Existential Graphs Software Dr. Russell Herman Department of Mathematics and Statistics University of North Carolina at Wilmington August 2003

Overview Test engine Using Peirce’s Alpha Model for Existential Graphs. Designed to test the engine Not ready for the end user. Ultimate Goal: To make assertions using predicate logic. Outline of Talk Introduce the Interface Simple Examples Future Development All men are mortal. Socrates is a man. Therefore ?????

Interface – Engine Test Expression Entry Variable List Truth Table – Full or Select Parsed Expressions Conclusions- not implemented yet

Interface – Menu Items Built-in Examples Modus Ponens Modus Tollens Conditional Instructions Symbols

Example 1 - Not A and B The Steps for Entering this Expression Type in Expression Not = ~ And = + A, B can also be full words or phrases But cannot be one of ~, +, *, (, ) Example later Click on Add The expression is parsed

Example 1 – Not A and B Add Expression Variables Expression Sheet of Assertion Truth Table 0’s - True 1’s - False Assert Determine when the expressions are true together A - False B - True

Example 2: Modus Ponens Add Several Expressions Conditional > A>B means “If A then B” Truth Table => Click Assert Only True when both A and B are True

Example 3 – Apples and Oranges Can Use Words Add Statements: Apples and Oranges and If Apples, then Bananas Truth Table Conjunction of last 2 columns true? Assert & Conclude Apples, Oranges and Bananas are all true

Pocket PC Version - Expressions Modus Ponens and Modus Tollens

Pocket PC Version - Tables Assertion Table only shows rows in which all assertions are true. Here is Modus Ponens from which only B true (0) can be concluded.

Pocket PC Version – 4 Variables Apples and Oranges Several Variables with many characters The Assertion Table only lists rows in which conjunction of expressions is true.

What is Missing to Date? 1. Automated – Minimum User Input 2. Read Large Sets of Statements 3. Output Conclusions 4. Use Quantifiers – All, Some, None, … Requires Peirce’s Beta Model

What is Doable? 1. Automated and Read Text Files Hide Engine Allow Manual Entry or Read Text Parse words like “and”, “or”, “not”, “if.. then” Last Two Features have recently been added!

Read Text Files Create the Text File Open File Parse Assert Results: Red - False (1) Blue - False (1) Green - True (0) Yellow - False (1)

Expressions with “and”, “or”, “not” Create Text File But without symbols Open File, Parse and Assert The Conclusions are the same as before

Last Example Results: A - ? (0 or 1) B - False (1) C - True (0) Enter and Add Two Expressions Assert What can one conclude?

What needs work 1. Automate Conclusions May output simple combinations of statements May need user input to determine what types of combinations 2. Implement Peirce’s Beta/Gamma Logic Alpha version is equivalent to Boolean Logic Beta Version follows basic rules and free of user creativity

Summary We have a prototypical engine that can Create truth tables Parse simple statements Can read in sets of statements from files Check validity of non-quantified statement sets We seek an engine that Is more automated Can treat quantifiers (all, some, none) Can parse more complicated statements Can make logical conclusions automatically

Thank you! A copy of this presentation is located at Questions and suggestions can be directed to Dr. Russell Herman Or Dr. Pattricia Turrisi UNC Wilmington, Wilmington, NC