Existential Graphs Software

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

2. 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 ?????

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

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

5. 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

6. A - False • B - True 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

7. 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

8. 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

9. Pocket PC Version - Expressions Modus Ponens and Modus Tollens

10. 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.

11. 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.

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

13. What is Doable? • 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!

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

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

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

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

18. 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

19. Thank you! A copy of this presentation is located at http://people.uncw.edu/hermanr/tech.htm Questions and suggestions can be directed to Dr. Russell Herman Or Dr. Pattricia Turrisi hermanr@uncw.eduturrisip@uncw.edu UNC Wilmington, Wilmington, NC