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

Saturation-based decision procedures for extensions of the guarded fragment

We apply the framework of Bachmair and Ganzinger for saturation-based theorem proving to derive a range of decision procedures for logical formalisms, starting with a simple terminological language EL, which allows for conjunction and existential restrictions only, and ending with extensions of the guarded fragment with equality, constants, functionality, number restrictions and compositional axioms of form S ◦ T ⊆ H. Our procedures are derived in a uniform way using standard saturation-based calculi enhanced with simplification rules based on the general notion of redundancy. We argue that such decision procedures can be applied for reasoning in expressive description logics, where they have certain advantages over traditionally used tableau procedures, such as optimal worst-case complexity and direct correctness proofs.Wir wenden das Framework von Bachmair und Ganzinger für saturierungsbasiertes Theorembeweisen an, um eine Reihe von Entscheidungsverfahren für logische Formalismen abzuleiten, angefangen von einer simplen terminologischen Sprache EL, die nur Konjunktionen und existentielle Restriktionen erlaubt, bis zu Erweiterungen des Guarded Fragment mit Gleichheit, Konstanten, Funktionalität, Zahlenrestriktionen und Kompositionsaxiomen der Form S ◦ T ⊆ H. Unsere Verfahren sind einheitlich abgeleitet unter Benutzung herkömmlicher saturierungsbasierter Kalküle, verbessert durch Simplifikationsregeln, die auf dem Konzept der Redundanz basieren. Wir argumentieren, daß solche Entscheidungsprozeduren für das Beweisen in ausdrucksvollen Beschreibungslogiken angewendet werden können, wo sie gewisse Vorteile gegenüber traditionell benutzten Tableauverfahren besitzen, wie z.B. optimale worst-case Komplexität und direkte Korrektheitsbeweise

A semantic web rule language for geospatial domains

Retrieval of geographically-referenced information on the Internet is now a common activity. The web is increasingly being seen as a medium for the storage and exchange of geographic data sets in the form of maps. The geospatial-semantic web (GeoWeb) is being developed to address the need for access to current and accurate geo-information. The potential applications of the GeoWeb are numerous, ranging from specialised application domains for storing and analysing geo-information to more common applications by casual users for querying and visualising geo-data, e.g. finding locations of services, descriptions of routes, etc. Ontologies are at the heart of W3C's semantic web initiative to provide the necessary machine understanding to the sheer volumes of information contained on the internet. For the GeoWeb to succeed the development of ontologies for the geographic domain are crucial. Semantic web technologies to represent ontologies have been developed and standardised. OWL, the Web Ontology Language, is the most expressive of these enabling a rich form of reasoning, thanks to its formal description logic underpinnings. Building geo-ontologies involves a continuous process of update to the originally modelled data to reflect change over time as well as to allow for ontology expansion by integrating new data sets, possibly from different sources. One of the main challenges in this process is finding means of ensuring the integrity of the geo-ontology and maintaining its consistency upon further evolution. Representing and reasoning with geographic ontologies in OWL is limited. Firstly, OWL is not an integrity checking language due to it's non-unique name and open world assumptions. Secondly, it can not represent spatial datatypes, can not compute information using spatial operators and does not have any form of spatial index. Finally, OWL does not support complex property composition needed to represent qualitative spatial reasoning over spatial concepts. To address OWL's representational inefficiencies, new ontology languages have been proposed based on the intersection or union of OWL (in particular the DL family corresponding to OWL) with logic programs (rule languages). In this work, a new Semantic Web Spatial Rule Language (SWSRL) is proposed, based on the syntactic core of the Description Logic Programs paradigm (DLP), and the semantics of a Logic Program. The language is built to support the expression of geospatial ontological axioms and geospatial integrity and deduction rules. A hybrid framework to integrate both qualitative symbolic information in SWSRL with quantitative, geometric information using spatial datatypes in a spatial database is proposed. Two notable features of SWSRL are 1) the language is based on a prioritised de fault logic that allows the expression of default integrity rules and their exceptions and 2) the implementation of the language uses an interleaved mode of inference for on the fly computation (either qualitative or quantitative) deduction of spatial relations. SWSRL supports an OGC complaint spatial syntax, and a standardised definition of rule meta data. Both features aid the construction, description, identification and categorisation of designed and implemented rules within large rule sets. The language and the developed engine are evaluated using synthetic as well as real data sets in the context of developing geographic ontologies for geographic information retrieval on the Semantic Web. Empirical experiments are also presented to test the scalability and applicability of the developed framework

Konzeptbasierte Argumentation in dynamischen Umgebungen

Argumentation systems play an important role when controversial points of views are to be considered in order to make decisions on inconsistent data. In this work a scalable framework for argumentation and decision support is outlined. This framework defines basic arguments and conflicts which refer to conceptual descriptions of the given state of affairs. Based on their meaning and preference relations that adopt specific viewpoints, it is possible to determine efficiently successful explanations depending on these viewpoints. We investigate our approach by examining soccer games, since many observed spatiotemporal behaviours in soccer can be interpreted differently

Decidable and undecidable extensions of ALC with compositionbased role inclusion axioms

This paper continues our investigation on the extension of the standard description logic ALC with role axioms of the form S ◦ T ⊑ R1 ⊔ · · · ⊔ Rn. We consider the concept satisfiability problem of ALC w.r.t. a set of role axioms of the proposed form. A set of these role axioms is called a role box. The original motivation for this kind of role axioms comes from foreseen applications in the field of qualitative spatial reasoning with description logics. In this paper, we define the logics ALC RA ⊖, ALCRA, and ALCRASG. Basically, both ALC RA ⊖ and ALCRA allow arbitrary role boxes containing axioms of the general form S ◦ T ⊑ R1 ⊔ · · · ⊔ Rn. In contrast to ALC RA ⊖, ALCRA requires additionally that all roles have to be interpreted as disjoint. This requirement is also originally motivated by qualitative spatial reasoning applications with ALCRA. Recently it turned out that ALC RA ⊖ is undecidable. In fact, already ALU RA ⊖ with role boxes containing axioms of the form R◦S ⊑ T is undecidable. A ver

Obstacles on the way to spatial reasoning with description logics -- undecidability of ALCRA

This paper presents the new description logic ALC RA ⊖. ALC RA ⊖ combines the well-known standard description logic ALC with compositionbased role axioms of the form S ◦ T ⊑ R1 ⊔ · · · ⊔ Rn. We argue that these axioms are nearly indispensable components in a description logic framework suitable for qualitative spatial reasoning tasks. An ALC RA ⊖ spatial reasoning example is presented, and the relationships to other descriptions logics are discussed (namely ALCRA, ALC R +, ALC⊕, ALCH R +). Unfortunately, the satisfiability problem of this new logic is undecidable. Due to the high relevance of role axioms of the proposed form for all kinds of qualitative reasoning tasks, the undecidability of ALC RA ⊖ is an important result.