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Mining Human Proofs from Machine Proofs

Presented by: 
Paulo Oliva Queen Mary University of London, Queen Mary University of London
Date: 
Tuesday 18th July 2017 - 11:00 to 12:00
Venue: 
INI Seminar Room 2
Abstract: 
When recently investigating an intuitionistic fragment of Lukasiewicz logic [1-4], we were able to discover several interesting theorems of this logic by searching for valid equations in the algebra of hoops. Our search for valid equations or counter-models was done using prover9 and mace4 (https://www.cs.unm.edu/~mccune/mace4/). In this talk I will describe some of the results obtained, mainly around double negation translations of the classical logic into the intuitionistic counter-part, but also the process by which we managed to translate prover9 equational proofs into human readable (and hopefully understandable) proofs.

Joint work with Rob Arthan.

[1] R Arthan and P Oliva, Negative translations for affine and Lukasiewicz logic, under review (http://www.eecs.qmul.ac.uk/~pbo/papers/paper045.pdf)
[2] R Arthan and P Oliva, On pocrims and hoops, Arxiv (https://arxiv.org/abs/1404.0816)
[3] R Arthan and P Oliva, On affine logic and Lukasiewicz logic, Arxiv (https://arxiv.org/abs/1404.0570)
[4] R Arthan and P Oliva, Dual hoops have unique halving, McCune Festschrift, LNAI 7788, pp. 165-180, 2013
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons