Logical Graphs, Truth Tables, Venn Diagrams • 5

Re: Laws of FormLyle Anderson
Re: Anderson, Lyle A. III (1981), “Systematic Analysis of Algorithms”,
Open Access Master’s Theses, Paper 1167, (1) (2).

Thanks, Lyle, your Chapter 4, “Dealing With Conditional Statements”, provides a detailed treatment of algorithmic branching constructs in general purpose programming languages but as you noted in saying, “we are already way outside the realm of truth tables with only 1 \text{s} and 0 \text{s}", it tangos with a much-higher-maintenance date than the one John Mingers brought to the dance.

I think we are making this problem harder than it needs to be.  Let’s go back to the original question and try to view it with fresh eyes.  All we have to decide is which candidate among the three-variable boolean functions f : \mathbb{B}^3 \to \mathbb{B} provides a reasonable mathematical proxy for what we mean when we say, ``\text{if}~ p ~\text{is true then}~ q ~\text{is true else}~ r ~\text{is true}".  Experience with informal-to-formal translation tells us there may be no functional form capturing every nuance of a natural language idiom but there is usually one serving all practical purposes in empirical and mathematical contexts.


cc: CyberneticsOntolog • Peirce List (1) (2) (3)Structural ModelingSystems Science
cc: FB | Logical GraphsLaws of Form

This entry was posted in Amphecks, Boolean Algebra, Boolean Functions, C.S. Peirce, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Propositional Calculus, Spencer Brown, Truth Tables, Venn Diagrams, Visualization and tagged , , , , , , , , , , , , , , . Bookmark the permalink.

2 Responses to Logical Graphs, Truth Tables, Venn Diagrams • 5

  1. Pingback: Survey of Animated Logical Graphs • 4 | Inquiry Into Inquiry

  2. Pingback: Survey of Animated Logical Graphs • 5 | Inquiry Into Inquiry

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.