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A Java implementation of Peirce’s Alpha 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.

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A Java implementation of Peirce’s Alpha Graphs

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  1. 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

  2. Overview • Existential Graphs • Project motivation • Demonstration

  3. 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)

  4. Existential GraphsSymbolization 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

  5. Existential GraphsInference Rules       Double Cut            (De)Iteration   Erasure    2k 1 2k 1     Insertion  2k+1 1 2k+1 1

  6. Existential GraphsSample Proof in EG H B H A A DE H B H A DE B H A DC E B H A B

  7. 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

  8. 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

  9. 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

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