Related papers: Generating Mutually Inductive Theorems from Concis…
Even though the ACL2 logic is first order, the ACL2 system offers several mechanisms providing users with some operations akin to higher order logic ones. In this paper, we propose a macro, named instance-of-defspec, to ease the reuse of…
Newcomers to ACL2 are sometimes surprised that ACL2 rejects formulas that they believe should be theorems, such as (REVERSE (REVERSE X)) = X. Experienced ACL2 users will recognize that the theorem only holds for intended values of X, and…
Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of…
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…
ACL2(ml) is an extension for the Emacs interface of ACL2. This tool uses machine-learning to help the ACL2 user during the proof-development. Namely, ACL2(ml) gives hints to the user in the form of families of similar theorems, and…
Text-to-image generation models that generate images based on prompt descriptions have attracted an increasing amount of attention during the past few months. Despite their encouraging performance, these models raise concerns about the…
Large language models (LLMs) have shown remarkable success across a wide range of natural language generation tasks, where proper prompt designs make great impacts. While existing prompting methods are normally restricted to providing…
A method is given that "inverts" a logic grammar and displays it from the point of view of the logical form, rather than from that of the word string. LR-compiling techniques are used to allow a recursive-descent generation algorithm to…
Large language models augmented with task-relevant documents have demonstrated impressive performance on knowledge-intensive tasks. However, regarding how to obtain effective documents, the existing methods are mainly divided into two…
This article describes the *Confluence Framework*, a novel framework for proving and disproving confluence using a divide-and-conquer modular strategy, and its implementation in CONFident. Using this approach, we are able to automatically…
GL is a verified tool for proving ACL2 theorems using Boolean methods such as BDD reasoning and satisfiability checking. In its typical operation, GL recursively traverses a term, computing a symbolic object representing the value of each…
Transformers have been shown to emulate logical deduction over natural language theories (logical rules expressed in natural language), reliably assigning true/false labels to candidate implications. However, their ability to generate…
The article presents several methods for the arithmetic of finite abelian groups. We introduce a tool - already used by Delsarte in [1] as I found out later - analogous to Dirichlet's convolution to obtain combinatorial results on these…
We present Generative Logic (GL), a deterministic architecture that starts from user-supplied axiomatic definitions written in a minimalist Mathematical Programming Language (MPL) and systematically explores a configurable region of their…
FGL is a successor to GL, a proof procedure for ACL2 that allows complicated finitary conjectures to be translated into efficient Boolean function representations and proved using SAT solvers. A primary focus of FGL is to allow greater…
We develop the first theory of control-flow graphs from first principles, and use it to create an algorithm for automatically synthesizing many variants of control-flow graph generators from a language's operational semantics. Our approach…
A method is given that "inverts" a logic grammar and displays it from the point of view of the logical form, rather than from that of the word string. LR-compiling techniques are used to allow a recursive-descent generation algorithm to…
Question Generation is the task of automatically creating questions from textual input. In this work we present a new Attentional Encoder--Decoder Recurrent Neural Network model for automatic question generation. Our model incorporates…
Despite the remarkable ability of large language models (LMs) to comprehend and generate language, they have a tendency to hallucinate and create factually inaccurate output. Augmenting LMs by retrieving information from external knowledge…
Large Language Models (LLMs) equipped with external tools have demonstrated enhanced performance on complex reasoning tasks. The widespread adoption of this tool-augmented reasoning is hindered by the scarcity of domain-specific tools. For…