Practical Exploration of Polyhedral Model Checking

2025-06-25

AI Summary

This work addresses the challenge of verifying spatial properties of polyhedral models (e.g., triangular/tetrahedral meshes). We propose an enhanced model-checking approach based on the spatial logic SLCS. Our method treats model-checking outcomes as atomic propositions fed back into the original model, enabling semantic enrichment and structural minimization. This feedback loop significantly reduces the length of subsequent spatial property specification formulas and uncovers implicit spatial structural features. Grounded in closure-space semantics, the approach is implemented within the PolyLogicA model checker and integrated with PolyVisualizer for intuitive, semantically faithful visualization. Experimental evaluation demonstrates that our technique preserves formal rigor while improving both the efficiency and interpretability of spatial analysis. It establishes a novel paradigm for automated verification and visualization in computer graphics and geometric modeling.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Computer Vision: Visual Reasoning & Symbolic Representations

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

This work explores the potential of spatial model checking of polyhedral models on a number of selected examples. In computer graphics polyhedral models can be found in the form of triangular surface meshes of tetrahedral volume meshes which are abundant. Spatial model checking is used to analyse spatial properties of interest of such models expressed in a suitable spatial logic. The original contributions of this paper are twofold. First we illustrate how a polyhedral model can be enriched by adding the outcome of one model checking session as an atomic proposition to the original model. This is useful as it provides a way to reduce the length of formulas to check on such models and to obtain more insightful results when these models are used for graphical visualisation. Second we show that this form of enrichment also enables practical model minimisation providing deeper insights in the basic spatial structure of the model in terms of the spatial logic properties it enjoys. This work is performed in the context of the geometric spatial model checker PolyLogicA, the visualizer PolyVisualizer and the polyhedral semantics of the Spatial Logic for Closure Spaces SLCS.

Problem

• Explores spatial model checking for polyhedral models
• Enriches models with model checking outcomes for insights
• Enables model minimization to understand spatial structure

Innovation

• Enriching polyhedral models with model checking outcomes
• Reducing formula length for insightful visualization
• Enabling practical model minimization via enrichment