Improvements and Extensions of the EG Applet

November 1, 2001

Improvements and Extensions

Areas of Interest• We want improvements and Extensions in 3 areas:

– Educational: The applet should be something that serves an educational purpose, i.e. it teaches logical concepts to the user.

– User-friendliness: The applet should be easy to understand and use.

– Functionality: The applet should have as many capabilities as possible.

• There will both be overlap as well as interference between these areas. E.g. increasing functionality may decrease user-friendliness (to much to choose from) as well as its educational value (cheating).

Improvements and Extensions

Educational Musts• The user needs to be able to load, save, and edit

proofs– User can ‘see’ the proof (steps don’t get lost)

– Justifications can be indicated as well

– Students can hand in proofs as HW

• User should be able to make mistakes– In Proof Area, user can insert or delete anything, while

program provides appropriate feedback (see Educational Modes)

• Have goal in separate place

Improvements and Extensions

Educational Modes• Different modes (see WinKE software)

– Unsupervised (user can do anything)

– Supervised (user can only perform valid steps)

– Assistant (steps are performed for user)

– Expert (automatic theorem proving)

– Other?

Improvements and Extensions

User-Friendly Goodies• Helpful Buttons

– Buttons for ‘P’, ‘Q’, etc.– Buttons for ‘’, ‘’, ‘’, ‘’, ‘’, and ‘’– Example: For ‘If P then Q’ graph, click ‘’

button, then ‘P’, and then ‘Q’ (needs automatic drawing routine).

• Undo

• Right Button for direct manipulation of graphs

Improvements and Extensions

Relation between EG and PL• Translate between PL and EG

– Problem: This is a many-to-many-more mapping– Solution: Automatically generate possible generations;

User picks preferred one– Or: have user do all the translation, and have system

merely check translation (more educational)– Can this be used for automatic proof generation?

• Buttons can reflect relation between PL and EG (and English):– Button says ‘If … then’ or ‘’, but when clicked the EG

graph appears.

Improvements and Extensions

Proofs as Movies• Ability to view and

edit proofs– User can play, rewind,

stop, fast-forward

– The proof can be edited

– Have window that shows miniature snapshots of proof

Improvements and Extensions

Automatic Drawing Routine• Tree to Graph automatic drawing routine

– Educational:• Clean up user mess• Exploit 2 dimensional visual space• Facilitates visual comparison between graphs and proofs• Automatic Drawing vs User Drawing mode?

– User-Friendliness:• Facilitates graph generation (see User-Friendly Goodies)• User does not have to create room before inserting things• Facilitates Proofs as Patterns (see Proofs as Patterns)• Facilitates Lift and Replace (see Lift and Replace)• Greatly facilitates proof editing (e.g. gluing parts of proofs together) as

visual operations can now be handled by operations over tree data structures (see Proofs as Movies)

Improvements and Extensions

Lift and Replace• ‘Lift and Replace’ Technique:

– To work on a subset of premises among many, ‘lift’ them from the main proof area, transform, and have the result replace the original section.

– This feature would be greatly facilitated by an automatic drawing routine.

– This feature facilitates doing explicit subproofs.

Improvements and Extensions

Proofs as Patterns• Apply common patterns to graph

– Reduce tedium and repetition– Patterns can be made like any other proof but saved as

patterns– Use greek letters to represent arbitrary subgraphs in

patterns– Pattern can be applied to graph to perform part of proof.– Using Lift and Replace, patterns can be applied to parts of

graph– Application of all this requires automatic drawing routine

Improvements and Extensions

Working Backwards• All rules of EG can easily be reversed:

– Double Cut and (De)Iteration are rules of equivalence, so they go both ways already

– The inverse of Erasure is Insertion on an even level

– The inverse of Insertion is Erasure from an odd level

• Therefore, we can work backwards from the conclusion to the premises by applying transformation rules

• Traditional systems do not have this feature!

Improvements and Extensions

Consequence Rule• Routine that checks whether a statement is a

logical consequence of a set of statements (see Fitch).– Useful for user, but care needs to be taken that

this does not get abused.– Application for Automated Theorem Proving