In practice, today's best ATP system are however still far weaker than trained mathematicians in most research domains. Machine learning from many proofs could be used to improveonthis.

Co-organized by Belarus and the United Nations Office of Counter-Terrorism (UNOCT), "Countering terrorism through innovative approaches and the use of new and emerging technologies" concluded on Wednesday in Minsk. The internet "expands technological boundaries literally every day" and AI, 3D printing biotechnology innovations, can help to achieve the Sustainable Development Goals (SDGs), said Vladimir Voronkov, the first-ever Under Secretary-General for the UN Counter-Terrorism Office. The Co-Chair's Summary issued at the end of the @BelarusMFA & @UN_OCT Conference stresses the urgent need to strengthen international cooperation to tackle terrorist abuse of #NewTechnologies & share innovative approaches to counter this threathttps://t.co/55b4vVUq1Y#BY2019UN But it also provides "live video broadcasting of brutal killings", he continued, citing the recent attack in the New Zealand city of Christchurch, where dozens of Muslim worshippers were killed by a self-avowed white supremacist. "This is done in order to spread fear and split society", maintained the UNOCT chief, warning of more serious developments, such as attempts by terrorists to create home-made biological weapons.

Large formal mathematical knowledge bases encode considerable parts of advanced mathematics and exact science, allowing deep semantic computer assistance and verification of complicated theories down to the atomic logical rules. An essential part of automated reasoning over such large theories are methods learning selection of relevant knowledge from the thousands of proofs in the corpora. Such methods in turn rely on efficiently computable features characterizing the highly structured and inter-related mathematical statements.  In this work we (i) propose novel semantic features characterizing the statements in such large semantic knowledge bases, (ii) propose and carry out their efficient implementation using deductive-AI data-structures such as substitution trees and discrimination nets, and (iii) show that they significantly improve the strength of existing knowledge selection methods and automated reasoning methods over the large formal knowledge bases. In particular, on a standard large-theory benchmark we improve the average predicted rank of a mathematical statement needed for a proof by 22% in comparison with state of the art. This allows us to prove 8% more theorems in comparison with state of the art.

The saturation-based reasoning methods are among the most theoretically developed ones and are used by most of the state-of-the-art first-order logic reasoners. In the last decade there was a sharp increase in performance of such systems, which I attribute to the use of advanced calculi and the intensified research in implementation techniques. However, nowadays we are witnessing a slowdown in performance progress, which may be considered as a sign that the saturation-based technology is reaching its inherent limits. The position I am trying to put forward in this paper is that such scepticism is premature and a sharp improvement in performance may potentially be reached by adopting new architectural principles for saturation. The top-level algorithms and corresponding designs used in the state-of-the-art saturation-based theorem provers have (at least) two inherent drawbacks: the insufficient flexibility of the used inference selection mechanisms and the lack of means for intelligent prioritising of search directions. In this position paper I analyse these drawbacks and present two ideas on how they could be overcome. In particular, I propose a flexible low-cost high-precision mechanism for inference selection, intended to overcome problems associated with the currently used instances of clause selection-based procedures. I also outline a method for intelligent prioritising of search directions, based on probing the search space by exploring generalised search directions. I discuss some technical issues related to implementation of the proposed architectural principles and outline possible solutions.