A unified theory of granularity, vagueness and approximation

Abstract: We propose a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this semantic view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We provide a new formulation of these ideas in terms of a theory of granular partitions. We show that this theory provides a general framework within which we can understand the relation between vague terms and concepts and the corresponding crisp portions of reality. We also sketch how it might be possible to formulate within this framework a theory of vagueness which dispenses with the notion of truth-value gaps and other artifacts of more familiar approaches. Central to our approach is the idea that judgments about reality involve in every case (1) a separation of reality into foreground and background of attention and (2) the feature of granularity. On this basis we attempt to show that even vague judgments made in naturally occurring contexts are not marked by truth-value indeterminacy. We distinguish, in addition to crisp granular partitions, also vague partitions, and reference partitions, and we explain the role of the latter in the context of judgments that involve vagueness. We conclude by showing how reference partitions provide an effective means by which judging subjects are able to temper the vagueness of their judgments by means of approximations

Transitions between 4-intersection values of planar regions

[EN] If A(t) and B(t) are subsets of the Euclidean plane which are continuously morphing, we investigate the question of whether they may morph directly from being disjoint to overlapping so that the boundary and interior of A(t) both intersect the boundary and interior of B(t) without first passing through a state in which only their boundaries intersect. More generally, we consider which 4-intersection values---binary 4-tuples specifying whether the boundary and interior of A(t) intersect the boundary and interior of B(t)---are adjacent to which in the sense that one may morph into the other without passing through a third value. The answers depend on what forms the regions A(t) and B(t) are allowed to assume and on the definition of continuous morphing of the sets.Bell, K.; Richmond, T. (2017). Transitions between 4-intersection values of planar regions. Applied General Topology. 18(1):183-202. doi:10.4995/agt.2017.6716.SWORD183202181C. Adams and R. Franzosa, Introduction to Topology: Pure and Applied, Pearson Prentice Hall, Upper Saddle River, NJ, 2008.Chen, J., Li, C., Li, Z., & Gold, C. (2001). A Voronoi-based 9-intersection model for spatial relations. International Journal of Geographical Information Science, 15(3), 201-220. doi:10.1080/13658810151072831Clementini, E., Sharma, J., & Egenhofer, M. J. (1994). Modelling topological spatial relations: Strategies for query processing. Computers & Graphics, 18(6), 815-822. doi:10.1016/0097-8493(94)90007-8Egenhofer, M. J., & Al-Taha, K. K. (1992). Reasoning about gradual changes of topological relationships. Lecture Notes in Computer Science, 196-219. doi:10.1007/3-540-55966-3_12Egenhofer‡, M. J., Clementini, E., & di Felice, P. (1994). Research Paper. International journal of geographical information systems, 8(2), 129-142. doi:10.1080/02693799408901990EGENHOFER, M. J., & FRANZOSA, R. D. (1991). Point-set topological spatial relations. International journal of geographical information systems, 5(2), 161-174. doi:10.1080/02693799108927841M. Egenhofer and R. Franzosa, On equivalence of topological relations, International Journal for Geographical Information Systems 8, no. 6 (1994), 133-152. https://doi.org/10.1016/0022-247X(85)90246-XFrancaviglia, S., Lechicki, A., & Levi, S. (1985). Quasi-uniformization of hyperspaces and convergence of nets of semicontinuous multifunctions. Journal of Mathematical Analysis and Applications, 112(2), 347-370. doi:10.1016/0022-247x(85)90246-xNedas, K. A., Egenhofer, M. J., & Wilmsen, D. (2007). Metric details of topological line–line relations. International Journal of Geographical Information Science, 21(1), 21-48. doi:10.1080/13658810600852164Roy, A. J., & Stell, J. G. (2001). Spatial relations between indeterminate regions. International Journal of Approximate Reasoning, 27(3), 205-234. doi:10.1016/s0888-613x(01)00033-0SMITH, T. R., & PARK, K. K. (1992). Algebraic approach to spatial reasoning. International journal of geographical information systems, 6(3), 177-192. doi:10.1080/0269379920890190

A survey of qualitative spatial representations

Representation and reasoning with qualitative spatial relations is an important problem in artificial intelligence and has wide applications in the fields of geographic information system, computer vision, autonomous robot navigation, natural language understanding, spatial databases and so on. The reasons for this interest in using qualitative spatial relations include cognitive comprehensibility, efficiency and computational facility. This paper summarizes progress in qualitative spatial representation by describing key calculi representing different types of spatial relationships. The paper concludes with a discussion of current research and glimpse of future work

Qualitative spatial logics for buffered geometries

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 a E 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

Qualitative Spatial Reasoning with Holed Regions

The intricacies of real-world and constructed spatial entities call for versatile spatial data types to model complex spatial objects, often characterized by the presence of holes. To date, however, relations of simple, hole-free regions have been the prevailing approaches for spatial qualitative reasoning. Even though such relations may be applied to holed regions, they do not take into consideration the consequences of the existence of the holes, limiting the ability to query and compare more complex spatial configurations. To overcome such limitations, this thesis develops a formal framework for spatial reasoning with topological relations over two-dimensional holed regions, called the Holed Regions Model (HRM), and a similarity evaluation method for comparing relations featuring a multi-holed region, called the Frequency Distribution Method (FDM). The HRM comprises a set of 23 relations between a hole-free and a single-holed region, a set of 152 relations between two single-holed regions, as well as the composition inferences enabled from both sets of relations. The inference results reveal that the fine-grained topological relations over holed regions provide more refined composition results in over 50% of the cases when compared with the results of hole-free regions relations. The HRM also accommodates the relations between a hole-free region and a multi-holed region. Each such relation is called a multi-element relation, as it can be deconstructed into a number of elements—relations between a hole-free and a singleholed region—that is equal to the number of holes, regarding each hole as if it were the only one. FDM facilitates the similarity assessment among multi-element relations. The similarity is evaluated by comparing the frequency summaries of the single-holed region relations. The multi-holed regions of the relations under comparison may differ in the number of holes. In order to assess the similarity of such relations, one multi-holed region is considered as the result of dropping from or adding holes to the other region. Therefore, the effect that two concurrent changes have on the similarity of the relations is evaluated. The first is the change in the topological relation between the regions, and the second is the change in a region’s topology brought upon by elimination or addition of holes. The results from the similarity evaluations examined in this thesis show that the topological placement of the holes in relation to the hole-free region influences relation similarity as much as the relation between the hole-free region and the host of the holes. When the relations under comparison have fewer characteristics in common, the placement of the holes is the determining factor for the similarity rankings among relations. The distilled and more correct composition and similarity evaluation results enabled by the relations over holed regions indicate that spatial reasoning over such regions differs from the prevailing reasoning over hole-free regions. Insights from such results are expected to contribute to the design of future geographic information systems that more adequately process complex spatial phenomena, and are better equipped for advanced database query answering

Qualitative Spatial Reasoning with Holed Regions

The intricacies of real-world and constructed spatial entities call for versatile spatial data types to model complex spatial objects, often characterized by the presence of holes. To date, however, relations of simple, hole-free regions have been the prevailing approaches for spatial qualitative reasoning. Even though such relations may be applied to holed regions, they do not take into consideration the consequences of the existence of the holes, limiting the ability to query and compare more complex spatial configurations. To overcome such limitations, this thesis develops a formal framework for spatial reasoning with topological relations over two-dimensional holed regions, called the Holed Regions Model (HRM), and a similarity evaluation method for comparing relations featuring a multi-holed region, called the Frequency Distribution Method (FDM). The HRM comprises a set of 23 relations between a hole-free and a single-holed region, a set of 152 relations between two single-holed regions, as well as the composition inferences enabled from both sets of relations. The inference results reveal that the fine-grained topological relations over holed regions provide more refined composition results in over 50% of the cases when compared with the results of hole-free regions relations. The HRM also accommodates the relations between a hole-free region and a multi-holed region. Each such relation is called a multi-element relation, as it can be deconstructed into a number of elements—relations between a hole-free and a singleholed region—that is equal to the number of holes, regarding each hole as if it were the only one. FDM facilitates the similarity assessment among multi-element relations. The similarity is evaluated by comparing the frequency summaries of the single-holed region relations. The multi-holed regions of the relations under comparison may differ in the number of holes. In order to assess the similarity of such relations, one multi-holed region is considered as the result of dropping from or adding holes to the other region. Therefore, the effect that two concurrent changes have on the similarity of the relations is evaluated. The first is the change in the topological relation between the regions, and the second is the change in a region’s topology brought upon by elimination or addition of holes. The results from the similarity evaluations examined in this thesis show that the topological placement of the holes in relation to the hole-free region influences relation similarity as much as the relation between the hole-free region and the host of the holes. When the relations under comparison have fewer characteristics in common, the placement of the holes is the determining factor for the similarity rankings among relations. The distilled and more correct composition and similarity evaluation results enabled by the relations over holed regions indicate that spatial reasoning over such regions differs from the prevailing reasoning over hole-free regions. Insights from such results are expected to contribute to the design of future geographic information systems that more adequately process complex spatial phenomena, and are better equipped for advanced database query answering

Reasoning with Mixed Qualitative-Quantitative Representations of Spatial Knowledge

Drastic transformations in human settlements are caused by extreme events. As a consequence, descriptions of an environment struck by an extreme event, based on spatial data collected before the event, become suddenly unreliable. On the other hand, time critical actions taken for responding to extreme events require up-to-date spatial information. Traditional methods for spatial data collection are not able to provide updated information rapidly enough, calling for the development of new data collection methods. Reports provided by actors involved in the response operations can be considered as an alternative source of spatial information. Indeed, reports often convey spatial descriptions of the environment. The extraction of spatial descriptions from such reports can serve a fundamental role to update existing information which is usually maintained within, and by means of, Geographic Information Systems. However, spatial information conveyed by human reports has qualitative characteristics, that strongly differ from the quantitative nature of spatial information stored in Geographic Information Systems. Methodologies for integrating qualitative and quantitative spatial information are required in order to exploit human reports for updating existing descriptions of spatial knowledge. Although a significant amount of research has been carried on how to represent and reason on qualitative data and qualitative information, relatively little work exists on developing techniques to combine the different methodologies. The work presented in this thesis extends previous works by introducing a hybrid reasoning system--able to deal with mixed qualitative-quantitative representations of spatial knowledge--combining techniques developed separately for qualitative spatial reasoning and quantitative data analysis. The system produces descriptions of the spatial extent of those entities that have been modified by the event (such as collapsed buildings), or that were not existing before the event (such as fire or ash clouds). Furthermore, qualitative descriptions are produced for all entities in the environment. The former descriptions allow for overlaying on a map the information interpreted from human reports, while the latter triggers warning messages to people involved in decision making operations. Three main system functionalities are investigated in this work: The first allows for translating qualitative information into quantitative descriptions. The second aims at translating quantitative information into qualitative relations. Finally, the third allows for performing inference operations with information given partly qualitatively and partly quantitatively for boosting the spatial knowledge the system is able to produce

Reasoning with Mixed Qualitative-Quantitative Representations of Spatial Knowledge

Drastic transformations in human settlements are caused by extreme events. As a consequence, descriptions of an environment struck by an extreme event, based on spatial data collected before the event, become suddenly unreliable. On the other hand, time critical actions taken for responding to extreme events require up-to-date spatial information. Traditional methods for spatial data collection are not able to provide updated information rapidly enough, calling for the development of new data collection methods. Reports provided by actors involved in the response operations can be considered as an alternative source of spatial information. Indeed, reports often convey spatial descriptions of the environment. The extraction of spatial descriptions from such reports can serve a fundamental role to update existing information which is usually maintained within, and by means of, Geographic Information Systems. However, spatial information conveyed by human reports has qualitative characteristics, that strongly differ from the quantitative nature of spatial information stored in Geographic Information Systems. Methodologies for integrating qualitative and quantitative spatial information are required in order to exploit human reports for updating existing descriptions of spatial knowledge. Although a significant amount of research has been carried on how to represent and reason on qualitative data and qualitative information, relatively little work exists on developing techniques to combine the different methodologies. The work presented in this thesis extends previous works by introducing a hybrid reasoning system--able to deal with mixed qualitative-quantitative representations of spatial knowledge--combining techniques developed separately for qualitative spatial reasoning and quantitative data analysis. The system produces descriptions of the spatial extent of those entities that have been modified by the event (such as collapsed buildings), or that were not existing before the event (such as fire or ash clouds). Furthermore, qualitative descriptions are produced for all entities in the environment. The former descriptions allow for overlaying on a map the information interpreted from human reports, while the latter triggers warning messages to people involved in decision making operations. Three main system functionalities are investigated in this work: The first allows for translating qualitative information into quantitative descriptions. The second aims at translating quantitative information into qualitative relations. Finally, the third allows for performing inference operations with information given partly qualitatively and partly quantitatively for boosting the spatial knowledge the system is able to produce

Usage de la cognition spatiale pour localiser les lieux d'activité lors d'une enquête Origine - Destination

Ce mémoire cerne la problématique de la description qualitative de la localisation d'un lieu décrit en langage naturel. C'est par une approche cognitive qu'est abordé successivement l'apprentissage de l'espace, le stockage de l'information et la restitution de l'information en langage naturel, par l'entremise des concepts de méronymie, de catégories hiérarchiques et de référents spatiaux. De ce cadre théorique, on propose de restructurer une base de données de lieux existants en y ajoutant des paramètres qui permettent de retrouver, d'une description en langage naturel précise ou floue, un lieu sans ambigüité dans une base de données grâce à une interface usager offrant divers modes de repérage spatial