Related papers: Set Theory for The (Smart) Masses
Unit testing represents the foundational basis of the software testing pyramid, beneath integration and end-to-end testing. Automated software testing researchers have proposed a variety of techniques to assist developers in this…
As computer systems grow ever larger and more complex, a crucial task in software development is for one person (the system expert) to communicate to another (the system novice) how a certain program works. This paper reports on the…
Sentence encoders map sentences to real valued vectors for use in downstream applications. To peek into these representations - e.g., to increase interpretability of their results - probing tasks have been designed which query them for…
Decision support systems for classification tasks are predominantly designed to predict the value of the ground truth labels. However, since their predictions are not perfect, these systems also need to make human experts understand when…
Large language models can perform various reasoning tasks by using chain-of-thought prompting, which guides them to find answers through step-by-step demonstrations. However, the quality of the prompts depends on the demonstrations given to…
Deterministic and nondeterministic finite automata (DFAs and NFAs) are abstract models of computation commonly taught in introductory computing theory courses. These models have important applications (such as fast regular expression…
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…
This paper tackles the problem of formulating and proving the completeness of focused-like proof systems in an automated fashion. Focusing is a discipline on proofs which structures them into phases in order to reduce proof search…
Advances in machine learning (ML) offer new possibilities for science education research. We report on early progress in the design of an ML-based tool to analyze students' mechanistic sensemaking, working from a coding scheme that is…
We apply the foundational proof certificate (FPC) framework to the problem of designing high-level outlines of proofs. The FPC framework provides a means to formally define and check a wide range of proof evidence. A focused proof system is…
Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…
Agentic theorem provers combine a reasoning model, retrieval, search, and a proof assistant verifier, yet it remains unclear which components actually improve finite-budget proof success and why they help on real mathematical workloads. We…
We focus on a type of linguistic formal reasoning where the goal is to reason over explicit knowledge in the form of natural language facts and rules (Clark et al., 2020). A recent work, named PRover (Saha et al., 2020), performs such…
Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It…
Among formal methods, the deductive verification approach allows establishing the strongest possible formal guarantees on critical software. The downside is the cost in terms of human effort required to design adequate formal specifications…
The challenge of formal proof generation has a rich history, but with modern techniques, we may finally be at the stage of making actual progress in real-life mathematical problems. This paper explores the integration of ChatGPT and basic…
Experimental designs reflect assumptions about variable relationships that determine what causal queries researchers can answer through the experiment. Accounting for and communicating these assumptions is essential for drawing valid,…
AI-driven autoformalization of mathematics is advancing rapidly. However, the type checker of a proof assistant guarantees only the logical correctness of proofs; it does not verify whether propositions and definitions faithfully capture…
Mathematical proofs are a cornerstone of control theory, and it is important to get them right. Deduction systems can help with this by mechanically checking the proofs. However, the structure and level of detail at which a proof is…
Interactive systems are commonly prototyped as web applications. This approach enables studies with functional prototypes on a large scale. However, setting up these studies can be complex due to implementing experiment procedures,…