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The field of geometric automated theorem provers has a long and rich history, from the early AI approaches of the 1960s, synthetic provers, to today algebraic and synthetic provers. The geometry automated deduction area differs from other…
Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than…
Development of Interactive Theorem Provers has led to the creation of big libraries and varied infrastructures for formal proofs. However, despite (or perhaps due to) their sophistication, the re-use of libraries by non-experts or across…
"Theorem proving is similar to the game of Go. So, we can probably improve our provers using deep learning, like DeepMind built the super-human computer Go program, AlphaGo." Such optimism has been observed among participants of AITP2017.…
The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous…
Techniques combining machine learning with translation to automated reasoning have recently become an important component of formal proof assistants. Such "hammer" tech- niques complement traditional proof assistant automation as…
We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original…
Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called…
While the advancement of large language models has spurred the development of AI agents to automate tasks, numerous use cases inherently require agents to collaborate with humans due to humans' latent preferences, domain expertise, or the…
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…
Automated Theorem Proving (ATP) is an established branch of Artificial Intelligence. The purpose of ATP is to design a system which can automatically figure out an algorithm either to prove or disprove a mathematical claim, on the basis of…
LLM-based formal proof assistants (e.g., in Lean) hold great promise for automating mathematical discovery. But beyond syntactic correctness, do these systems truly understand mathematical structure as humans do? We investigate this…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
Large language models are emerging as scientific assistants, but evaluating their ability to reason from empirical data remains challenging. Benchmarks derived from published studies and human annotations inherit publication bias,…
The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…
We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…
Large language models (LLMs) have shown increasing in-context learning capabilities through scaling up model and data size. Despite this progress, LLMs are still unable to solve algorithmic reasoning problems. While providing a rationale…
Viewing formal mathematical proofs as logical terms provides a powerful and elegant basis for analyzing how human experts tend to structure proofs and how proofs can be structured by automated methods. We pursue this approach by (1)…
Mathematical reasoning demands two critical, complementary skills: constructing rigorous proofs for true statements and discovering counterexamples that disprove false ones. However, current AI efforts in mathematics focus almost…