Dimensional Inconsistency Measures and Postulates in Spatio-Temporal Databases

Abstract

The problem of managing spatio-temporal data arises in many applications, such as location-based services, environmental monitoring, geographic information systems, and many others. Often spatio-temporal data arising from such applications turn out to be inconsistent, i.e., representing an impossible situation in the real world. Though several inconsistency measures have been proposed to quantify in a principled way inconsistency in propositional knowledge bases, little effort has been done so far on inconsistency measures tailored for the spatio-temporal setting.
 In this paper, we define and investigate new measures that are particularly suitable for dealing with inconsistent spatio-temporal information, because they explicitly take into account the spatial and temporal dimensions, as well as the dimension concerning the identifiers of the monitored objects. Specifically, we first define natural measures that look at individual dimensions (time, space, and objects), and then propose measures based on the notion of a repair. We then analyze their behavior w.r.t. common postulates defined for classical propositional knowledge bases, and find that the latter are not suitable for spatio-temporal databases, in that the proposed inconsistency measures do not often satisfy them. In light of this, we argue that also postulates should explicitly take into account the spatial, temporal, and object dimensions and thus define “dimension-aware” counterparts of common postulates, which are indeed often satisfied by the new inconsistency measures. Finally, we study the complexity of the proposed inconsistency measures.

Semantic inconsistency measures using 3-valued logics

“…As the semantic inconsistency measures were defined using the interpretation of the atoms, it is not surprising that they are not good at satisfying properties concerning sets of formulas. There is a similarity here with an approach to measuring inconsistency in spatio-temporal databases (see [23]) where the data has dimensions. For that reason new dimensional inconsistency measures were proposed that are more appropriate in that case.…”

“…A key aspect of understanding inconsistency is the ability to measure it. Application areas being investigated for inconsistency measures include software engineering [56,36], network intrusion detection [38], ontology systems [47,55], knowledgebase systems [37,44,42], databases [16,4,5,43,35,34], temporal information [25], spatio-temporal information [12,23], probabilistic information [13,46], finance [18], process specifications [11], and answer set programming [39,53].…”

A Paraconsistency Framework for Inconsistency Handling in Qualitative Spatial and Temporal Reasoning

“…In the realm of temporal reasoning, a recent work has extended this measure to linear temporal logic [14]. Furthermore, independently of qualitative reasoning, [18] introduces measures specifically designed to deal with inconsistent quantitative spatio-temporal information.…”

Guest Editorial: Reasoning With Inconsistent, Incomplete, and Uncertain Knowledge

“…6,7 Approaches that are complementary to those mentioned previously aim at quantifying the amount of inconsistent and uncertain information in knowledge bases. 8,9 Quantifying and monitoring the amount of inconsistency helps get information on the health status of data, whose quality is more and more important nowadays. Indeed, having information on the quality of data used in machine learning and datadriven approaches is crucial, as poor-quality data can have serious adverse consequences on the quality of decisions made using AI systems.…”