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Existential Graphs Software
Dr. Russell HermanDepartment of Mathematics and Statistics
University of North Carolina at Wilmington
August 2003
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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 ?????
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Interface – Engine Test
Expression Entry
Variable List
Truth Table – Full or Select
Parsed Expressions
Conclusions- not implemented yet
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Interface – Menu Items
Built-in Examples Modus Ponens Modus Tollens Conditional
Instructions Symbols
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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
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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
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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
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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
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Pocket PC Version - Expressions
Modus Ponens and Modus Tollens
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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.
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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.
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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
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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!
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Read Text Files
Create the Text File
Open File
Parse
Assert
Results:
•Red - False (1)
•Blue - False (1)
•Green - True (0)
•Yellow - False (1)
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Expressions with “and”, “or”, “not”
Create Text File
But without symbols
Open File, Parse and Assert
The Conclusions are the same as before
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Last Example
Results:
•A - ? (0 or 1)
•B - False (1)
•C - True (0)
Enter and Add Two Expressions
Assert
What can one conclude?
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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
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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
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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
[email protected] [email protected]
UNC Wilmington, Wilmington, NC