The logical operators of conjunction, disjunction and negation as expressed in pattern logic.
These can be used to derive additional operators such as Material Implication and shed light on the meaning of DeMorgan's Laws
Given any two logical occasions, we can represent their conjunction via two occasions of predication which establish what is commonly present-in both. The occasion at the center is representative of "alpha and beta".
Given any two logical occasions, we can represent their disjunction via two occasions of predication which establish what is commonly said-of both. The occasion at the center is representative of "alpha or beta".
Given the pattern for intersection above, one might naturally ask how this relates to the "Law of Intersection [L7]" already introduced where the logical symbol for conjunction was introduced:
The answer is that the law of intersection tells how a simple act of predication can be understood as an instance of inclusive intersect from the perspective of the occasion which is providing the intrinsic aspect through the Thing Channel. In the Law above, this is the gamma occasion. A rendering of this law in English would be "Alpha means gamma counter-predicates beta", or in other words, gamma is-present-in beta. As such, there is a consequence, as the law goes on that "Gamma equals Alpha intersecting Beta" and because intersection is commutative, we also have "Gamma equals Beta intersecting alpha".
So, every occasion of predication is itself (the gray occasions of Inclusion, or SEH\\ in the conjunction and disjunction trickle diagrams above), an act of inclusive intersection, but when there are two (or more) of these predications converging on a common occasion, the expression becomes of an overlapping intersect (imagine the typical overlapping circles of a Venn Diagram).
The pattern for "Negation" is built with the primitive pattern of a Non-predication (OEH-\) or Else (SEH-\) occasion. This establishes the sense that an occasion is "not that" in the broadest sense in which what is being claimed is anything that is not specifically "that" or inclusive of "that". It might be something entirely other, or even still something less than "that".
The pattern for "Complement" is built with the primitive pattern of a Disjoint (OEH-\) or Succession (SEH-\) occasion. This establishes the sense that an occasion is "not that" in an exclusionary sense in which what is stated is, more narrowly than negation, everything that is entirely other than "that", and therefore having no part in common with "that".
The articles below pertain to Logical Operators.