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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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‘Simple’ proofs of cut-elimination II: intuitionistic logic

Posted on September 7, 2020September 10, 2020 by Anupam Das

Cut-elimination for intuitionistic logic has particular significance to proof theorists due to the constructive nature of the logic. Cut-free proofs give rise to significant computational information, including interpolants of implications and, in the case of predicate logic, witnesses of existentials. Moreover, the process of cut-elimination can itself be viewed as a computational process thanks to…

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What proof mining is about, Part IV: Kohlenbach & friends

Posted on August 2, 2020August 13, 2020 by Andrei Sipoș

(Parts I, II, III) After the developments recounted at the end of the previous post, proof mining lay dormant for a number of years; and it was during this period that it got its current name, as per the suggestion of Dana Scott. It was not just a renaming, but a refinement of the concept:…

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What proof mining is about, Part III: The Heroic Age of Unwinding Proofs

Posted on July 3, 2020August 2, 2020 by Andrei Sipoș

(Parts I, II) “The 2456th Century was matter-oriented, as most Centuries were, so he had a right to expect a basic compatibility from the very beginning. It would have none of the utter confusion (for anyone born matter-oriented) of the energy vortices of the 300s, or the field dynamics of the 600s.” (Isaac Asimov, The…

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