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Tag: deep inference

Linear inferences of size 7

Posted on October 1, 2020October 8, 2020 by Alex Rice

In Anupam’s recent post, he introduced the linear inferences switch and medial. By computational search it had been shown that all linear inferences with 6 or fewer variables are derivable from these two inferences. He also gave an 8 variable linear inference which is not derivable from switch and medial and posed the question of…

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A new linear inference of size 8

Posted on June 25, 2020June 26, 2020 by Anupam Das

Linear inferences are propositional tautologies of the form , where and are formulas with at most one occurrence of each propositional variable. These form a -complete set, but surprisingly little is known about their structure, despite their importance in structural proof theory (and beyond). In this post I will cover some of the background on…

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Checking proofs with very low complexity

Posted on June 12, 2020June 12, 2020 by Anupam Das

The very notion of mathematical proof is founded upon the idea that a proof is ‘routine’ to check. While it may be difficult to actually prove a mathematical theorem, a proof should allow us to verify its truth . But exactly how much effort is required to check a proof, in terms of computational complexity?…

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