1,346 research outputs found

    Deciding regular grammar logics with converse through first-order logic

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    We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. This translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. A consequence of the translation is that the general satisfiability problem for regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Using the same method, we show how some other modal logics can be naturally translated into GF2, including nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed point-operators.Comment: 34 page

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

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    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

    A semantic web rule language for geospatial domains

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    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

    Conservative Extensions and Satisfiability in Fragments of First-Order Logic : Complexity and Expressive Power

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    In this thesis, we investigate the decidability and computational complexity of (deductive) conservative extensions in expressive fragments of first-order logic, such as two-variable and guarded fragments. Moreover, we also investigate the complexity of (query) conservative extensions in Horn description logics with inverse roles. Aditionally, we investigate the computational complexity of the satisfiability problem in the unary negation fragment of first-order logic extended with regular path expressions. Besides complexity results, we also study the expressive power of relation-changing modal logics. In particular, we provide translations intto hybrid logic and compare their expressive power using appropriate notions of bisimulations

    Answering regular path queries over SQ ontologies

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    We study query answering in the description logic SQ supporting qualified number restrictions on both transitive and non-transitive roles. Our main contributions are a tree-like model property for SQ-knowledge bases and, building upon this, an optimal automata-based algorithm for answering positive existential regular path queries in 2EXPTIME
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