Multi-agent epistemic planning (MEP) is the task of generating action sequences that achieve goals specified over both the physical world and agents’ mental states. It plays an important role in research domains such as game theory, computational economics, and cognitive science. While dynamic epistemic logic (DEL) provides an expressive framework for MEP, it requires complete, model-based specifications of the initial state and action effects, and suffers from undecidability due to the unbounded nesting of beliefs. In this work, we propose a modal variant of the situation calculus that captures much of the expressive power of the DEL approach. Inspired by the cognitive concept Theory of Mind (ToM), we introduce action theories with hierarchical structures, allowing agents to reason about other agents' action theories up to bounded depths. We develop a regression method that reduces reasoning about future states to reasoning about the initial state. By preserving bounded-order ToM throughout the regression process, our approach ensures the decidability of the planning problem. Finally, we propose an algorithm to find the optimal solution, namely, to find the shortest action sequence that achieves the goal.

Logical image understanding involves interpreting and reasoning about the relationships and consistency within an image's visual content. This capability is essential in applications such as industrial inspection, where logical anomaly detection is critical for maintaining high-quality standards and minimizing costly recalls. Previous research in anomaly detection (AD) has relied on prior knowledge for designing algorithms, which often requires extensive manual annotations, significant computing power, and large amounts of data for training. Autoregressive, multimodal Vision Language Models (AVLMs) offer a promising alternative due to their exceptional performance in visual reasoning across various domains. Despite this, their application to logical AD remains unexplored. In this work, we investigate using AVLMs for logical AD and demonstrate that they are well-suited to the task. Combining AVLMs with format embedding and a logic reasoner, we achieve SOTA performance on public benchmarks, MVTec LOCO AD, with an AUROC of 86.0% and an F1-max of 83.7% along with explanations of the anomalies. This significantly outperforms the existing SOTA method by 18.1% in AUROC and 4.6% in F1-max score.

The unification of logic and probability has been seen as a long-standing concern in philosophy and mathematical logic. In this paper, we propose a new general probabilistic modal logic of belief and only-believing in the situation calculus. Our logic can express both continuous and discrete degrees of belief. More importantly, expressing degrees of belief for arbitrary first-order formulas in a dynamic setting is possible for the first time, going well beyond previous proposals where fluents are assumed to be nullary or discrete. We show that our notion of belief retains many of the properties known from the previous related work.