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The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
Chain-of-Thought (CoT) has become a cornerstone of reasoning in large language models, yet its effectiveness is constrained by the limited expressiveness of discrete token sampling. Recent latent reasoning approaches attempt to alleviate…
We study the existence of optimal and p-optimal proof systems for classes in the Boolean hierarchy over $\mathrm{NP}$. Our main results concern $\mathrm{DP}$, i.e., the second level of this hierarchy: If all sets in $\mathrm{DP}$ have…
The honesty of large language models (LLMs) is a critical alignment challenge, especially as advanced systems with chain-of-thought (CoT) reasoning may strategically deceive humans. Unlike traditional honesty issues on LLMs, which could be…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Large Language Models (LLMs) employ Chain-of-Thought (CoT) reasoning to deconstruct complex problems. While longer CoTs are often presumed superior, this paper challenges that notion, arguing that longer is not always better. Drawing on…
As Large Language Models (LLMs) increasingly assist secure software development, their ability to meet the rigorous demands of Rust program verification remains unclear. Existing evaluations treat Rust verification as a black box, assessing…
We solve MIT's Linear Algebra 18.06 course and Columbia University's Computational Linear Algebra COMS3251 courses with perfect accuracy by interactive program synthesis. This surprisingly strong result is achieved by turning the course…
Squeezed cat quantum error correction (QEC) codes have garnered attention because of their robustness against photon-loss and excitation errors while maintaining the biased-noise property of cat codes. In this work, we reveal the utility of…
Many language tasks can be modeled as classification problems where a large language model (LLM) is given a prompt and selects one among many possible answers. We show that the classification error in such problems scales as a power law in…
Large language models (LLMs) have recently shown strong performance on mathematical benchmarks. At the same time, they are prone to hallucination and sycophancy, often providing convincing but flawed proofs for incorrect mathematical…
Modern Large Language Models (LLMs) have shown impressive performances in user-facing tasks such as question answering, as well as consistent improvements in reasoning capabilities. Still, the way these models encode knowledge seems…
Knowledge Tracing (KT) models students' knowledge states based on learning interactions to predict performance. While deep learning-based KT models have boosted predictive accuracy, most models rely on deterministic vector embeddings and…
A propositional logic program $P$ may be identified with a $P_fP_f$-coalgebra on the set of atomic propositions in the program. The corresponding $C(P_fP_f)$-coalgebra, where $C(P_fP_f)$ is the cofree comonad on $P_fP_f$, describes…
Large language models (LLMs) are increasingly used for tasks that implicitly reduce to Boolean satisfiability (SAT), yet their reasoning ability on SAT remains unclear. We present a systematic study of LLMs on 2-SAT and 3-SAT, together with…
Chain-of-Thought (CoT) reasoning enhances large language models (LLMs) by decomposing complex problems into step-by-step solutions, improving performance on reasoning tasks. However, current CoT disclosure policies vary widely across…
Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built. This is particularly challenging when…
In applications that use knowledge representation (KR) techniques, in particular those that combine data-driven and logic methods, the domain of objects is not an abstract unstructured domain, but it exhibits a dedicated, deep structure of…
Current Large Language Models (LLMs) exhibit limited ability to understand table structures and to apply precise numerical reasoning, which is crucial for tasks such as table question answering (TQA) and table-based fact verification (TFV).…
Fact Verification requires fine-grained natural language inference capability that finds subtle clues to identify the syntactical and semantically correct but not well-supported claims. This paper presents Kernel Graph Attention Network…