arXiv subjects

Vincenzo Ciancia

Publications and source records attributed to Vincenzo Ciancia.

At least 19 recordsLinked to original sources

arXiv2026

Dynamic Polyhedral Logic

We introduce spatio-temporal polyhedral reachability logics, extending dynamic topological logic with polyhedral semantics and a path-based spatial reachability operator. Formulas are interpreted over polyhedra, with admissible valuations ranging over polyhedral subsets; the spatial modality is interpreted as interior, the binary operator $γ(φ,ψ)$ expresses reachability of a $ψ$-point through a $φ$-region, and the temporal modalities are interpreted by a PL-homeomorphism and its inverse. We define h-dynamic reachability spaces and axiomatize the corresponding h-dynamic extensions of the known reachability logics of topological, finite, Alexandroff, and polyhedral spaces. The main result is soundness and completeness for the intended classes of invertible dynamical systems.

cs.LO↗

arXiv2026

Spatial Model Checking of Images via Minimised Models and Branching Bisimilarity

Spatial models are of increasing interest in traditional computer science domains and beyond. Spatial minimisation procedures are crucial for efficient model checking of such models that are often large in size. For the recent notion of spatial bisimilarity for quasi-discrete closure models, called `Compatible Paths' (CoPa) bisimilarity, an effective minimisation method is proposed, and shown to be correct. Reasoning about space represented by quasi-discrete closure models involves two different conditional reachability modalities: a forward reachability, similar to that used in temporal logic, and a backward modality, representing the fact that a point can be reached from another point, under certain conditions. The core of our minimisation method is the encoding of closure models as labelled transition systems, enabling minimisation algorithms for branching bisimilarity to compute CoPa equivalence classes. A prototype toolchain, VoxMinX, is proposed to validate the minimisation method. VoxMinX preserves the relationship between equivalence classes and sets of pixels in the original image. Experimental validation of the toolchain via benchmark examples demonstrates a promising speed-up in model checking of spatial properties for models of realistic size.

cs.LO↗

arXiv2026

Weak Simplicial Bisimilarity and Minimisation for Polyhedral Model Checking

The work described in this paper builds on the polyhedral semantics of the Spatial Logic for Closure Spaces (SLCS) and the geometric spatial model checker PolyLogicA. Polyhedral models are central in domains that exploit mesh processing, such as 3D computer graphics. A discrete representation of polyhedral models is given by cell poset models, which are amenable to geometric spatial model checking on polyhedral models using the logical language SLCS$η$, a weaker version of SLCS. In this work we show that the mapping from polyhedral models to cell poset models preserves and reflects SLCS$η$. We also propose weak simplicial bisimilarity on polyhedral models and weak $\pm$-bisimilarity on cell poset models, where by ``weak'' we mean that the relevant equivalence is coarser than the corresponding one for SLCS, leading to a greater reduction of the size of models and thus to more efficient model checking. We show that the proposed bisimilarities enjoy the Hennessy-Milner property, i.e. two points are weakly simplicial bisimilar iff they are logically equivalent for SLCS$η$. Similarly, two cells are weakly $\pm$-bisimilar iff they are logically equivalent in the poset-model interpretation of SLCS$η$. Furthermore we present a model minimisation procedure and prove that it correctly computes the minimal model with respect to weak $\pm$-bisimilarity, i.e. with respect to logical equivalence of SLCS$η$. The procedure works via an encoding into LTSs and then exploits branching bisimilarity on those LTSs, exploiting the minimisation capabilities as included in the mCRL2 toolset. Various examples show the effectiveness of the approach.

cs.LO↗

arXiv2025

On Bisimilarity for Quasi-discrete Closure Spaces

Closure spaces, a generalisation of topological spaces, have shown to be a convenient theoretical framework for spatial model checking. The closure operator of closure spaces and quasi-discrete closure spaces induces a notion of neighborhood akin to that of topological spaces that build on open sets. For closure models and quasi-discrete closure models, in this paper we present three notions of bisimilarity that are logically characterised by corresponding modal logics with spatial modalities: (i) CM-bisimilarity for closure models (CMs) is shown to generalise topo-bisimilarity for topological models and to be an instantiation of neighbourhood bisimilarity, when CMs are seen as (augmented) neighbourhood models. CM-bisimilarity corresponds to equivalence with respect to the infinitary modal logic IML that includes the modality ${\cal N}$ for ``being near to''. (ii) CMC-bisimilarity, with `CMC' standing for CM-bisimilarity with converse, refines CM-bisimilarity for quasi-discrete closure spaces, carriers of quasi-discrete closure models. Quasi-discrete closure models come equipped with two closure operators, Direct ${\cal C}$ and Converse ${\cal C}$, stemming from the binary relation underlying closure and its converse. CMC-bisimilarity, is captured by the infinitary modal logic IMLC including two modalities, Direct ${\cal N}$ and Converse ${\cal N}$, corresponding to the two closure operators. (iii) CoPa-bisimilarity on quasi-discrete closure models, which is weaker than CMC-bisimilarity, is based on the notion of compatible paths. The logical counterpart of CoPa-bisimilarity is the infinitary modal logic ICRL with modalities Direct $ζ$ and Converse $ζ$, whose semantics relies on forward and backward paths, respectively. It is shown that CoPa-bisimilarity for quasi-discrete closure models relates to divergence-blind stuttering equivalence for Kripke models.

cs.LO↗

arXiv2025

A Multi-Resolution Benchmark Framework for Spatial Reasoning Assessment in Neural Networks

This paper presents preliminary results in the definition of a comprehensive benchmark framework designed to systematically evaluate spatial reasoning capabilities in neural networks, with a particular focus on morphological properties such as connectivity and distance relationships. The framework is currently being used to study the capabilities of nnU-Net, exploiting the spatial model checker VoxLogicA to generate two distinct categories of synthetic datasets: maze connectivity problems for topological analysis and spatial distance computation tasks for geometric understanding. Each category is evaluated across multiple resolutions to assess scalability and generalization properties. The automated pipeline encompasses a complete machine learning workflow including: synthetic dataset generation, standardized training with cross-validation, inference execution, and comprehensive evaluation using Dice coefficient and IoU (Intersection over Union) metrics. Preliminary experimental results demonstrate significant challenges in neural network spatial reasoning capabilities, revealing systematic failures in basic geometric and topological understanding tasks. The framework provides a reproducible experimental protocol, enabling researchers to identify specific limitations. Such limitations could be addressed through hybrid approaches combining neural networks with symbolic reasoning methods for improved spatial understanding in clinical applications, establishing a foundation for ongoing research into neural network spatial reasoning limitations and potential solutions.

cs.LG↗

arXiv2025

Practical Exploration of Polyhedral Model Checking

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.

cs.LO↗

arXiv2024

Logics of polyhedral reachability

Polyhedral semantics is a recently introduced branch of spatial modal logic, in which modal formulas are interpreted as piecewise linear subsets of an Euclidean space. Polyhedral semantics for the basic modal language has already been well investigated. However, for many practical applications of polyhedral semantics, it is advantageous to enrich the basic modal language with a reachability modality. Recently, a language with an Until-like spatial modality has been introduced, with demonstrated applicability to the analysis of 3D meshes via model checking. In this paper, we exhibit an axiom system for this logic, and show that it is complete with respect to polyhedral semantics. The proof consists of two major steps: First, we show that this logic, which is built over Grzegorczyk's system $\mathsf{Grz}$, has the finite model property. Subsequently, we show that every formula satisfied in a finite poset is also satisfied in a polyhedral model, thereby establishing polyhedral completeness.

cs.LO↗

arXiv2024

Weak Simplicial Bisimilarity for Polyhedral Models and SLCS_eta -- Extended Version

In the context of spatial logics and spatial model checking for polyhedral models -- mathematical basis for visualisations in continuous space -- we propose a weakening of simplicial bisimilarity. We additionally propose a corresponding weak notion of $\pm$-bisimilarity on cell-poset models, a discrete representation of polyhedral models. We show that two points are weakly simplicial bisimilar iff their repesentations are weakly $\pm$-bisimilar. The advantage of this weaker notion is that it leads to a stronger reduction of models than its counterpart that was introduced in our previous work. This is important, since real-world polyhedral models, such as those found in domains exploiting mesh processing, typically consist of large numbers of cells. We also propose SLCS_eta, a weaker version of the Spatial Logic for Closure Spaces (SLCS) on polyhedral models, and we show that the proposed bisimilarities enjoy the Hennessy-Milner property: two points are weakly simplicial bisimilar iff they are logically equivalent for SLCS_eta. Similarly, two cells are weakly $\pm$-bisimilar iff they are logically equivalent in the poset-model interpretation of SLCS_eta. This work is performed in the context of the geometric spatial model checker PolyLogicA and the polyhedral semantics of SLCS.

cs.LO↗

arXiv2022

Geometric Model Checking of Continuous Space

Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed for the topological interpretation of Modal Logic. The Spatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachability connectives that, in turn, can be used for expressing interesting spatial properties, such as "being near to" or "being surrounded by". SLCS constitutes the kernel of a solid logical framework for reasoning about discrete space, such as graphs and digital images, interpreted as quasi discrete closure spaces. Following a recently developed geometric semantics of Modal Logic, we propose an interpretation of SLCS in continuous space, admitting a geometric spatial model checking procedure, by resorting to models based on polyhedra. Such representations of space are increasingly relevant in many domains of application, due to recent developments of 3D scanning and visualisation techniques that exploit mesh processing. We introduce PolyLogicA, a geometric spatial model checker for SLCS formulas on polyhedra and demonstrate feasibility of our approach on two 3D polyhedral models of realistic size. Finally, we introduce a geometric definition of bisimilarity, proving that it characterises logical equivalence.

cs.LO↗

arXiv2021

On Bisimilarities for Closure Spaces - Preliminary Version

Closure spaces are a generalisation of topological spaces obtained by removing the idempotence requirement on the closure operator. We adapt the standard notion of bisimilarity for topological models, namely Topo-bisimilarity, to closure models -- we call the resulting equivalence CM-bisimilarity -- and refine it for quasi-discrete closure models. We also define two additional notions of bisimilarity that are based on paths on space, namely Path-bisimilarity and Compatible Path-bisimilarity, CoPa-bisimilarity for short. The former expresses (unconditional) reachability, the latter refines it in a way that is reminishent of Stuttering Equivalence on transition systems. For each bisimilarity we provide a logical characterisation, using variants of the Spatial Logic for Closure Spaces (SLCS). We also address the issue of (space) minimisation via the three equivalences.

cs.LO↗

arXiv2020

Using Spatial Logic and Model Checking for Nevus Segmentation

Spatial and spatio-temporal model checking techniques have a wide range of application domains, among which large scale distributed systems and signal and image analysis. In the latter domain, automatic and semi-automatic contouring in Medical Imaging has shown to be a very promising and versatile application that can greatly facilitate the work of professionals in this domain, while supporting explainability, easy replicability and exchange of medical image analysis methods. In recent work we have applied this model-checking technique to the (3D) contouring of tumours and related oedema in magnetic resonance images of the brain. In the current work we address the contouring of (2D) images of nevi. One of the challenges of treating nevi images is their considerable inhomogeneity in shape, colour, texture and size. To deal with this challenge we use a texture similarity operator, in combination with spatial logic operators. We apply our technique on images of a large public database and compare the results with associated ground truth segmentation provided by domain experts.

cs.LO↗

arXiv2020

A spatial model checker in GPU (extended version)

The tool voxlogica merges the state-of-the-art library of computational imaging algorithms ITK with the combination of declarative specification and optimised execution provided by spatial logic model checking. The analysis of an existing benchmark for segmentation of brain tumours via a simple logical specification reached state-of-the-art accuracy. We present a new, GPU-based version of voxlogica and discuss its implementation, scalability, and applications.

cs.LO↗

arXiv2020

Towards Spatial Bisimilarity for Closure Models: Logical and Coalgebraic Characterisations

The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial structures, such as finite graphs and digital images, with applications in various case studies including medical image analysis. These recent developments required a generalisation step, from topological spaces to closure spaces. In this work we initiate the study of bisimilarity and minimisation algorithms that are consistent with the closure spaces semantics. For this purpose we employ coalgebraic models. We present a coalgebraic definition of bisimilarity for quasi-discrete models, which is adequate with respect to a spatial logic with reachability operators, complemented by a free and open-source minimisation tool for finite models. We also discuss the non-quasi-discrete case, by providing a generalisation of the well-known set-theoretical notion of topo-bisimilarity, and a categorical definition, in the same spirit as the coalgebraic rendition of neighbourhood frames, but employing the covariant power set functor, instead of the contravariant one. We prove its adequacy with respect to infinitary modal logic.

cs.LO↗

arXiv2018

VoxLogicA: a Spatial Model Checker for Declarative Image Analysis (Extended Version)

Spatial and spatio-temporal model checking techniques have a wide range of application domains, among which large scale distributed systems and signal and image analysis. We explore a new domain, namely (semi-)automatic contouring in Medical Imaging, introducing the tool VoxLogicA which merges the state-of-the-art library of computational imaging algorithms ITK with the unique combination of declarative specification and optimised execution provided by spatial logic model checking. The result is a rapid, logic based analysis development methodology. The analysis of an existing benchmark of medical images for segmentation of brain tumours shows that simple VoxLogicA analysis can reach state-of-the-art accuracy, competing with best-in-class algorithms, with the advantage of explainability and replicability. Furthermore, due to a two-orders-of-magnitude speedup compared to the existing general-purpose spatio-temporal model checker topochecker, VoxLogicA enables interactive development of analysis of 3D medical images, which can greatly facilitate the work of professionals in this domain.

cs.LO↗

arXiv2018

Spatial Logics and Model Checking for Medical Imaging (Extended Version)

Recent research on spatial and spatio-temporal model checking provides novel image analysis methodologies, rooted in logical methods for topological spaces. Medical Imaging (MI) is a field where such methods show potential for ground-breaking innovation. Our starting point is SLCS, the Spatial Logic for Closure Spaces -- Closure Spaces being a generalisation of topological spaces, covering also discrete space structures -- and topochecker, a model-checker for SLCS (and extensions thereof). We introduce the logical language ImgQL ("Image Query Language"). ImgQL extends SLCS with logical operators describing distance and region similarity. The spatio-temporal model checker topochecker is correspondingly enhanced with state-of-the-art algorithms, borrowed from computational image processing, for efficient implementation of distancebased operators, namely distance transforms. Similarity between regions is defined by means of a statistical similarity operator, based on notions from statistical texture analysis. We illustrate our approach by means of two examples of analysis of Magnetic Resonance images: segmentation of glioblastoma and its oedema, and segmentation of rectal carcinoma.

cs.LO↗

arXiv2016

Model Checking Spatial Logics for Closure Spaces

Spatial aspects of computation are becoming increasingly relevant in Computer Science, especially in the field of collective adaptive systems and when dealing with systems distributed in physical space. Traditional formal verification techniques are well suited to analyse the temporal evolution of programs; however, properties of space are typically not taken into account explicitly. We present a topology-based approach to formal verification of spatial properties depending upon physical space. We define an appropriate logic, stemming from the tradition of topological interpretations of modal logics, dating back to earlier logicians such as Tarski, where modalities describe neighbourhood. We lift the topological definitions to the more general setting of closure spaces, also encompassing discrete, graph-based structures. We extend the framework with a spatial surrounded operator, a propagation operator and with some collective operators. The latter are interpreted over arbitrary sets of points instead of individual points in space. We define efficient model checking procedures, both for the individual and the collective spatial fragments of the logic and provide a proof-of-concept tool.

cs.LO↗

arXiv2016

Nominal Cellular Automata

The emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their computational capabilities, with a special focus on the emergent behavioural properties of this new model and their significance in the context of computation-oriented interpretations of physical phenomena. A preliminary investigation of the relations between Nominal Cellular Automata and Wolfram's Elementary Cellular Automata is also carried out.

cs.FL↗

arXiv2016

From Collective Adaptive Systems to Human Centric Computation and Back: Spatial Model Checking for Medical Imaging

Recent research on formal verification for Collective Adaptive Systems (CAS) pushed advancements in spatial and spatio-temporal model checking, and as a side result provided novel image analysis methodologies, rooted in logical methods for topological spaces. Medical Imaging (MI) is a field where such technologies show potential for ground-breaking innovation. In this position paper, we present a preliminary investigation centred on applications of spatial model checking to MI. The focus is shifted from pure logics to a mixture of logical, statistical and algorithmic approaches, driven by the logical nature intrinsic to the specification of the properties of interest in the field. As a result, novel operators are introduced, that could as well be brought back to the setting of CAS.

cs.LO↗