A DeMorgan Law derived from Narrative

Wanting to relate narratives to the traditional Boolean “calculus”, here are some of the kinds of assumptions needed for a test case:

·        A kind of  temp_collection {A,B, C, … } that can be interchanged with the comma-separated narrative pattern ‘A,B,C,…’

·        Blocking this kind of temp_collection replaces it with a temp_collection having each of its elements blocked. In other words (A,B,C,…)* is equivalent to (A*,B*,C*,…).

With those assumptions we can limp towards a derivation of the De Morgan Law

not( A or B ) = not( A ) and not( B ).

First to represent “A or B” in our current framework, we put A and B in a temp_collection, along with a blockage of the alternatives. Thus ‘A or B’ is written:

{ []*, A, B }

To negate that, we write

{ []*, A, B }*

Distributing the outer blockage, gives us

{ []**, A*, B*}

Which “writes back out” as the narrative [], A*,B*. This is endpoint equivalent to ‘A*,B*’. The ‘,’ is transcribed as “and”.

This gives us a hint at doing traditional logic with narratives  - with a heavy reliance on temp_collection behavior and blockage properties. It would be worth isolating the narrative equivalences needed to support a discussion of the infinite.