of concrete type and abstract type   Our inquiry into the differential aspects of logical conjunction will pay dividends as we study the … Continue reading →

Differential Expansions of Propositions Panoptic View • Enlargement Maps The enlargement or shift operator exhibits a wealth of interesting and useful properties in its own right, so it pays to examine a few of the more salient features playing out … Continue reading →

Differential Expansions of Propositions Panoptic View • Difference Maps In the previous post we computed what is variously described as the difference map, the difference proposition, or the local proposition of the proposition at the point where and In the … Continue reading →

Differential Expansions of Propositions Worm’s Eye View Let’s run through the initial example again, keeping an eye on the meanings of the formulas which develop along the way.  We begin with a proposition or a boolean function whose venn diagram … Continue reading →

Differential Expansions of Propositions Bird’s Eye View An efficient calculus for the realm of logic represented by boolean functions and elementary propositions makes it feasible to compute the finite differences and the differentials of those functions and propositions. For example, … Continue reading →

Cactus Language for Propositional Logic Table 1 shows the cactus graphs, the corresponding cactus expressions, their logical meanings under the so‑called existential interpretation, and their translations into conventional notations for a sample of basic propositional forms. Table 1. Syntax and … Continue reading →