Related papers: Geometric Model Checking of Continuous Space
Humans possess spatial reasoning abilities that enable them to understand spaces through multimodal observations, such as vision and sound. Large multimodal reasoning models extend these abilities by learning to perceive and reason, showing…
We introduce FloorplanQA, a diagnostic benchmark for evaluating spatial reasoning in large language models (LLMs). FloorplanQA is grounded in structured representations of indoor scenes, such as (e.g., kitchens, living rooms, bedrooms,…
Most CAD or other spatial data models, in particular boundary representation models, are called "topological" and represent spatial data by a structured collection of "topological primitives" like edges, vertices, faces, and volumes. These…
We report on COOL-MC, a model checking tool for fixpoint logics that is parametric in the branching type of models (nondeterministic, game-based, probabilistic etc.) and in the next-step modalities used in formulae. The tool implements…
Hyperproperties have shown to be a powerful tool for expressing and reasoning about information-flow security policies. In this paper, we investigate the problem of statistical model checking (SMC) for hyperproperties. Unlike exhaustive…
We study the Scalar Field Cosmology (SFC) using the geometric language of the phase space. We define and study an ensemble of dynamical systems as a Banach space with a Sobolev metric. The metric in the ensemble is used to measure a…
The ability to understand and reason about spatial relationships between objects in images is an important component of visual reasoning. This skill rests on the ability to recognize and localize objects of interest and determine their…
This paper presents a transformational approach for model checking two important classes of metric temporal logic (MTL) properties, namely, bounded response and minimum separation, for nonhierarchical object-oriented Real-Time Maude…
Scalar field comparison is a fundamental task in scientific visualization. In topological data analysis, we compare topological descriptors of scalar fields -- such as persistence diagrams and merge trees -- because they provide succinct…
Graded path modalities count the number of paths satisfying a property, and generalize the existential (E) and universal (A) path modalities of CTL*. The resulting logic is called GCTL*. We settle the complexity of satisfiability of GCTL*,…
3D spatial reasoning is the ability to analyze and interpret the positions, orientations, and spatial relationships of objects within the 3D space. This allows models to develop a comprehensive understanding of the 3D scene, enabling their…
We introduce a machine learning approach to model checking temporal logic, with application to formal hardware verification. Model checking answers the question of whether every execution of a given system satisfies a desired temporal logic…
The molecular computing has been successfully employed to solve more and more complex computation problems. However, as an important complex problem, the model checking are still far from fully resolved under the circumstance of molecular…
In this paper we explore the use of spatial clustering algorithms as a new computational approach for modeling the cosmic web. We demonstrate that such algorithms are efficient in terms of computing time needed. We explore three distinct…
Large Language Models (LLMs) have demonstrated unprecedented capabilities across various natural language processing tasks. Their ability to process and generate viable text and code has made them ubiquitous in many fields, while their…
Although Multimodal Large Language Models have achieved remarkable progress, they still struggle with complex 3D spatial reasoning due to the reliance on 2D visual priors. Existing approaches typically mitigate this limitation either…
Spatial reasoning is a key aspect of cognitive psychology and remains a bottleneck for current vision-language models (VLMs). While extensive research has aimed to evaluate or improve VLMs' understanding of basic spatial relations, such as…
Large language models (LLMs) generalize smoothly across continuous semantic spaces, yet strict logical reasoning demands the formation of discrete decision boundaries. Prevailing theories relying on linear isometric projections fail to…
This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…
Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis…