Transcript A Java implementation of Peirce`s Existential Graphs

A Java implementation of Peirce’s
Alpha Graphs
Bram van Heuveln (RPI)
Dennis Higgins (SUNY Oneonta)
SUNY Oneonta undergraduate programmers:
Elizabeth Hatfield, Debbie Kilpatrick, Lut Wong
Overview
• Existential Graphs
• Project motivation
• Demonstration
Existential Graphs
Peirce’s 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)
Existential Graphs
Symbolization
Traditional
EG
‘P’
P
P
‘not P’
~P
P
‘P and Q’
P&Q
P
Q
‘P or Q’
PQ
P
Q
‘if P then Q’
P Q
P
Q
Existential Graphs
Inference Rules
Double Cut

(De)Iteration
 
Erasure

Insertion




    



2k

1
2k+1 1





2k


1
2k+1 1
Existential Graphs
Sample Proof in EG
H
B
H
A
A
DE
H
B
H
A
DE
B
H
A
H
A
DC
B
E
B
Motivation
Strength 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
Motivation
Student 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
Motivation
Further 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