Existential Graphs Software

Dr. Russell HermanDepartment 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 AssertOnly 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 & ConcludeApples, 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

http://people.uncw.edu/hermanr/tech.htm

Questions and suggestions can be directed to

Dr. Russell Herman

Or

Dr. Pattricia Turrisi

hermanr@uncw.edu turrisip@uncw.edu

UNC Wilmington, Wilmington, NC