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Recent advances in automated theorem proving (ATP) through LLMs have highlighted the potential of formal reasoning with Lean 4 codes. However, ATP has not yet be revolutionized by the recent posttraining scaling as demonstrated by Open AI…
Although traditional symbolic reasoning methods are highly interpretable, their application in knowledge graphs link prediction has been limited due to their computational inefficiency. A new RNNNTP method is proposed in this paper, using a…
The most promising recent methods for AI reasoning require applying variants of reinforcement learning (RL) either on rolled out trajectories from the LLMs, even for the step-wise rewards, or large quantities of human-annotated trajectory…
Empirical methods to examine the capability of Large Language Models (LLMs) to use Automated Theorem Prover (ATP) reasoning strategies are studied. We evaluate the performance of State of the Art models from December 2023 and August 2024 on…
We study whether a Large Language Model can learn the deterministic sequence of trees generated by the iterated prime factorization of the natural numbers. Each integer is mapped into a rooted planar tree and the resulting sequence $…
Non-classical logics are used in a wide spectrum of disciplines, including artificial intelligence, computer science, mathematics, and philosophy. The de-facto standard infrastructure for automated theorem proving, the TPTP World, currently…
Automated Theorem Proving (ATP) represents a core research direction in artificial intelligence for achieving formal reasoning and verification, playing a significant role in advancing machine intelligence. However, current large language…
We are interested in understanding how well Transformer language models (TLMs) can perform reasoning tasks when trained on knowledge encoded in the form of natural language. We investigate their systematic generalization abilities on a…
In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the…
Artificial Neural Networks are powerful function approximators capable of modelling solutions to a wide variety of problems, both supervised and unsupervised. As their size and expressivity increases, so too does the variance of the model,…
Undergraduate students of artificial intelligence often struggle with representing knowledge as logical sentences. This is a skill that seems to require extensive practice to obtain, suggesting a teaching strategy that involves the…
Neural networks have succeeded in many reasoning tasks. Empirically, these tasks require specialized network structures, e.g., Graph Neural Networks (GNNs) perform well on many such tasks, but less structured networks fail. Theoretically,…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
We report on the results of evaluating the competency of a first-order ontology for its use with automated theorem provers (ATPs). The evaluation follows the adaptation of the methodology based on competency questions (CQs)…
Theorem proving serves as a major testbed for evaluating complex reasoning abilities in large language models (LLMs). However, traditional automated theorem proving (ATP) approaches rely heavily on formal proof systems that poorly align…
Natural language explanations play a fundamental role in Natural Language Inference (NLI) by revealing how premises logically entail hypotheses. Recent work has shown that the interaction of large language models (LLMs) with theorem provers…
Theorem proving in natural mathematical language - the mixture of symbolic and natural language used by humans - plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet…
Large Language Models (LLMs) have demonstrated impressive real-world utility, exemplifying artificial useful intelligence (AUI). However, their ability to reason adaptively and robustly -- the hallmarks of artificial general intelligence…
Recent advances in large language models (LLMs) have shown remarkable progress, yet their capacity for logical ``slow-thinking'' reasoning persists as a critical research frontier. Current inference scaling paradigms suffer from two…
We introduce a new framework to evaluate and improve first-order (FO) ontologies using automated theorem provers (ATPs) on the basis of competency questions (CQs). Our framework includes both the adaptation of a methodology for evaluating…