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Despite recent advances in the field of explainable artificial intelligence systems, a concrete quantitative measure for evaluating the usability of such systems is nonexistent. Ensuring the success of an explanatory interface in…
We present a novel approach for teaching logic and the metatheory of logic to students who have some experience with functional programming. We define concepts in logic as a series of functional programs in the language of the proof…
Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…
ACL2 has long supported user-defined simplifiers, so-called metafunctions and clause processors, which are installed when corresponding rules of class :meta or :clause-processor are proved. Historically, such simplifiers could access the…
We describe the first results of a project of analyzing in which theories formal proofs can be ex- pressed. We use this analysis as the basis of interoperability between proof systems.
Data lakehouses run sensitive workloads, where AI-driven automation raises concerns about trust, correctness, and governance. We argue that API-first, programmable lakehouses provide the right abstractions for safe-by-design, agentic…
The integration of experimental technologies with large language models (LLMs) is transforming scientific research. It positions AI as a versatile research assistant rather than a mere problem-solving tool. In the field of power systems,…
In AI-rich higher education, polished written mathematics has become easier to produce than trustworthy evidence of understanding. This article develops a human-scale methodology for service mathematics, with informatics as its main running…
Teaching assistants (TAs) are essential to grading and feedback provision in proof-based courses, yet these tasks are time-intensive and difficult to scale. Although Large Language Models (LLMs) have been studied for grading and feedback,…
Proof assistants play a dual role as programming languages and logical systems. As programming languages, proof assistants offer standard modularity mechanisms such as first-class functions, type polymorphism and modules. As logical…
We present Llemma, a large language model for mathematics. We continue pretraining Code Llama on the Proof-Pile-2, a mixture of scientific papers, web data containing mathematics, and mathematical code, yielding Llemma. On the MATH…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
We present an approach to program reasoning which inserts between a program and its verification conditions an additional layer, the denotation of the program expressed in a declarative form. The program is first translated into its…
Intelligent tutoring systems have long enabled automated immediate feedback on student work when it is presented in a tightly structured format and when problems are very constrained, but reliably assessing free-form mathematical reasoning…
The construction of high-quality parallel corpora for translation research has increasingly evolved from simple sentence alignment to complex, multi-layered annotation tasks. This methodological shift presents significant challenges for…
We further develop the theoretical framework of proof mining, a program in mathematical logic that seeks to quantify and extract computational information from prima facie `non-computational' proofs from the mainstream mathematical…
We present StepFun-Prover Preview, a large language model designed for formal theorem proving through tool-integrated reasoning. Using a reinforcement learning pipeline that incorporates tool-based interactions, StepFun-Prover can achieve…
Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications. Recently, there has been a surge in data-driven methods to complement traditional numerical simulations…
This article discusses the challenges of testing software systems with increasingly integrated AI and LLM functionalities. LLMs are powerful but unreliable, and labeled ground truth for testing rarely scales. Metamorphic Testing solves this…
With the ever-increasing volume of data, there is an urgent need to provide expressive and efficient tools to support Big Data analytics. The declarative logical language Datalog has proven very effective at expressing concisely graph,…