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This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…
Students of our department solve algebraic exercises in mathematical logic in a computerized environment. They construct transformations step by step and the program checks the syntax, equivalence of expressions and completion of the task.…
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…
This paper from 2012 is the second in a series of three papers. All three papers deal with interpretability logics and related matters. In the first paper a construction method was exposed to obtain models of these logics. Using this…
Mathematical reasoning remains a significant challenge for Large Language Models (LLMs) due to hallucinations. When combined with formal proof assistants like Lean, these hallucinations can be eliminated through rigorous verification,…
Retrieval-Augmented Generation (RAG) enhances language models by combining retrieval with generation. However, its current workflow remains largely text-centric, limiting its applicability in geoscience. Many geoscientific tasks are…
Empirical methods in geoparsing have thus far lacked a standard evaluation framework describing the task, metrics and data used to compare state-of-the-art systems. Evaluation is further made inconsistent, even unrepresentative of…
Accurate modeling and explaining geospatial tabular data (GTD) are critical for understanding geospatial phenomena and their underlying processes. Recent work has proposed a novel transformer-based deep learning model named GeoAggregator…
The problem-solving in automated theorem proving (ATP) can be interpreted as a search problem where the prover constructs a proof tree step by step. In this paper, we propose a deep reinforcement learning algorithm for proof search in…
The Isabelle proof assistant comes equipped with a very powerful tactic for term simplification. While tremendously useful, the results of simplifying a term do not always match the user's expectation: sometimes, the resulting term is not…
Formally verifying software properties is a highly desirable but labor-intensive task. Recent work has developed methods to automate formal verification using proof assistants, such as Coq and Isabelle/HOL, e.g., by training a model to…
Recent reasoning-focused language models such as DeepSeek R1 and OpenAI o1 have demonstrated strong performance on structured reasoning benchmarks including GSM8K, MATH, and multi-hop question answering tasks. However, their performance…
Teaching language models to use tools is an important milestone towards building general assistants, but remains an open problem. While there has been significant progress on learning to use specific tools via fine-tuning, language models…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results,…
With the rapid rise of generative AI in higher education and the unreliability of current AI detection tools, developing policies that encourage student learning and critical thinking has become increasingly important. This study examines…
We have developed a web-based pedagogical proof assistant, the Proof Tree Builder, that lets you apply rules upwards from the initial goal in sequent calculus and Hoare logic for a simple imperative language. We equipped our tool with a…
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,…
In discourse studies concessions are considered among those argumentative strategies that increase persuasion. We aim to empirically test this hypothesis by calculating the distribution of argumentative concessions in persuasive vs.…
Hand pose estimation has matured rapidly in recent years. The introduction of commodity depth sensors and a multitude of practical applications have spurred new advances. We provide an extensive analysis of the state-of-the-art, focusing on…