A Java implementation of Peirce’s Existential Graphs

Bram van Heuveln

Dennis Higgins

faculty advisors

Elizabeth Hatfield, Debbie Kilpatrick, Lut Wong

student programmers

Overview

• Background and Motivation

• Problem Specification

• Design Choices

• Current State and Future Developments

• Demonstration!

Background and motivation

Peirce’s Existential Graphs• A graphical logic system

– system to symbolize and infer statements

• Developed by Peirce almost 100 years ago.• Peirce studied semiotics: the relationship between

symbols, meanings, and users. – Peirce found the linear notation and accompanying rules

of traditional logic systems restrictive, involved, and unintuitive.

– Existential Graphs allow the user to express logical statements in a completely graphical way.

Background and motivation

Syntax of EG

‘P’

‘not P’

‘P and Q’

‘P or Q’

‘if P then Q’

Traditional EG

P P

~P, P’

P&Q, P*Q, PQ

P|Q, P+Q, PQ

PQ, P Q

P

Q

QP

P

QP

Background and motivation

Inference Rules of EGDouble Cut

(De)Iteration

Erasure

Insertion

P P

QPQ

QP

QP

P

Q

PP

Background and motivation

Example

Prove:(AB) C~C~B

Traditional (Fitch) EG

(A B) C

~C

B

A B

C

~C

~B

A.

A.

A.

3 I

1,4 E

2 R

3-6 ~I

BA

BA

C

C

C

A

B

CB

DE

DC

E

1.

2.

3.

4.

5.

6.

7.

Background and motivation

Strength of EG• Compact

– Only Propositions and Cuts; Only 4 rules

• Easy to use– Less chance of making mistakes

• Fast– Transform rather than rewrite

• Intuitive– Many logical relationships come for free

• Maximum Logical Power– Expressively complete; deductively complete

Background and motivation

Initial Student ResponseBram has taught Existential Graphs in logic class:• Even though students were forced to draw successive

snapshots, students were more happy with Existential Graphs than traditional systems:– easier– faster– less mistakes– more fun

• Students were excited at the idea of having an interactive interface

Background and motivation

Further Motivation for the Project• Interface for construction and manipulation of

Existential Graphs does not seem to exist• Conceptual advantages of the dynamic character of

logic proofs in EG remain unexplored• Software can be used in logic class• Implementation in Java, so that an applet can be put

on a home page for public use• Good experience

– Completed project can be presented at conference

Problem Specification

Required Functionality• The user should be able to:

– Generate Existential Graphs• Draw, delete, move, resize, and copy propositions and cuts

– Manipulate Existential Graphs• Apply rules of inference

• The system should:– Keep track of the logical relationships as expressed by

the Existential Graphs

– Check if the rules of inference are correctly applied by the user

Problem Specification

Desired added Functionality• File I/O

– To load and save existential graphs

– To load and save proofs as a series of images

• Proof Editor– Video buttons to play and rewind proofs

– Edit existing proofs

• Help and Tutorial– Instructions for use

– Examples

Problem Specification

Data StructureWanted! A data structure that is able to:• represent the abstract logical structure of an

Existential Graph,• store geometrical information of the actual size

and location of graph components, and• facilitate manipulations of the abstract logical

structure as well as of the geometrical information, thus forming some kind of interface between these two

Design Choices

Preliminary Decisions• The GUI will have two distinct parts:

– Work Area• place where the user has full editing capabilities to generate

individual Existential Graphs

– Proof Area• place where the user places finished Existential Graphs and

manipulates them conforming to the legal rules of inference

• A nested linked list data structure will be used– Abstract logical relationships represented by nesting

– Specific graphical information stored in each element

Design Choices

Project PhasingWe decided to implement in two phases:

• Phase one: develop an interface for the Work Area– Requires interface with full editing capabilities

– Requires data structure with full representation and manipulation capabilities

• Phase two: provide an interface for the Proof Area– After Phase 1, this should be a piece of cake!

Design Choices

Task Divisions• Debbie and Elizabeth: Interface lay-out design

– Frames, Panels, Buttons, etc.

• Elizabeth: Manipulation of Propositions– Add, move, and delete using keyboard and mouse

• Lut: Manipulation of Cuts– Move and resize using mouse

• Dennis: Data Structure• Bram: File I/O

Design Choices

JTreeDennis found a Java foundation class JTree, which

can be used for the nested structure– The Sheet of Assertion (SA) is the root of the Jtree,

children of the SA are the graphs that are ‘on’ the SA, children of these children are graphs at level 1, etc. Propositions form the leafs of the Jtree

– JTree supports various useful operations such as getting a node’s children, finding a parent for a given child, finding a path from the root to a node, etc.

– JTree has a built-in interface to display itself.

Design Choices

NodeGuyThe JTree nodes can hold user data. We made the

class NodeGuy which gets put into every JTree node. NodeGuy represents either a cut or a proposition, and contains the geometric information of this item.

This fairly simple class thus provides a go-between for the JTree and the Work Area. Each of these major classes can access and update NodeGuy information, and use it to display the expression in the proper way.

Current State and Future Developments

Phase 1: Work Area

The Work Area is as good as completed:• Our current program supports drawing, moving,

copying, and deleting propositions and cuts. Cuts can also be resized.

• The data structure gets correctly updated in accordance with the changes in graphical information and logical relationships.

Current State and Future Developments

Phase 2: Proof AreaThe Proof Area shouldn’t take too much time:• Move graphs from Work Area to Proof Area• Double Cut: Similar to adding/deleting cut• Iteration: Copy• Deiteration: Needs equivalence test• Erasure: Delete group• Insertion: Make graph in Work Area and move

to Proof Area