Category Archives: Propositional Equation Reasoning Systems

Exemplary Proofs Using no more than the axioms and theorems recorded so far, it is possible to prove a multitude of much more complex theorems.  A number of all‑time favorites are linked below. Peirce’s Law Blog Series • (1) • … Continue reading →

Frequently Used Theorems (concl.) C3.  Dominant Form Theorem The third of the frequently used theorems of service to this survey is one Spencer Brown annotates as Consequence 3 (C3) or Integration.  A better mnemonic might be dominance and recession theorem (DART), but … Continue reading →

Frequently Used Theorems (cont.) C2.  Generation Theorem One theorem of frequent use goes under the nickname of the weed and seed theorem (WAST).  The proof is just an exercise in mathematical induction, once a suitable basis is laid down, and … Continue reading →

Frequently Used Theorems To familiarize ourselves with equational proofs in logical graphs let’s run though the proofs of a few basic theorems in the primary algebra. C1.  Double Negation Theorem The first theorem goes under the names of Consequence 1 (C1), … Continue reading →

Equational Inference All the initials have the form of equations.  This means the inference steps they license are reversible.  The proof annotation scheme employed below makes use of double bars to mark this fact, though it will often be left … Continue reading →

Logical Interpretation One way of assigning logical meaning to the initial equations is known as the entitative interpretation (En).  Under En, the axioms read as follows. Another way of assigning logical meaning to the initial equations is known as the existential interpretation … Continue reading →