A Formal Approach to Qualitative Reasoning on Topological Properties of Networks (original) (raw)

Qualitative and Topological Relationships

1993

In this paper, we present a spatial logic which can be used to reason about topological and spatial relationships among objects in spatial databases. The main advantages of such a formalism are its rigorousness, clear semantics and sound inference mechanism. We also show how the formalism can be extended to include orientation and metrical information. Comparisons with other formalisms are discussed. 10 The fourth of these axioms is dierent to our previous publication (Randell, Cui and Cohn 1992), as we have recently discovered a counterexample to the old axiom { originally the axiom was 8x8y[[P(x;conv(y))^P(y;conv(x))] ! O(x; y)]. Also, it should be noted that whereas we previously assumed (eg Randell, Cui and Cohn 1992) that conv is only well sorted when dened on one piece regions, we have now dropped this restriction since on consideration the axioms for conv are also clearly true for non one piece regions.

On the relationships between topological measures in real-world networks

Networks and Heterogeneous Media, 2008

Over the past several years, a number of measures have been introduced to characterize the topology of complex networks. We perform a statistical analysis of real data sets, representing the topology of different realworld networks. First, we show that some measures are either fully related to other topological measures or that they are significantly limited in the range of their possible values. Second, we observe that subsets of measures are highly correlated, indicating redundancy among them. Our study thus suggests that the set of commonly used measures is too extensive to concisely characterize the topology of complex networks. It also provides an important basis for classification and unification of a definite set of measures that would serve in future topological studies of complex networks.

Qualitative and Topological Relationships in Spatial Databases

Symposium on Large Spatial Databases, 1993

In this paper, we present a spatial logic which can be used to reason about topological and spatial relationships among objects in spatial databases. The main advantages of such a formalism are its rigorousness, clear semantics and sound inference mechanism. We also show how the formalism can be extended to include orientation and metrical information. Comparisons with other formalisms are discussed.

TOPOLOGY AND THE INFORMATION STRUCTURING

In this paper, we aim at a dynamical, structurally-phenomenological approach, from a multidisciplinary point of view, starting from today's information technology and from the last theories of the second half of the 20 th century, which are connected to non-linear dynamics, fractal geometry, topology and complex systems theory. Shannon and Weaver's information theory grasps only the quantitative aspect, through associating information to entropy and the second law of thermodynamics, so that only artificial languages and information technology finally implement the qualitative aspect of information. The proof that information is involved in all the processes, at all scales and levels of reality, is the very difficulty of defining information. The network topology, just as the knot theory in the information technology, highlight an apparently surprising aspect, that is, topology is the suitable mathematical instrument for formalizing information. Topology of information might represent the modality of grasping information in its qualitative form, as the way to unify reality, and reality with cognition, through information.

Expressing topological connectivity of spatial databases

Lecture Notes in Computer Science, 2000

We consider two-dimensional spatial databases defined in terms of polynomial inequalities and focus on the potential of programming languages for such databases to express queries related to topological connectivity. It is known that the topological connectivity test is not first-order expressible. One approach to obtain a language in which connectivity queries can be expressed would be to extend FO+Poly with a generalized (or Lindström) quantifier expressing that two points belong to the same connected component of a given database. For the expression of topological connectivity, extensions of first-order languages with recursion have been studied (in analogy with the classical relational model). Two such languages are spatial Datalog and FO+Poly+While. Although both languages allow the expression of non-terminating programs, their (proven for FO+Poly+While and conjectured for spatial Datalog) computational completeness makes them interesting objects of study. Previously, spatial Datalog programs have been studied for more restrictive forms of connectivity (e.g., piece-wise linear connectivity) and these programs were proved to correctly test connectivity on restricted classes of spatial databases (e.g., linear databases) only. In this paper, we present a spatial Datalog program that correctly tests topological connectivity of arbitrary compact (i.e., closed and bounded) spatial databases. In particular, it is guaranteed to terminate on this class of databases. This program is based on a first-order description of a known topological property of spatial databases, namely that locally they are conical. We also give a very natural implementation of topological connectivity in FO+Poly+While, that is based on a first-order implementation of the curve selection lemma, and that works correctly on arbitrary spatial databases inputs. Finally, we raise the question whether topological connectivity of arbitrary spatial databases can also be expressed in spatial Datalog.

Inferring network properties from topological and spectral analysis

Self-organized complex systems can be analyzed in terms of their topological structure. This can unveil relevant properties related to robustness and efficiency. We show how a suitable combination of topological and spectral analysis may improve the understanding of the mechanisms and the driving force which lead to the spontaneous formation of the internet network at the Autonomous System level.

Topological properties in ontology-based applications

Intelligent Systems Design and Applications, 2011

Representation and reasoning with spatial properties is essential in several application domains where ontologies are being successfully applied; e.g., Information Fusion systems. This requires a full characterization of the semantics of relations such as adjacent, included, overlapping, etc. Nevertheless, ontologies are not expressive enough to directly support widely-use spatial or topological theories, such as the Region Connection Calculus (RCC). In

A topological model to assess networks connectivity and reliability: recent development

2013

The acceleration of the interconnectivity of networ ks of all sorts brings to the front scene the issue of networks performance measure. Recently, one observed an accelerating course towards quantitative probabilistic models to describe and assess network s’ Connectivity, as being the main vector of performance. However, modelling realistic networks is still far from being satisfactorily achieved usi ng quantitative probabilistic models. On the other hand, little room had been lift to exp loring the potential of topological models to devel op qualitative and semi- quantitative models in order to assess networks connectivity. In this paper, we are exploring the potential of the topological modellin g. The proposed model is based on describing the no depair connectivity using binary scalars of different orders (tensors). Preliminary results of our explo rations sounded very promoting.