О древовидной форме поиска опровержения в интеллектуальных системах с логическими возможностями

Работа посвящена изучению возможностей интеллектуальных систем, которые предоставляет древовидная форма поиска опровержения в спучае использования резолюционной техники, включая правила парамодуляционного типа. Рассматриваются исчисления так называемых литеральных деревьев, которые предназначены для установления невыполнимости формул классической логики первого порядка как с равенством, так и без него. Приводятся результаты об их корректности и полноте.Робота присвячена вивченню можливостей інтелектуальних систем, які надає деревовидна форма пошуку спростування при використанні резолюційної техніки, включаючи правила парамодуляційного типу. Розглядаються числення так званих літеральних дерев, які призначені для встановлення невиконання формул класичної логіки першого порядку як з рівністю, так і без неї. Наводяться результати про їх коректність та повноту.The paper is devoted to the study of intelligent system possibilities given by the tree-like form of refutation search when using the resolution technique with paramodulation-type rules. Calculation of so-called literal trees intended for the establishment of formula unsatisfiability of first-order classic logic, both with equality and without it, are considered. Results about their correctness and completeness are given

gym-saturation: Gymnasium environments for saturation provers (System description)

This work describes a new version of a previously published Python package - gym-saturation: a collection of OpenAI Gym environments for guiding saturation-style provers based on the given clause algorithm with reinforcement learning. We contribute usage examples with two different provers: Vampire and iProver. We also have decoupled the proof state representation from reinforcement learning per se and provided examples of using a known ast2vec Python code embedding model as a first-order logic representation. In addition, we demonstrate how environment wrappers can transform a prover into a problem similar to a multi-armed bandit. We applied two reinforcement learning algorithms (Thompson sampling and Proximal policy optimisation) implemented in Ray RLlib to show the ease of experimentation with the new release of our package.Comment: 13 pages, 3 figures. This version of the contribution has been accepted for publication, after peer review but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/978-3-031-43513-3_1

Spanning Matrices via Satisfiability Solving

We propose a new encoding of the first-order connection method as a Boolean satisfiability problem. The encoding eschews tree-like presentations of the connection method in favour of matrices, as we show that tree-like calculi have a number of drawbacks in the context of satisfiability solving. The matrix setting permits numerous global refinements of the basic connection calculus. We also show that a suitably-refined calculus is a decision procedure for the Bernays-Sch\"onfinkel class

Leo-III Version 1.1 (System description)

Leo-III is an automated theorem prover for (polymorphic) higher-order logic which supports all common TPTP dialects, including THF, TFF and FOF as well as their rank-1 polymorphic derivatives. It is based on a paramodulation calculus with ordering constraints and, in tradition of its predecessor LEO-II, heavily relies on cooperation with external first-order theorem provers. Unlike LEO-II, asynchronous cooperation with typed first-order provers and an agent-based internal cooperation scheme is supported. In this paper, we sketch Leo-III's underlying calculus, survey implementation details and give examples of use