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Formal Verification of a Topological Spatial Relations Model for Geographic Information Systems in Coq

https://doi.org/10.3390/math11051079
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/3-540-45949-9openalex-snapshot
Isabelle/HOL: A Proof Assistant for Higher-Order Logic
inferredcites →https://doi.org/10.1007/978-3-319-20615-8_17openalex-snapshot
Mizar: State-of-the-art and Beyond
inferredcites →https://doi.org/10.1007/978-3-642-39634-2_14openalex-snapshot
A Machine-Checked Proof of the Odd Order Theorem
inferredcites →https://doi.org/10.1007/978-3-642-61701-0openalex-snapshot
General Topology
inferredcites →https://doi.org/10.1007/978-3-662-07964-5openalex-snapshot
Interactive Theorem Proving and Program Development
inferredcites →https://doi.org/10.1007/978-981-19-2456-9_21openalex-snapshot
A Formalization of Topological Spaces in Coq
inferredcites →https://doi.org/10.1007/s00500-022-07627-2openalex-snapshot
Approximation operators and accuracy measures of rough sets from an infra-topology view
inferredcites →https://doi.org/10.1007/s10462-022-10346-7openalex-snapshot
Rough sets models inspired by supra-topology structures
inferredcites →https://doi.org/10.1007/s10817-009-9155-4openalex-snapshot
A Formally Verified Compiler Back-end
inferredcites →https://doi.org/10.1016/j.hm.2008.01.001openalex-snapshot
The emergence of open sets, closed sets, and limit points in analysis and topology
inferredcites →https://doi.org/10.1016/s0049-237x(08)71114-5openalex-snapshot
Elements of Recursion Theory
inferredcites →https://doi.org/10.1017/fmp.2017.1openalex-snapshot
A FORMAL PROOF OF THE KEPLER CONJECTURE
inferredcites →https://doi.org/10.1080/02693799108927841openalex-snapshot
Point-set topological spatial relations
inferredcites →https://doi.org/10.1080/10106049.2019.1622602openalex-snapshot
A hybrid GIS-assisted framework to integrate Dempster–Shafer theory of evidence and fuzzy sets in risk analysis: an application in hydrocarbon exploration
inferredcites →https://doi.org/10.1080/13658810600894323openalex-snapshot
Formalizing natural‐language spatial relations between linear objects with topological and metric properties
inferredcites →https://doi.org/10.1080/13658810802001305openalex-snapshot
Topological feature vectors for exploring topological relationships
inferredcites →https://doi.org/10.1080/13658816.2012.739691openalex-snapshot
A formalization for semantic location granules
inferredcites →https://doi.org/10.1080/13658816.2022.2119476openalex-snapshot
Research themes of geographical information science during 1991–2020: a retrospective bibliometric analysis
inferredcites →https://doi.org/10.1080/15230406.2015.1088798openalex-snapshot
Modeling spatiotemporal topological relationships between moving object trajectories along road networks based on region connection calculus
inferredcites →https://doi.org/10.1080/15230406.2022.2104377openalex-snapshot
Topological relationship model for geographical flows
inferredcites →https://doi.org/10.1112/s1461157000000449openalex-snapshot
The Relative Consistency of the Axiom of Choice Mechanized Using Isabelle⁄zf
inferredcites →https://doi.org/10.1145/2591012openalex-snapshot
Formally verified mathematics
inferredcites →https://doi.org/10.1145/2993600.2993611openalex-snapshot
Formal Verification of Smart Contracts
inferredcites →https://doi.org/10.1145/3110268openalex-snapshot
Kami: a platform for high-level parametric hardware specification and its modular verification
inferredcites →https://doi.org/10.1145/3479645.3479683openalex-snapshot
A Conceptual Framework for Uncertainty Analysis in Map-Based Urban Spatial Planning
inferredcites →https://doi.org/10.1155/2022/5553774openalex-snapshot
A Formal Representation of the Semantics of Structural Geological Models
inferredcites →https://doi.org/10.3390/electronics9020255openalex-snapshot
A Formal Verification Framework for Security Issues of Blockchain Smart Contracts
inferredcites →https://doi.org/10.3390/ijgi11040218openalex-snapshot
A Generalized 9-Intersection Model for Topological Relations between Regions with Holes
inferredcites →https://doi.org/10.3390/math9010038openalex-snapshot
Formalization of the Equivalence among Completeness Theorems of Real Number in Coq
inferredcites →https://doi.org/10.3390/math9121377openalex-snapshot
Formalizing Calculus without Limit Theory in Coq
inferredcites →https://doi.org/10.48550/arxiv.0905.3713openalex-snapshot
A formal proof of the four color theorem
inferredcites →https://doi.org/10.7551/mitpress/9153.001.0001openalex-snapshot
Certified Programming with Dependent Types

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1007/s11424-026-5318-1openalex-snapshot
A Comparative Review of ZFC, NBG, and MK Axiom Systems: Theoretical Foundations and Formalization in Coq
inferred← citeshttps://doi.org/10.1016/j.dajour.2023.100353openalex-snapshot
A quantitative fuzzy-valued intersection matrix for obtaining fuzzy relationships between vague spatial objects
inferred← citeshttps://doi.org/10.1109/access.2025.3552634openalex-snapshot
A Review on Mechanical Proving and Formalization of Mathematical Theorems
inferred← citeshttps://doi.org/10.1155/ijmm/2123865openalex-snapshot
Counterpart of Boundary Topological Operators Within the Framework of Primal Topological Spaces
inferred← citeshttps://doi.org/10.1155/jom/3550345openalex-snapshot
Properties of Supra Equivalent Subsets and Their Applications via Supra R 0 Spaces
inferred← citeshttps://doi.org/10.1155/jom/8990430openalex-snapshot
Applications of δ ‐Open Sets via Separation Axioms, Covering Properties, and Rough Set Models
inferred← citeshttps://doi.org/10.22436/jmcs.031.03.02openalex-snapshot
Generalized π -weak closed sets and some applications on weak structures
inferred← citeshttps://doi.org/10.22436/jmcs.034.03.01openalex-snapshot
Introduction to temporal topology
inferred← citeshttps://doi.org/10.22436/jmcs.035.02.01openalex-snapshot
Supra finite soft-open sets and applications to operators and continuity
inferred← citeshttps://doi.org/10.3390/math11122757openalex-snapshot
A Machine Proof System of Point Geometry Based on Coq
inferred← citeshttps://doi.org/10.3390/math11224567openalex-snapshot
A Formal Representation for Intelligent Decision-Making in Games
inferred← citeshttps://doi.org/10.3934/math.2024758openalex-snapshot
Topologically indistinguishable relations and separation axioms
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