Investigation of the tradeoff between expressiveness and complexity in description logics with spatial operators

Le Logiche Descrittive sono una famiglia di formalismi molto espressivi per la rappresentazione della conoscenza. Questi formalismi sono stati investigati a fondo dalla comunit\ue0 scientifica, ma, nonostante questo grosso interesse, sono state definite poche Description Logics con operatori spaziali e tutte centrate sul Region Connection Calculus. Nella mia tesi considero tutti i pi\uf9 importanti formalismi di Qualitative Spatial Reasoning per mereologie, mereo-topologie e informazioni sulla direzione e studio alcune tecniche generali di ibridazione. Nella tesi presento un\u2019introduzione ai principali formalismi di Qualitative Spatial Reasoning e le principali famiglie di Description Logics. Nel mio lavoro, introduco anche le tecniche di ibridazione per estendere le Description Logics al ragionamento su conoscenza spaziale e presento il potere espressivo dei linguaggi ibridi ottenuti. Vengono presentati infine un risultato generale di para-decidibilit\ue0 per logiche descrittive estese da composition-based role axioms e l\u2019analisi del tradeoff tra espressivit\ue0 e propriet\ue0 computazionali delle logiche descrittive spaziali.Description Logics are a family of expressive Knowledge-Representation formalisms that have been deeply investigated. Nevertheless the few examples of DLs with spatial operators in the current literature are defined to include only the spatial reasoning capabilities corresponding to the Region Connection Calculus. In my thesis I consider all the most important Qualitative Spatial Reasoning formalisms for mereological, mereo-topological and directional information and investigate some general hybridization techniques. I will present a short overview of the main formalisms of Qualitative Spatial Reasoning and the principal families of DLs. I introduce the hybridization techniques to extend DLs to QSR and present the expressiveness of the resulting hybrid languages. I also present a general paradecidability result for undecidable languages equipped with composition-based role axioms and the tradeoff analysis of expressiveness and computational properties for the spatial DLs

Reasoning about Cardinal Directions between Extended Objects

Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model, known as Cardinal Direction Calculus (CDC), for representing direction relations between connected plane regions. CDC is perhaps the most expressive qualitative calculus for directional information, and has attracted increasing interest from areas such as artificial intelligence, geographical information science, and image retrieval. Given a network of CDC constraints, the consistency problem is deciding if the network is realizable by connected regions in the real plane. This paper provides a cubic algorithm for checking consistency of basic CDC constraint networks, and proves that reasoning with CDC is in general an NP-Complete problem. For a consistent network of basic CDC constraints, our algorithm also returns a 'canonical' solution in cubic time. This cubic algorithm is also adapted to cope with cardinal directions between possibly disconnected regions, in which case currently the best algorithm is of time complexity O(n^5)

A Linked Data representation of the Nomenclature of Territorial Units for Statistics

The recent publication of public sector information (PSI) data sets has brought to the attention of the scientific community the redundant presence of location based context. At the same time it stresses the inadequacy of current Linked Data services for exploiting the semantics of such contextual dimensions for easing entity retrieval and browsing. In this paper describes our approach for supporting the publication of geographical subdivisions in Linked Data format for supporting the e-government and public sector in publishing their data sets. The topological knowledge published can be reused in order to enrich the geographical context of other data sets, in particular we propose an exploitation scenario using statistical data sets described with the SCOVO ontology. The topological knowledge is then exploited within a service that supports the navigation and retrieval of statistical geographical entities for the EU territory. Geographical entities, in the extent of this paper, are linked data resources that describe objects that have a geographical extension. The data and services presented in this paper allows the discovery of resources that contain or are contained by a given entity URI and their representation within map widgets. We present an approach for a geography based service that helps in querying qualitative spatial relations for the EU statistical geography (proper containment so far). We also provide a rationale for publishing geographical information in Linked Data format based on our experience, within the EnAKTing project, in publishing UK PSI data