1. ESFOR Panel Application Developers’ Wish Lists for Automated Theorem Provers

2. Panelists David Crocker –Escher Technologies Software development and services (Perfect developer) Provably correct software –Embedded control software, device drivers, … Bernd Fisher –Nasa Ames Research Centre Certifying auto-generated software Proving correctness of safety policies Automatic derivation of algorithms Simon Colton (chair) –Imperial College London Mathematical and scientific discovery (bioinformatics) Integration of reasoning techniques

3. My Usage of ATP High end user –Work with Sorge, Meier and McCasland –Proving algebraic classification theorems –See paper in CADE proceedings –Hopefully Volker and Andreas are here… Low end user –ATP integrated into a larger ML system For doing mathematical/scientific theory formation –Usually throw away any results proved by Otter –Example: sigma(sigma(n)) = 4  isprime(n) proved by Otter (few axioms)

4. A Low-end User’s Wish List 1. Something you can give me but probably don’t want to: –Usable pieces of software 2. Something you might want to give me but probably can’t: –Robustness to ‘noise’

5. Please make your software easier for me to use!!!! Works for windows as well as linux (yes, I mean that) Single executables Good default settings Manual and tutorial Nice input/output syntax No need to have you guys around Otter has all of the above –That’s why I use it!

6. Please make your software easier for my programs to use!!! While we wait for a universal –Mathematics software bus… Input/output translation routines Timeouts which actually time out Communication protocols (e.g., sockets) Even Otter doesn’t have these –Perhaps the last one

7. Noise in ATP Noise is a well known problem in machine learning We deal with knowledge in logical syntax –No data really But there may still be ‘noise’ –Typos –Missing axioms –Incorrectly defined concepts –Incorrectly formed conjectures This may become particularly important –In the MKM era… –But also as bioinformatics builds up large knowledge bases

8. Can your Software fix it… Given a ‘nearly-true’ theorem I want an ATP system to say: –“Well, it’s not true, but if you change this, then I can prove it for you, mate” –Rather than just saying: “No” Some possibilities –Put extra axioms in / remove axioms –Change definitions –Reformulate conjecture statements

9. An Inspiring Example RNG031-6 non-theorem In rings, the following property holds: –  w x ((((w*w)*x)*(w*w))=id) Our TM system modified this to be: –In Rings, If (  b (b*b = b+b)) then  w x ((((w*w)*x)*(w*w))=id) Nice symmetry to it Otter proved this See disproving workshop proceedings

10. Can you meet the challenge? We did this using induction –Machine learning over Falsifying and supporting examples Can you do this using deduction? Surely deduction is better than induction –In an automated theorem proving setting