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