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 Graphs Symbolization ‘P’ ‘not P’ ‘P and Q’ ‘P or Q’ ‘if P then Q’ TraditionalEG PP ~ P P & Q P  Q P  Q P Q QP P QP

5. Existential Graphs Inference Rules Double Cut (De)Iteration Erasure Insertion        12k  1   12k+1  1 

6. Existential Graphs Sample Proof in EG A B DE DC E BHAH ABH HAB DE H HAB

7. 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

8. 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

9. 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