Existential Graphs Software

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Existential Graphs Software

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

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Overview

• Test engine
• Using Peirces 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
Parsed Expressions
Variable List
Truth Table Full or Select
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
• 0s - True
• 1s - False
• Assert
• Determine when the expressions are true together

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Example 2 Modus Ponens

• Add Several Expressions
• Conditional gt
• AgtB means
• If A then B
• Truth Table gt
• Click Assert
• Only 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 Conclude
• Apples, 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?

• Automated Minimum User Input
• Read Large Sets of Statements
• Output Conclusions
• Use Quantifiers All, Some, None,
• Requires Peirces Beta Model

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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!
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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

• Enter and Add Two Expressions
• Assert
• What can one conclude?

• Results
• A - ? (0 or 1)
• B - False (1)
• C - True (0)

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What needs work

• Automate Conclusions
• May output simple combinations of statements
• May need user input to determine what types of
  combinations
• Implement Peirces 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
• hermanr_at_uncw.edu
  turrisip_at_uncw.edu
• UNC Wilmington, Wilmington, NC