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This paper proposes an integration of temporal logical reasoning and Partially Observable Markov Decision Processes (POMDPs) to achieve interpretable decision-making under uncertainty with macro-actions. Our method leverages a fragment of…

With the rapid advancement of mathematical reasoning capabilities in Large Language Models (LLMs), AI systems are increasingly being adopted in educational settings to support students' comprehension of problem-solving processes. However, a…

This paper introduces a notion of generalised geometric logic. Connections of generalised geometric logic with L-topological system and L-topological space are established.

Deficiency in expressive power of the first-order logic has led to developing its numerous extensions by fixed point operators, such as Least Fixed-Point (LFP), inflationary fixed-point (IFP), partial fixed-point (PFP), etc. These logics…

There are many examples of dualities between topological spaces and algebras in the literature. Particularly, many of those examples come from the algebraic counterpart of a logical system, e.g, boolean and heyting algebras, MV-algebras,…

The present work aims to give a unity of logic via standard sequential, unpolarized games. Specifically, our vision is that there must be mathematically precise concepts of linear refinement and intuitionistic restriction of logic such that…

In this paper we show how the theory of monads can be used to deduce in a uniform manner several duality theorems involving categories of relations on one side and categories of algebras with homomorphisms preserving only some operations on…

Multimodal Large Language Models (MLLMs) demonstrate remarkable capabilities but often struggle with complex, multi-step mathematical reasoning, where minor errors in visual perception or logical deduction can lead to complete failure.…

Existing GNN-based Human-Object Interaction (HOI) detection methods rely on simple MLPs to fuse instance features and propagate information. However, this mechanism is largely empirical and lack of targeted information propagation process.…

We offer a simple graphical representation for proofs of intuitionistic logic, which is inspired by proof nets and interaction nets (two formalisms originating in linear logic). This graphical calculus of proofs inherits good features from…

This paper asks whether large language models (LLMs) can be used to study the strategic foundations of conflict and cooperation. I introduce LLMs as experimental subjects in a repeated security dilemma and evaluate whether they reproduce…

Geometric problem solving constitutes a critical branch of mathematical reasoning, requiring precise analysis of shapes and spatial relationships. Current evaluations of geometric reasoning in vision-language models (VLMs) face limitations,…

Graphical user interface (GUI) has become integral to modern society, making it crucial to be understood for human-centric systems. However, unlike natural images or documents, GUIs comprise artificially designed graphical elements arranged…

Multimodal Large Language Models (MLLMs) have achieved remarkable progress but continue to struggle with geometric reasoning, primarily due to the perception bottleneck regarding fine-grained visual elements. While formal languages have…

Scientific reasoning, the process through which humans apply logic, evidence, and critical thinking to explore and interpret scientific phenomena, is essential in advancing knowledge reasoning across diverse fields. However, despite…

Existing open-source multimodal large language models (MLLMs) generally follow a training process involving pre-training and supervised fine-tuning. However, these models suffer from distribution shifts, which limit their multimodal…

Human-Object Interaction (HOI) detection is a longstanding computer vision problem concerned with predicting the interaction between humans and objects. Current HOI models rely on a vocabulary of interactions at training and inference time,…

In the realm of vision-language understanding, the proficiency of models in interpreting and reasoning over visual content has become a cornerstone for numerous applications. However, it is challenging for the visual encoder in Large…

The G\"odel translation provides an embedding of the intuitionistic logic $\mathsf{IPC}$ into the modal logic $\mathsf{Grz}$, which then embeds into the modal logic $\mathsf{GL}$ via the splitting translation. Combined with Solovay's…

Cobordism categories are known to be compact closed. They can therefore be used to define non-degenerate models of multiplicative linear logic by combining the Int construction with double glueing. In this work we detail such construction…