Zarathustra Goertzel

Jan Jakubův, Karel Chvalovský, Zarathustra Goertzel et al.

As a present to Mizar on its 50th anniversary, we develop an AI/TP system that automatically proves about 60\% of the Mizar theorems in the hammer setting. We also automatically prove 75\% of the Mizar theorems when the automated provers are helped by using only the premises used in the human-written Mizar proofs. We describe the methods and large-scale experiments leading to these results. This includes in particular the E and Vampire provers, their ENIGMA and Deepire learning modifications, a number of learning-based premise selection methods, and the incremental loop that interleaves growing a corpus of millions of ATP proofs with training increasingly strong AI/TP systems on them. We also present a selection of Mizar problems that were proved automatically.

Ben Goertzel, Vitaly Bogdanov, Michael Duncan et al.

An introduction to the OpenCog Hyperon framework for Artificiai General Intelligence is presented. Hyperon is a new, mostly from-the-ground-up rewrite/redesign of the OpenCog AGI framework, based on similar conceptual and cognitive principles to the previous OpenCog version, but incorporating a variety of new ideas at the mathematical, software architecture and AI-algorithm level. This review lightly summarizes: 1) some of the history behind OpenCog and Hyperon, 2) the core structures and processes underlying Hyperon as a software system, 3) the integration of this software system with the SingularityNET ecosystem's decentralized infrastructure, 4) the cognitive model(s) being experimentally pursued within Hyperon on the hopeful path to advanced AGI, 5) the prospects seen for advanced aspects like reflective self-modification and self-improvement of the codebase, 6) the tentative development roadmap and various challenges expected to be faced, 7) the thinking of the Hyperon team regarding how to guide this sort of work in a beneficial direction ... and gives links and references for readers who wish to delve further into any of these aspects.

Sergey Rodionov, Zarathustra Amadeus Goertzel, Ben Goertzel

This report summarizes a short study of the performance of GPT-4 on the ETHICS dataset. The ETHICS dataset consists of five sub-datasets covering different fields of ethics: Justice, Deontology, Virtue Ethics, Utilitarianism, and Commonsense Ethics. The moral judgments were curated so as to have a high degree of agreement with the aim of representing shared human values rather than moral dilemmas. GPT-4's performance is much better than that of previous models and suggests that learning to work with common human values is not the hard problem for AI ethics.

Zarathustra Goertzel, Karel Chvalovský, Jan Jakubův et al.

We describe several additions to the ENIGMA system that guides clause selection in the E automated theorem prover. First, we significantly speed up its neural guidance by adding server-based GPU evaluation. The second addition is motivated by fast weight-based rejection filters that are currently used in systems like E and Prover9. Such systems can be made more intelligent by instead training fast versions of ENIGMA that implement more intelligent pre-filtering. This results in combinations of trainable fast and slow thinking that improves over both the fast-only and slow-only methods. The third addition is based on "judging the children by their parents", i.e., possibly rejecting an inference before it produces a clause. This is motivated by standard evolutionary mechanisms, where there is always a cost to producing all possible offsprings in the current population. This saves time by not evaluating all clauses by more expensive methods and provides a complementary view of the generated clauses. The methods are evaluated on a large benchmark coming from the Mizar Mathematical Library, showing good improvements over the state of the art.

Zarathustra Amadeus Goertzel

In this work in progress, we demonstrate a new use-case for the ENIGMA system. The ENIGMA system using the XGBoost implementation of gradient boosted decision trees has demonstrated high capability to learn to guide the E theorem prover's inferences in real-time. Here, we strip E to the bare bones: we replace the KBO term ordering with an identity relation as the minimal possible ordering, disable literal selection, and replace evolved strategies with a simple combination of the clause weight and FIFO (first in first out) clause evaluation functions. We experimentally demonstrate that ENIGMA can learn to guide E as well as the smart, evolved strategies even without these standard automated theorem prover functionalities. To this end, we experiment with XGBoost's meta-parameters over a dozen loops.

Zarathustra Goertzel, Jan Jakubův, Josef Urban

In this work we describe a new learning-based proof guidance -- ENIGMAWatch -- for saturation-style first-order theorem provers. ENIGMAWatch combines two guiding approaches for the given-clause selection implemented for the E ATP system: ProofWatch and ENIGMA. ProofWatch is motivated by the watchlist (hints) method and based on symbolic matching of multiple related proofs, while ENIGMA is based on statistical machine learning. The two methods are combined by using the evolving information about symbolic proof matching as an additional information that characterizes the saturation-style proof search for the statistical learning methods. The new system is experimentally evaluated on a large set of problems from the Mizar Library. We show that the added proof-matching information is considered important by the statistical machine learners, and that it leads to improvements in E's Performance over ProofWatch and ENIGMA.