Symmetry in the Euclidean world: Groups of isometries of planar and spatial objects

2017 ◽  
pp. 69-153
Keyword(s):  
Spatial Objects ◽  
Groups Of Isometries

scholarly journals A spatio-temporal specification language and its completeness & decidability

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Tengfei Li ◽  
Jing Liu ◽  
Haiying Sun ◽  
Xiang Chen ◽  
Lipeng Zhang ◽  
...  
Keyword(s):  
Intelligent Transportation System ◽  
Cyber Physical Systems ◽  
Specification Language ◽  
Finite Model ◽  
Critical Systems ◽  
Physical Systems ◽  
Spatial Objects ◽  
Temporal Properties ◽  
Spatio Temporal ◽  
Temporal Specification

AbstractIn the past few years, significant progress has been made on spatio-temporal cyber-physical systems in achieving spatio-temporal properties on several long-standing tasks. With the broader specification of spatio-temporal properties on various applications, the concerns over their spatio-temporal logics have been raised in public, especially after the widely reported safety-critical systems involving self-driving cars, intelligent transportation system, image processing. In this paper, we present a spatio-temporal specification language, STSL PC, by combining Signal Temporal Logic (STL) with a spatial logic S4 u, to characterize spatio-temporal dynamic behaviors of cyber-physical systems. This language is highly expressive: it allows the description of quantitative signals, by expressing spatio-temporal traces over real valued signals in dense time, and Boolean signals, by constraining values of spatial objects across threshold predicates. STSL PC combines the power of temporal modalities and spatial operators, and enjoys important properties such as finite model property. We provide a Hilbert-style axiomatization for the proposed STSL PC and prove the soundness and completeness by the spatio-temporal extension of maximal consistent set and canonical model. Further, we demonstrate the decidability of STSL PC and analyze the complexity of STSL PC. Besides, we generalize STSL to the evolution of spatial objects over time, called STSL OC, and provide the proof of its axiomatization system and decidability.

scholarly journals Kant On Temporal Extension: Embodied, Indexical Idealism

Kant-Studien ◽  
2019 ◽  
Vol 110 (3) ◽  
pp. 498-511
Author(s):  
Truls Wyller
Keyword(s):  
Human Subjects ◽  
Transcendental Idealism ◽  
Spatial Objects ◽  
Temporal Duration ◽  
Kantian View ◽  
Laws Of Motion ◽  
Second Analogy

Abstract I defend what I take to be a genuinely Kantian view on temporal extension: time is not an object but a human horizon of concrete particulars. As such, time depends on the existence of embodied human subjects. It does not, however, depend on those subjects determined as spatial objects. Starting with a realist notion of “apperception” as applied to indexical space (1), I proceed with the need for external criteria of temporal duration (2). In accordance with Kant’s Second Analogy of Experience, these criteria are found in concepts and laws of motion and change (3). I then see what follows from this for a reasonable notion of transcendental idealism (4). Finally, in support of my Kantian conclusions, I argue for the transcendentally subjective nature of particular temporal extension (5).

scholarly journals Order in Space: A General Formalism for Spatial Reasoning

1997 ◽  
Vol 06 (04) ◽  
pp. 423-450 ◽  
Author(s):  
Baher A. El-Geresy ◽  
Alia I. Abdelmoty
Keyword(s):  
Space Dimension ◽  
Spatial Reasoning ◽  
Spatial Information ◽  
Spatial Objects ◽  
Temporal Domain ◽  
Spatial Information Systems ◽  
Connected Set ◽  
General Constraints ◽  
Different Types ◽  
Composition Table

In this paper we propose a general approach for reasoning in space. The approach is composed of a set of two general constraints to govern the spatial relationships between objects in space, and two rules to propagate relationships between those objects. The approach is based on a novel representation of the topology of the space as a connected set of components using a structure called adjacency matrix which can capture the topology of objects of different complexity in any space dimension. The formalism is used to explain spatial compositions resulting in indefinite and definite relations and it is shown to be applicable to reasoning in the temporal domain. The main contribution of the formalism is that it provides means for constructing composition tables for objects with arbitrary complexity in any space dimension. A new composition table between spatial objects of different types is presented. A major advantage of the method is that reasoning between objects of any complexity can be achieved in a defined limited number of steps. Hence, the incorporation of spatial reasoning mechanisms in spatial information systems becomes possible.

scholarly journals Countable groups of isometries on Banach spaces

2010 ◽  
Vol 362 (08) ◽  
pp. 4385-4431 ◽  
Author(s):  
Valentin Ferenczi ◽  
Elói Medina Galego
Keyword(s):  
Banach Spaces ◽  
Groups Of Isometries

scholarly journals Modeling of Agricultural Spatial Objects with Heterogeneous Dynamically Changing Spatial Structure

2018 ◽  
Author(s):  
R V Brezhnev ◽  
◽  
Yu A Maglinets ◽  
K V Raevich ◽  
G M Tsibulski ◽  
...  
Keyword(s):  
Spatial Structure ◽  
Spatial Objects

scholarly journals A Model of Fuzzy Topological Relations for Simple Spatial Objects in GIS

2015 ◽  
Vol 21 (2) ◽  
pp. 389-408
Author(s):  
BO LIU ◽  
DAJUN LI ◽  
JIAN RUAN ◽  
LIBO ZHANG ◽  
LAN YOU ◽  
...  
Keyword(s):  
Fuzzy Topology ◽  
Topological Relations ◽  
Line Segments ◽  
New Model ◽  
Spatial Objects ◽  
Fuzzy Models ◽  
Fuzzy Topological Space ◽  
Fuzzy Objects ◽  
Fuzzy Regions ◽  
Geographic Information Sciences

The goal of this paper is to present a new model of fuzzy topological relations for simple spatial objects in Geographic Information Sciences (GIS). The concept of computational fuzzy topological space is applied to simple fuzzy objects to efficiently and more accurately solve fuzzy topological relations, extending and improving upon previous research in this area. Firstly, we propose a new definition for simple fuzzy line segments and simple fuzzy regions based on computational fuzzy topology. And then, we also propose a new model to compute fuzzy topological relations between simple spatial objects, an analysis of the new model exposes:(1) the topological relations of two simple crisp objects; (2) the topological relations between one simple crisp object and one simple fuzzy object; (3) the topological relations between two simple fuzzy objects. In the end, we have discussed some examples to demonstrate the validity of the new model, through an experiment and comparisons of existing models, we showed that the proposed method can make finer distinctions, as it is more expressive than the existing fuzzy models.

scholarly journals INTEGRATION BETWEEN SURFACE AND SUBSURFACE SPATIAL OBJECTS FOR DEVELOPING OMAN 3D SDI BASED ON THE CITYGML STANDARD

2019 ◽  
Vol XLII-4/W16 ◽  
pp. 79-84
Author(s):  
K. Al Kalbani ◽  
A. Abdul Rahman
Keyword(s):  
Data Structure ◽  
Spatial Data ◽  
3D Model ◽  
Infrastructure Management ◽  
Data Infrastructure ◽  
3D City Models ◽  
Spatial Objects ◽  
The World ◽  
Geospatial Tools ◽  
City Models

Abstract. The paper investigates the capability to integrate the surface and subsurface 3D spatial objects data structure within the 3D spatial data infrastructure (3D SDI) based on the CityGML standards. In fact, a number of countries around the world have started applying the 3D city models for their planning and infrastructure management. While others are still working toward 3D SDI by using CityGML standards. Moreover, most of these initiatives focus on the surface spatial objects with less interest to model subsurface spatial objects. However, dealing with 3D SDI requires both surface and subsurface spatial objects with clear consideration on the issues and challenges in terms of the data structure. On the other hand, the study has used geospatial tools and databases such as FME, PostgreSQL-PostGIS, and 3D City Database to generate the 3D model and to test the capability for integrating the surface and subsurface 3D spatial objects data structure within the 3D SDI. This paper concludes by describing a framework that aims to integrate surface and subsurface 3D geospatial objects data structure in Oman SDI. The authors believe that there are possible solutions based on CityGML standards for surface and subsurface 3D spatial objects. Moreover, solving the issues in data structure can establish a better vision and open new avenues for the 3D SDI.

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