Cellular automata

Abstract

Propositional calculus with 3 variables. 256 different concepts. We studied the relation between concepts. The type of relation is an implication. We can see that simple rules are relate to complex rule by an implication. Rule 255 is relate to all others rules.

Basic concepts

Starting by these points p-list A and p-list B, where implication is defined as an inclusion of truth table, we can define the rule that a prepositional sentence A implies another prepositional sentence B if all the 1s of A truth table are also 1s in B truth table. So if A in 3 variable propositional sentences is represented by an octet, we can say that 00001001 implies 00011001 but not 00000001. Applying this concept at the rules of automata of the propositional calculus of three variables we can create a graph of the dependencies of the rules by each other. The implication between rules are visible at the following link. By the table 3 of Sheet1 we can see that rule1 implies rule5 that implies rule31 that implies rule95. At the following link the calcolus. At the following link the image of all implication between rules (d3 image)