Related papers: Aristotle: IMO-level Automated Theorem Proving
Recent advances in foundational models have yielded reasoning systems capable of achieving a gold-medal standard at the International Mathematical Olympiad. The transition from competition-level problem-solving to professional research,…
Instrumental goals such as resource acquisition, power-seeking, and self-preservation are key to contemporary AI alignment research, yet the phenomenon's ontology remains under-theorised. This article develops an ontological account of…
We present LISA, a proof system and proof assistant for constructing proofs in schematic first-order logic and axiomatic set theory. The logical kernel of the system is a proof checker for first-order logic with equality and schematic…
Starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. Our axiom sets have been formalized in the Isabelle/HOL…
While task-specific demonstrations show early success in applying large language models (LLMs) to automate some astronomical research tasks, they only provide incomplete views of all necessary capabilities in solving astronomy problems,…
This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service…
A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the…
The rapid evolution of autonomous, agentic artificial intelligence within financial services has introduced an existential architectural crisis: large language models (LLMs) are probabilistic, non-deterministic systems operating in domains…
Large language models (LLMs) and large multimodal models (LMMs) promise to accelerate biomedical discovery, yet their reliability remains unclear. We introduce ARIEL (AI Research Assistant for Expert-in-the-Loop Learning), an open-source…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
Automated theorem proving (ATP) has become an appealing domain for exploring the reasoning ability of the recent successful generative language models. However, current ATP benchmarks mainly focus on symbolic inference, but rarely involve…
Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…
Formal methods (FM) are reliable but costly to apply, often requiring years of expert effort in industrial-scale projects such as seL4, especially for theorem proving. Recent advances in large language models (LLMs) have made automated…
Numerous theorems, such as those in geometry, are often presented in multimodal forms (e.g., diagrams). Humans benefit from visual reasoning in such settings, using diagrams to gain intuition and guide the proof process. Modern Multimodal…
This study explores the integration of generative artificial intelligence (AI), specifically large language models, with multi-modal analogical reasoning as an innovative approach to enhance science, technology, engineering, and mathematics…
Multimodal reasoning remains a fundamental challenge in artificial intelligence. Despite substantial advances in text-based reasoning, even state-of-the-art models such as GPT-o3 struggle to maintain strong performance in multimodal…
Humans are black boxes -- we cannot observe their neural processes, yet society functions by evaluating verifiable arguments. AI explainability should follow this principle: stakeholders need verifiable reasoning chains, not mechanistic…
As automated reasoning systems advance rapidly, there is a growing need for research-level formal mathematical problems to accurately evaluate their capabilities. To address this, we present Formal Conjectures, an evolving benchmark of…
Existing benchmarks for AI reasoning provide limited insight into how closely these capabilities resemble human reasoning in naturalistic contexts. We present an adaptation of the Watson & Holmes detective tabletop game as a new benchmark…