A Java implementation of Peirce

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A Java implementation of Peirces Alpha Graphs

• Bram van Heuveln (RPI)
• Dennis Higgins (SUNY Oneonta)
• SUNY Oneonta undergraduate programmers
• Elizabeth Hatfield, Debbie Kilpatrick, Lut Wong

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Overview

• Existential Graphs
• Project motivation
• Demonstration

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Existential Graphs Peirces Existential Graphs

• A graphical logic system developed by C.S. Peirce
  almost 100 years ago.
• Peirce studied semiotics the relationship
  between symbols, meanings, and users.
• Peirce stressed the power of iconic
  representations
• Existential Graphs allow the user to express
  logical statements in a completely graphical way.
• Alpha (Propositional Logic)
• Beta (Predicate Logic)
• Gamma (Modal Logic)

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Existential GraphsSymbolization
Traditional
EG
P
P
P
not P
P
P
P and Q
P Q
Q
P
P or Q
P ? Q
Q
P
if P then Q
P ?Q
Q
P
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Existential GraphsInference Rules
?
?
?
?
?
?
Double Cut
?
?
?
?
?
?
?
?
?
?
?
(De)Iteration
?
?
Erasure
?
?
?
1
2k
1
2k
?
?
?
?
Insertion
?
1
2k1
1
2k1
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Existential GraphsSample Proof in EG
A
B
H
A
H
DE
A
B
H
H
DE
H
A
B
DC
E
B
H
A
B
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MotivationStrength of EG

• Compact
• Only Simple Propositions and Cuts
• Only 4 inference rules
• Fast
• Derivations take few steps
• Transform rather than rewrite
• Intuitive
• Graphical representation is easy to manipulate
• Many logical relationships become obvious
• Maximum Logical Power
• Deductively sound and complete

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MotivationStudent Response

• Bram has taught Existential Graphs in logic
  classes
• Even though students were forced to draw
  successive snapshots, students expressed
  preference of Existential Graphs over traditional
  logic systems
• easier
• more fun!
• Students were excited at the idea of having an
  interactive interface

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MotivationFurther Motivation

• Conceptual advantages of EG remain unexplored
• Do students gain a deep understanding of logical
  relationships using EG?
• How do EG and standard logic systems compare and
  relate?
• Does use of EG reveal features that can speed up
  automatic theorem proving?
• Good interface for Existential Graphs did not
  seem to exist