Related papers: Designing a Theorem Prover
Correctness proofs for floating point programs are difficult to verify. To simplify the task, a similar, but less complex system, known as logarithmic arithmetic can be used. The Boyer-Moore Theorem Prover, NQTHM, mechanically verified the…
In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…
Large language models have demonstrated remarkable capabilities in natural language processing tasks requiring multi-step logical reasoning capabilities, such as automated theorem proving. However, challenges persist within theorem proving,…
The advent of large language models trained on code (code LLMs) has led to significant progress in language-to-code generation. State-of-the-art approaches in this area combine LLM decoding with sample pruning and reranking using test cases…
Large language models (LLMs) present an opportunity to scale high-quality personalized education to all. A promising approach towards this means is to build dialog tutoring models that scaffold students' problem-solving. However, even…
In recent years, program verifiers and interactive theorem provers have become more powerful and more suitable for verifying large programs or proofs. This has demonstrated the need for improving the user experience of these tools to…
Large Language Models (LLMs) with reasoning are trained to iteratively generate and refine their answers before finalizing them, which can help with applications to mathematics and code generation. We apply code generation with reasoning…
Large Language Models (LLMs) have revolutionized natural language processing, yet they struggle with inconsistent reasoning, particularly in novel domains and complex logical sequences. This research introduces Proof of Thought, a framework…
Proof Designer is a computer software program designed to help Mathematics students learn to write mathematical proofs. Under the guidance of the user, Proof Designer assists in writing outlines of proofs in elementary set theory. Proof…
Intermediate reasoning or acting steps have successfully improved large language models (LLMs) for handling various downstream natural language processing (NLP) tasks. When applying LLMs for code generation, recent works mainly focus on…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
We present a prototype tool for automated reasoning for Coalition Logic, a non-normal modal logic that can be used for reasoning about cooperative agency. The theorem prover CLProver is based on recent work on a resolution-based calculus…
The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…
Recently, researchers have been working toward the development of practical general-purpose protocols for verifiable computation. These protocols enable a computationally weak verifier to offload computations to a powerful but untrusted…
Automatic (i.e., computer-assisted) theorem proving (ATP) can come in many flavors. This document presents early steps in our effort towards defining object-oriented theorem proving (OOTP) as a new style of ATP. Traditional theorem proving…
Systems now exist which are able to compile unification grammars into language models that can be included in a speech recognizer, but it is so far unclear whether non-trivial linguistically principled grammars can be used for this purpose.…
Neural theorem proving combines large language models (LLMs) with proof assistants such as Lean, where the correctness of formal proofs can be rigorously verified, leaving no room for hallucination. With existing neural theorem provers…
Theorem proving is fundamental to program verification, where the automated proof of Verification Conditions (VCs) remains a primary bottleneck. Real-world program verification frequently encounters hard VCs that existing Automated Theorem…
The combination of verifiable languages and LLMs has significantly influenced both the mathematical and computer science communities because it provides a rigorous foundation for theorem proving. Recent advancements in the field provide…
As language models (LMs) deliver increasing performance on a range of NLP tasks, probing classifiers have become an indispensable technique in the effort to better understand their inner workings. A typical setup involves (1) defining an…