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Complex reasoning aims to draw a correct inference based on complex rules. As a hallmark of human intelligence, it involves a degree of explicit reading comprehension, interpretation of logical knowledge and complex rule application. In…
Automatic assessment of code, in particular to support education, is an important feature included in several Learning Management Systems (LMS), at least to some extent. Several kinds of assessments can be designed, such as exercises asking…
Autoformalization aims to convert informal mathematical proofs into machine-verifiable formats, bridging the gap between natural and formal languages. However, ensuring semantic alignment between the informal and formalized statements…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
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…
Autoformalization, the task of automatically translating natural language descriptions into a formal language, poses a significant challenge across various domains, especially in mathematics. Recent advancements in large language models…
Foundations of formal languages, as subfield of theoretical computer science, are part of typical upper secondary education curricula. There is very little research on the potential difficulties that students at this level have with this…
The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
Many students in introductory programming courses fare poorly in the code writing tasks of the final summative assessment. Such tasks are designed to assess whether novices have developed the analytical skills to translate from the given…
As learning difficulty is crucial for machine learning (e.g., difficulty-based weighting learning strategies), previous literature has proposed a number of learning difficulty measures. However, no comprehensive investigation for learning…
Formal mathematical reasoning remains a critical challenge for artificial intelligence, hindered by limitations of existing benchmarks in scope and scale. To address this, we present FormalMATH, a large-scale Lean4 benchmark comprising…
Large language models (LLMs) can now generate physics practice problems in real time, yet the educational value of these items hinges on rapid, reliable post-generation vetting. In this exploratory study, we investigated which automated…
Curriculum learning (CL), motivated by the intuition that learning in increasing order of difficulty should ease generalization, is commonly adopted both in pre-training and post-training of large language models (LLMs). The intuition of CL…
As real logic programmers normally use cut (!), an effective learning procedure for logic programs should be able to deal with it. Because the cut predicate has only a procedural meaning, clauses containing cut cannot be learned using an…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
Translating natural language into formal language such as First-Order Logic (FOL) is a foundational challenge in NLP with wide-ranging applications in automated reasoning, misinformation tracking, and knowledge validation. In this paper, we…
Autoformalization plays a crucial role in formal mathematical reasoning by enabling the automatic translation of natural language statements into formal languages. While recent advances using large language models (LLMs) have shown…