Chess, one of the oldest and most universally played board games, presents an ideal testbed due to the wealth of both policy data and language data. In terms of policy data, it is reported that over ten million games are played daily on Chess.com, the most frequented online chess platform.

We further transfer those PGNs into text which helps us build mixed game-language datasets from these sources.

Three Chinese nationals have been arrested in Georgia on suspicion of attempting to illegally purchase 2kg of uranium. Lasha Maghradze, deputy head of the nation's State Security Service (SSG), told a news briefing the group planned to pay $400,000 (£300,570) for the nuclear material in the capital, Tblisi, before transporting it to China via Russia. The alleged plot was unearthed by intelligence agents while one member of the group was attempting to buy the radioactive substance on the black market, he said. The three pleaded not guilty at a court in Tblisi and have been placed in custody to prevent them fleeing the country, according to public broadcaster Georgia Today. They face up to five years in prison under a provision of Georgia's criminal code banning the purchasing of nuclear material.

As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based problem-solving agents, the demand for process-level verifiability is rapidly increasing yet underexplored. To fill these gaps, we present a principled formulation of problem-solving as a deterministic Markov decision process; a novel framework, FPS (Formal Problem-Solving), which utilizes existing FTP (formal theorem proving) environments to perform process-verified problem-solving; and D-FPS (Deductive FPS), decoupling solving and answer verification for better human-alignment. The expressiveness, soundness and completeness of the frameworks are proven. We construct three benchmarks on problem-solving: FormalMath500, a formalization of a subset of the MATH500 benchmark; MiniF2F-Solving and PutnamBench-Solving, adaptations of FTP benchmarks MiniF2F and PutnamBench. For faithful, interpretable, and human-aligned evaluation, we propose RPE (Restricted Propositional Equivalence), a symbolic approach to determine the correctness of answers by formal verification. We evaluate four prevalent FTP models and two prompting methods as baselines, solving at most 23.77% of FormalMath500, 27.47% of MiniF2F-Solving, and 0.31% of PutnamBench-Solving.

The study of propositional logic -- fundamental to the theory of computing -- is a cornerstone of the undergraduate computer science curriculum. Learning to solve logical proofs requires repeated guided practice, but undergraduate students often lack access to on-demand tutoring in a judgment-free environment. In this work, we highlight the need for guided practice tools in undergraduate mathematics education and outline the desiderata of an effective practice tool. We accordingly develop LogicLearner, a web application for guided logic proof practice. LogicLearner consists of an interface to attempt logic proofs step-by-step and an automated proof solver to generate solutions on the fly, allowing users to request guidance as needed. We pilot LogicLearner as a practice tool in two semesters of an undergraduate discrete mathematics course and receive strongly positive feedback for usability and pedagogical value in student surveys. To the best of our knowledge, LogicLearner is the only learning tool that provides an end-to-end practice environment for logic proofs with immediate, judgment-free feedback.

Computational Social Science (CSS) is an emerging field driven by the unprecedented availability of human-generated content for researchers. This field, however, presents a unique set of challenges due to the nature of the theories and datasets it explores, including highly subjective tasks and complex, unstructured textual corpora. Among these challenges, one of the less well-studied topics is the pervasive presence of noise. This thesis aims to address this gap in the literature by presenting a series of interconnected case studies that examine different manifestations of noise in CSS. These include character-level errors following the OCR processing of historical records, archaic language, inconsistencies in annotations for subjective and ambiguous tasks, and even noise and biases introduced by large language models during content generation. This thesis challenges the conventional notion that noise in CSS is inherently harmful or useless. Rather, it argues that certain forms of noise can encode meaningful information that is invaluable for advancing CSS research, such as the unique communication styles of individuals or the culture-dependent nature of datasets and tasks. Further, this thesis highlights the importance of nuance in dealing with noise and the considerations CSS researchers must address when encountering it, demonstrating that different types of noise require distinct strategies.

Current LLM pipelines account for only one possible tokenization for a given string, ignoring exponentially many alternative tokenizations during training and inference. For example, the standard Llama3 tokenization of penguin is [p,enguin], yet [peng,uin] is another perfectly valid alternative. In this paper, we show that despite LLMs being trained solely on one tokenization, they still retain semantic understanding of other tokenizations, raising questions about their implications in LLM safety. Put succinctly, we answer the following question: can we adversarially tokenize an obviously malicious string to evade safety and alignment restrictions? We show that not only is adversarial tokenization an effective yet previously neglected axis of attack, but it is also competitive against existing state-of-the-art adversarial approaches without changing the text of the harmful request. We empirically validate this exploit across three state-of-the-art LLMs and adversarial datasets, revealing a previously unknown vulnerability in subword models.

Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various automated reasoning tools in recent years. This paper presents a recipe for the simultaneous deployment of different forms of deep and shallow embeddings in classical higher-order logic, enabling not only flexible interactive and automated theorem proving and counterexample finding at meta and object level, but also automated faithfulness proofs between the logic embeddings. The approach, which is fruitful for logic education, research and application, is deliberately illustrated here using simple propositional modal logic. However, the work presented is conceptual in nature and not limited to such a simple logic context. Keywords: Logic embeddings Faithfulness Automated Reasoning 1 Motivation and Introduction Deep embeddings of logics, or more generally of domain-specific languages, in a suitable metalogic, such as the classical higher-order logic (HOL) [23,4], are typically based on explicitly introduced abstract data types that essentially axioma-tize the inductively defined character of the new language.