Related papers: Geometric Model Checking of Continuous Space
We introduce MCMAS-SLK, a BDD-based model checker for the verification of systems against specifications expressed in a novel, epistemic variant of strategy logic. We give syntax and semantics of the specification language and introduce a…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We overview the theory of classical MDS, along with its…
We introduce a hybrid spatiotemporal logic for automotive safety applications (HSTL), focused on highway driving. Spatiotemporal logic features specifications about vehicles throughout space and time, while hybrid logic enables precise…
This paper explores the spatial reasoning capability of large language models (LLMs) over textual input through a suite of five tasks aimed at probing their spatial understanding and computational abilities. The models were tested on both…
Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. They have been used to reason about beliefs, lies, and group epistemic behaviour inspired by social…
Geometric Problem Solving (GPS) poses a unique challenge for Multimodal Large Language Models (MLLMs), requiring not only the joint interpretation of text and diagrams but also iterative visuospatial reasoning. While existing approaches…
The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in…
Empowered by large-scale training, vision-language models (VLMs) achieve strong image and video understanding, yet their ability to perform spatial reasoning in both static scenes and dynamic videos remains limited. Recent advances try to…
Finiteness spaces constitute a categorical model of Linear Logic (LL) whose objects can be seen as linearly topologised spaces, (a class of topological vector spaces introduced by Lefschetz in 1942) and morphisms as continuous linear maps.…
We survey existing approaches to the formal verification of statecharts using model checking. Although the semantics and subset of statecharts used in each approach varies considerably, along with the model checkers and their specification…
Multimodal large language models (MLLMs) have achieved significant progress in image and language tasks due to the strong reasoning capability of large language models (LLMs). Nevertheless, most MLLMs suffer from limited spatial reasoning…
The standard model of cosmology ($\Lambda$CDM) is facing a serious crisis caused by the inconsistencies in the measurements of some fundamental cosmological parameters (Hubble constant $H_{0}$ and cosmic curvature parameter $\Omega_{k}$ for…
Closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have…
Many embedded and real-time systems have a inherent probabilistic behaviour (sensors data, unreliable hardware,...). In that context, it is crucial to evaluate system properties such as "the probability that a particular hardware fails".…
In the recent work [Metrically round and sleek metric spaces, \emph{The Journal of Analysis} (2022), pp 1--17], the authors proved some results on metrically round and sleek linear metric spaces and metric spaces. In continuation, the…
Vision-Language Models (VLMs) have recently witnessed significant progress in visual comprehension. As the permitting length of image context grows, VLMs can now comprehend a broader range of views and spaces. Current benchmarks provide…
Recent advancements in Multimodal Large Language Models (MLLMs) have significantly enhanced performance on 2D visual tasks. However, improving their spatial intelligence remains a challenge. Existing 3D MLLMs always rely on additional 3D or…
Vision-Language Models (VLMs) have been increasingly applied in real-world scenarios due to their outstanding understanding and reasoning capabilities. Although VLMs have already demonstrated impressive capabilities in common visual…
Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its distinguished subcategories (such as the one of compact spaces).…
Camera-based Semantic Scene Completion (SSC) is gaining attentions in the 3D perception field. However, properties such as perspective and occlusion lead to the underestimation of the geometry in distant regions, posing a critical issue for…