We introduce a novel learning and planning framework that replaces traditional reward-based optimisation with constructive logical inference. In our model, actions, transitions, and goals are represented as logical propositions, and decision-making proceeds by building constructive proofs under intuitionistic logic. This method ensures that state transitions and policies are accepted only when supported by verifiable preconditions -- eschewing probabilistic trial-and-error in favour of guaranteed logical validity. We implement a symbolic agent operating in a structured gridworld, where reaching a goal requires satisfying a chain of intermediate subgoals (e.g., collecting keys to open doors), each governed by logical constraints. Unlike conventional reinforcement learning agents, which require extensive exploration and suffer from unsafe or invalid transitions, our constructive agent builds a provably correct plan through goal chaining, condition tracking, and knowledge accumulation. Empirical comparison with Q-learning demonstrates that our method achieves perfect safety, interpretable behaviour, and efficient convergence with no invalid actions, highlighting its potential for safe planning, symbolic cognition, and trustworthy AI. This work presents a new direction for reinforcement learning grounded not in numeric optimisation, but in constructive logic and proof theory.

As Large Langue Models have been shown to memorize real-world facts, the need to update this knowledge in a controlled and efficient manner arises. Designed with these constraints in mind, Knowledge Editing (KE) approaches propose to alter specific facts in pretrained models. However, they have been shown to suffer from several limitations, including their lack of contextual robustness and their failure to generalize to logical implications related to the fact. To overcome these issues, we propose SAKE, a steering activation method that models a fact to be edited as a distribution rather than a single prompt. Leveraging Optimal Transport, SAKE alters the LLM behavior over a whole fact-related distribution, defined as paraphrases and logical implications. Several numerical experiments demonstrate the effectiveness of this method: SAKE is thus able to perform more robust edits than its existing counterparts.

Large language models (LLMs) have shown significant achievements in solving a wide range of tasks. Recently, LLMs' capability to store, retrieve and infer with symbolic knowledge has drawn a great deal of attention, showing their potential to understand structured information. However, it is not yet known whether LLMs can understand Description Logic (DL) ontologies. In this work, we empirically analyze the LLMs' capability of understanding DL-Lite ontologies covering 6 representative tasks from syntactic and semantic aspects. With extensive experiments, we demonstrate both the effectiveness and limitations of LLMs in understanding DL-Lite ontologies. We find that LLMs can understand formal syntax and model-theoretic semantics of concepts and roles. However, LLMs struggle with understanding TBox NI transitivity and handling ontologies with large ABoxes. We hope that our experiments and analyses provide more insights into LLMs and inspire to build more faithful knowledge engineering solutions.

Knights and knaves problems represent a classic genre of logical puzzles where characters either tell the truth or lie. The objective is to logically deduce each character's identity based on their statements. The challenge arises from the truth-telling or lying behavior, which influences the logical implications of each statement. Solving these puzzles requires not only direct deductions from individual statements, but the ability to assess the truthfulness of statements by reasoning through various hypothetical scenarios. As such, knights and knaves puzzles serve as compelling examples of suppositional reasoning. In this paper, we introduce $\textit{TruthQuest}$, a benchmark for suppositional reasoning based on the principles of knights and knaves puzzles. Our benchmark presents problems of varying complexity, considering both the number of characters and the types of logical statements involved. Evaluations on $\textit{TruthQuest}$ show that large language models like Llama 3 and Mixtral-8x7B exhibit significant difficulties solving these tasks. A detailed error analysis of the models' output reveals that lower-performing models exhibit a diverse range of reasoning errors, frequently failing to grasp the concept of truth and lies. In comparison, more proficient models primarily struggle with accurately inferring the logical implications of potentially false statements.

The runaway train of machine (and deep) learning has, in my opinion, reached an alarming level — alarming in the most negative sense. It is one thing to be excited about a useful technology (say, one…

While knowledge representation and reasoning are considered the keys for human-level artificial intelligence, connectionist networks have been shown successful in a broad range of applications due to their capacity for robust learning and flexible inference under uncertainty. The idea of representing symbolic knowledge in connectionist networks has been well-received and attracted much attention from research community as this can establish a foundation for integration of scalable learning and sound reasoning. In previous work, there exist a number of approaches that map logical inference rules with feed-forward propagation of artificial neural networks (ANN). However, the discriminative structure of an ANN requires the separation of input/output variables which makes it difficult for general reasoning where any variables should be inferable. Other approaches address this issue by employing generative models such as symmetric connectionist networks, however, they are difficult and convoluted. In this paper we propose a novel method to represent propositional formulas in restricted Boltzmann machines which is less complex, especially in the cases of logical implications and Horn clauses. An integration system is then developed and evaluated in real datasets which shows promising results.