Large language models (LLMs) have achieved impressive progress in natural language processing tasks but still struggle with complex logical reasoning. We observe that in propositional logic question-answering (QA), LLMs' performance varies with the order of training samples during fine-tuning. Motivated by this, we propose a data-driven approach to automatically determine the fine-tuning sample order, enhancing the logical QA performance of LLMs. Specifically, we first quantify the logical reasoning complexity of propositional reasoning samples and then stratify the training data into several subsets of ascending complexity. Subsequently, we fine-tune the LLMs on these subsets, progressing from low to high reasoning complexity. Experimental results demonstrate that our approach outperforms single-stage fine-tuning baselines across diverse reasoning benchmarks.

Large language models (LLMs) have achieved remarkable successes on various tasks. However, recent studies have found that there are still significant challenges to the logical reasoning abilities of LLMs, which can be categorized into the following two aspects: (1) Logical question answering: LLMs often fail to generate the correct answer within a complex logical problem which requires sophisticated deductive, inductive or abductive reasoning given a collection of premises and constrains. (2) Logical consistency: LLMs are prone to producing responses contradicting themselves across different questions. For example, a state-of-the-art question-answering LLM Macaw, answers Yes to both questions Is a magpie a bird? and Does a bird have wings? but answers No to Does a magpie have wings?. To facilitate this research direction, we comprehensively investigate the most cutting-edge methods and propose a detailed taxonomy. Specifically, to accurately answer complex logic questions, previous methods can be categorized based on reliance on external solvers, prompts, and fine-tuning. To avoid logical contradictions, we discuss concepts and solutions of various logical consistencies, including implication, negation, transitivity, factuality consistencies, and their composites. In addition, we review commonly used benchmark datasets and evaluation metrics, and discuss promising research directions, such as extending to modal logic to account for uncertainty and developing efficient algorithms that simultaneously satisfy multiple logical consistencies.

New perspectives keep emerging in the logical study of social interactions, witnessed by yet another collection of research papers. Once our focus of reasoning shifts from an individual to a social setting, interesting issues naturally arise. The central question is the following: how is an individual’s attitude related to that of others and that of a group, especially when we take into account the informative communication between agents, as well as the structures of a group? This has been studied to various extent in social epistemology, social choice theory, social norms theory, etc. In this context, our main concern is logic: how can a logical approach shed light on our reasoning about these scenarios? We are not giving a comprehensive overview but just to mention some research that is mostly relevant. Communication between agents, public or private, has been extensively studied in dynamic epistemic logic (e.g. [1, 9, 10]) and dynamic epistemic logic has become a standard methodology in modelling dynamical changes of agent’s attitudes. Social network logics have been developed recently, adding social structures of a group as a core component to logic models and formal languages [2, 5–8, 11]. The papers included in this special issue provide us with further new insights about our understanding of social settings. In what follows, we briefly summarize their ideas and some main results.

An unrealistic assumption in classical extensive game theory is that the complete game tree is fully perceivable by all players. To weaken this assumption, a class of games (called games with short sight) was proposed in literature, modelling the game scenarios where players have only limited fores ight of the game tree due to bounded resources and limited computational ability. As a consequence, the notions of equilibria in classical game theory were refined to fit games with short sight. A crucial issue that thus arises is to determine whether a strategy profile is a solution to a game. To study this issue and address the underlying idea and theory on players’ decisions in such games, we adopt a logical way. Specifically, we develop a logic called DLS through which features of these games are demonstrated. More importantly, it enables us to characterize the solutions to these games via formulas of this logic. Moreover, we study the algorithm for model checking DLS, which is shown to be PTIME-complete in the size of the model. This work not only provides an insight into a more realistic model in game theory, but also enriches the possible applications of logic.

In this article, we study a minimal change approach to preference dynamics. We treat a set of preferences as a special kind of theory, and define minimal change preference contraction and revision operations in the spirit of the Alchourrón, Gärdenfors, and Makinson theory of belief revision. We characterise minimal contraction of preference sets by a set of postulates and prove a representation theorem. We also give a linear time algorithm which implements minimal contraction by a single preference. We then define minimal contraction by a set of preferences, and show that the problem of a minimal contraction by a set of preferences is NP-hard.