The Logic of NEAR and FAR

Du, Heshan; Alechina, Natasha; Stock, Kristin; Jackson, M. J.

doi:10.1007/978-3-319-01790-7_26

Cited by 9 publications

(14 citation statements)

References 35 publications

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“…As explained in our previous work (Du et al, 2013), though the relations are named N EAR and F AR, we do not attempt to model human notions of nearness or proximity, which is influenced by several factors, such as absolute distance, relative distance, frame of reference, object size, travelling costs and reachability, travelling distance and attractiveness of objects (Guesgen & Albrecht, 2000). In this work, we provide a strict mathematical definition for the calculation of whether two objects are to be considered as being N EAR or F AR, based on a margin of error σ.…”

Section: Introductionmentioning

confidence: 71%

“…Though several definitions and lemmas have been presented in our previous work (Du et al, 2013;Du & Alechina, 2014b), the proofs presented here are more complete, structured, accurate (small errors are corrected) and simplified.…”

Section: Soundness and Completeness Of Lbptmentioning

confidence: 99%

“…Lemma 9 is proved using LBPT axioms and facts (such as Axiom 3, Facts 14, 15) in the same way as proving the lemma for LNF (see Du et al, 2013). The full proof of Lemma 9 is provided in Appendix A.…”

Section: Metric Model Lemmamentioning

confidence: 99%

“…In our previous work (Du et al, 2013;Du & Alechina, 2014b), we presented a slightly different way to prove the Path-Consistency Lemma for LNF and LBPT respectively: the first empty interval is obtained using the strengthening operator, this is, g 1 ∩ (g 2 • g 3 ) = ∅ and g i = ∅, where i ∈ {1, 2, 3}. g i may be {0} or a primitive interval, or it can be written as…”

Section: Path-consistency Lemmamentioning

confidence: 99%

“…In this paper, we present a series of new qualitative spatial logics developed for validating matches between spatial objects: a logic of NEAR and FAR for buffered points (LNF) (Du, Alechina, Stock, & Jackson, 2013), a logic of NEAR and FAR for buffered geometries (LNFS) and a logic of part and whole for buffered geometries (LBPT) (Du & Alechina, 2014a, 2014b. The notion of buffer (ISO Technical Committee 211, 2003) is used to model the uncertainty in geometry representations, tolerating slight differences up to a margin of error or a level of tolerance σ ∈ R ≥0 .…”

Section: Introductionmentioning

confidence: 99%

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Qualitative Spatial Logics for Buffered Geometries

Du¹,

Alechina²

2016

jair

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This paper describes a series of new qualitative spatial logics for checking consistency of sameAs and partOf matches between spatial objects from different geospatial datasets, especially from crowd-sourced datasets. Since geometries in crowd-sourced data are usually not very accurate or precise, we buffer geometries by a margin of error or a level of tolerance σ ∈ R ≥0 , and define spatial relations for buffered geometries. The spatial logics formalize the notions of 'buffered equal' (intuitively corresponding to 'possibly sameAs'), 'buffered part of' ('possibly partOf'), 'near' ('possibly connected') and 'far' ('definitely disconnected'). A sound and complete axiomatisation of each logic is provided with respect to models based on metric spaces. For each of the logics, the satisfiability problem is shown to be NP-complete. Finally, we briefly describe how the logics are used in a system for generating and debugging matches between spatial objects, and report positive experimental evaluation results for the system.

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Section: Introductionmentioning

confidence: 71%

Section: Soundness and Completeness Of Lbptmentioning

confidence: 99%

Section: Metric Model Lemmamentioning

confidence: 99%

Section: Path-consistency Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Qualitative Spatial Logics for Buffered Geometries

Du¹,

Alechina²

2016

jair

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Open Research Areas in Distance Geometry

Liberti

2018

Open Problems in Optimization and Data Analysis

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New Error Measures and Methods for Realizing Protein Graphs from Distance Data

d'Ambrosio

Lavor

et al. 2017

Discrete Comput Geom

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The interval Distance Geometry Problem (i DGP) consists in finding a realization in R K of a simple undirected graph G = (V, E) with nonnegative intervals assigned to the edges in such a way that, for each edge, the Euclidean distance between the realization of the adjacent vertices is within the edge interval bounds. In this paper, we focus on the application to the conformation of proteins in space, which is a basic step in determining protein function: given interval estimations of some of the inter-atomic distances, find their shape. Among different families of methods for accomplishing this task, we look at mathematical programming based methods, which are well suited for dealing with intervals. The basic question we want to answer is: what is the best such method for the problem? The most meaningful error measure for evaluating solution quality is the coordinate root mean square deviation. We first introduce a new error measure which addresses a particular feature of protein backbones, i.e. many partial reflections also yield acceptable backbones. We then present a set of new and existing quadratic and semidefinite programming formulations of this problem, and a set of new and existing methods for solving these formulations. Finally, we perform a computational evaluation of all the feasible solver+formulation combinations according to new and existing error measures, finding that the best methodology is a new heuristic method based on multiplicative weights updates.

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The Logic of NEAR and FAR

Cited by 9 publications

References 35 publications

Qualitative Spatial Logics for Buffered Geometries

Qualitative Spatial Logics for Buffered Geometries

Open Research Areas in Distance Geometry

New Error Measures and Methods for Realizing Protein Graphs from Distance Data

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