Minimal Definition Signatures: Computation and Application to Ontology Alignment

In computer science, ontologies define a domain to facilitate knowledge representation and sharing, in a machine processable way. Ontologies approximate an actual world representation, and thus ontologies will differ for many reasons. Therefore knowledge sharing, and in general semantic interoperability, is inherently hindered or even precluded between heterogenous ontologies. Ontology matching addresses this fundamental issue by producing alignments, i.e. sets of correspondences that describe relations between semantically related entities of different ontologies. However, alignments are typically incomplete. In order to support and improve ontology alignment, and semantic interoperability in general, this thesis exploits the notion of implicit definability. Implicit definability is a semantic property of ontologies, signatures, and concepts (and roles) stating that whenever the signature is fixed under a given ontology then the definition of a particular concept (or role) is also fixed. This thesis introduces the notion of minimal definition signature (MDS) from which a given entity is implicitly definable, and presents a novel approach that provides an efficient way to compute in practice all MDSs of the definable entities. Furthermore, it investigates the application of MDSs in the context of alignment generation, evaluation, and negotiation (whereby agents cooperatively establish a mutually acceptable alignment to support opportunistic communication within open environments). As implicit definability permits defined entities to be removed without semantic loss, this thesis argues, that if the meaning of the defined entity is wholly fixed by the terms of its definition, only the terms in the definition are required to be mapped in order to map the defined entity itself; thus implicit definability entails a new type of definability-based correspondence correspondence. Therefore this thesis defines and explores the properties of definability- based correspondences, and extends several ontology alignment evaluation metrics in order to accommodate their assessment. As task signature coverage is a prerequisite of many knowledge-based tasks (e.g. service invocation), a definability-based, efficient approximation approach to obtaining minimal signature cover sets is presented. Moreover, this thesis outlines a specific alignment negotiation approach and shows that by considering definability, agents are better equipped to: (i) determine whether an alignment provides the necessary coverage to achieve a particular task (align the whole ontology, formulate a message or query); (ii) adhere to privacy and confidentiality constraints; and (iii) minimalise the cardinality of the resulting mutual alignment

Interpolants and Explicit Definitions in Extensions of the Description Logic EL

We show that the vast majority of extensions of the description logic $\mathcal{EL}$ do not enjoy the Craig interpolation nor the projective Beth definability property. This is the case, for example, for $\mathcal{EL}$ with nominals, $\mathcal{EL}$ with the universal role, $\mathcal{EL}$ with a role inclusion of the form $r\circ s\sqsubseteq s$, and for $\mathcal{ELI}$. It follows in particular that the existence of an explicit definition of a concept or individual name cannot be reduced to subsumption checking via implicit definability. We show that nevertheless the existence of interpolants and explicit definitions can be decided in polynomial time for standard tractable extensions of $\mathcal{EL}$ (such as $\mathcal{EL}^{++}$) and in ExpTime for $\mathcal{ELI}$ and various extensions. It follows that these existence problems are not harder than subsumption which is in sharp contrast to the situation for expressive DLs. We also obtain tight bounds for the size of interpolants and explicit definitions and the complexity of computing them: single exponential for tractable standard extensions of $\mathcal{EL}$ and double exponential for $\mathcal{ELI}$ and extensions. We close with a discussion of Horn-DLs such as Horn-$\mathcal{ALCI}$

Interpolants and Explicit Definitions in Extensions of the Description Logic EL

We show that the vast majority of extensions of the description logic EL do not enjoy the Craig interpolation nor the projective Beth definability property. This is the case, for example, for EL with nominals, EL with the universal role, EL with role hierarchies and transitive roles, and for ELI. It follows in particular that the existence of an explicit definition of a concept or individual name cannot be reduced to subsumption checking via implicit definability. We show that nevertheless the existence of interpolants and explicit definitions can be decided in polynomial time for standard tractable extensions of EL (such as EL++) and in ExpTime for ELI and various extensions. It follows that these existence problems are not harder than subsumption which is in sharp contrast to the situation for expressive DLs. We also obtain tight bounds for the size of interpolants and explicit definitions and the complexity of computing them: single exponential for tractable standard extensions of EL and double exponential for ELI and extensions. We close with a discussion of Horn-DLs such as Horn-ALCI.</jats:p

Living without Beth and Craig: Definitions and Interpolants in the Guarded and Two-Variable Fragments

In logics with the Craig interpolation property (CIP) the existence of an interpolant for an implication follows from the validity of the implication. In logics with the projective Beth definability property (PBDP), the existence of an explicit definition of a relation follows from the validity of a formula expressing its implicit definability. The two-variable fragment, FO2, and the guarded fragment, GF, of first-order logic both fail to have the CIP and the PBDP. We show that nevertheless in both fragments the existence of interpolants and explicit definitions is decidable. In GF, both problems are 3ExpTime-complete in general, and 2ExpTime-complete if the arity of relation symbols is bounded by a constant c not smaller than 3. In FO2, we prove a coN2ExpTime upper bound and a 2ExpTime lower bound for both problems. Thus, both for GF and FO2 existence of interpolants and explicit definitions are decidable but harder than validity (in case of FO2 under standard complexity assumptions)

Patterns for Heterogeneous TBox Mappings to Bridge Different Modelling Decisions

Correspondence patterns have been proposed as templates of commonly used alignments between heterogeneous elements in ontologies, although design tools are currently not equipped with handling these definition alignments nor pattern alignments. We aim to address this by, first, formalising the notion of design pattern; secondly, defining typical modelling choice patterns and their alignments; and finally, proposing algorithms for integrating automatic pattern detection into existing ontology design tools. This gave rise to six formalised pattern alignments and two efficient local search and pattern matching algorithms to propose possible pattern alignments to the modeller

Facilitating file retrieval on resource limited devices

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The rapid development of mobile technologies has facilitated users to generate and store files on mobile devices. However, it has become a challenging issue for users to search efficiently and effectively for files of interest in a mobile environment that involves a large number of mobile nodes. In this thesis, file management and retrieval alternatives have been investigated to propose a feasible framework that can be employed on resource-limited devices without altering their operating systems. The file annotation and retrieval framework (FARM) proposed in the thesis automatically annotates the files with their basic file attributes by extracting them from the underlying operating system of the device. The framework is implemented in the JME platform as a case study. This framework provides a variety of features for managing the metadata and file search features on the device itself and on other devices in a networked environment. FARM not only automates the file-search process but also provides accurate results as demonstrated by the experimental analysis. In order to facilitate a file search and take advantage of the Semantic Web Technologies, the SemFARM framework is proposed which utilizes the knowledge of a generic ontology. The generic ontology defines the most common keywords that can be used as the metadata of stored files. This provides semantic-based file search capabilities on low-end devices where the search keywords are enriched with additional knowledge extracted from the defined ontology. The existing frameworks annotate image files only, while SemFARM can be used to annotate all types of files. Semantic heterogeneity is a challenging issue and necessitates extensive research to accomplish the aim of a semantic web. For this reason, significant research efforts have been made in recent years by proposing an enormous number of ontology alignment systems to deal with ontology heterogeneities. In the process of aligning different ontologies, it is essential to encompass their semantic, structural or any system-specific measures in mapping decisions to produce more accurate alignments. The proposed solution, in this thesis, for ontology alignment presents a structural matcher, which computes the similarity between the super-classes, sub-classes and properties of two entities from different ontologies that require aligning. The proposed alignment system (OARS) uses Rough Sets to aggregate the results obtained from various matchers in order to deal with uncertainties during the mapping process of entities. The OARS uses a combinational approach by using a string-based and linguistic-based matcher, in addition to structural-matcher for computing the overall similarity between two entities. The performance of the OARS is evaluated in comparison with existing state of the art alignment systems in terms of precision and recall. The performance tests are performed by using benchmark ontologies and the results show significant improvements, specifically in terms of recall on all groups of test ontologies. There is no such existing framework, which can use alignments for file search on mobile devices. The ontology alignment paradigm is integrated in the SemFARM to further enhance the file search features of the framework as it utilises the knowledge of more than one ontology in order to perform a search query. The experimental evaluations show that it performs better in terms of precision and recall where more than one ontology is available when searching for a required file.Education Commission of Pakistan and the University of Engineering & Technology, Peshawa

Improving Model Finding for Integrated Quantitative-qualitative Spatial Reasoning With First-order Logic Ontologies

Many spatial standards are developed to harmonize the semantics and specifications of GIS data and for sophisticated reasoning. All these standards include some types of simple and complex geometric features, and some of them incorporate simple mereotopological relations. But the relations as used in these standards, only allow the extraction of qualitative information from geometric data and lack formal semantics that link geometric representations with mereotopological or other qualitative relations. This impedes integrated reasoning over qualitative data obtained from geometric sources and “native” topological information – for example as provided from textual sources where precise locations or spatial extents are unknown or unknowable. To address this issue, the first contribution in this dissertation is a first-order logical ontology that treats geometric features (e.g. polylines, polygons) and relations between them as specializations of more general types of features (e.g. any kind of 2D or 1D features) and mereotopological relations between them. Key to this endeavor is the use of a multidimensional theory of space wherein, unlike traditional logical theories of mereotopology (like RCC), spatial entities of different dimensions can co-exist and be related. However terminating or tractable reasoning with such an expressive ontology and potentially large amounts of data is a challenging AI problem. Model finding tools used to verify FOL ontologies with data usually employ a SAT solver to determine the satisfiability of the propositional instantiations (SAT problems) of the ontology. These solvers often experience scalability issues with increasing number of objects and size and complexity of the ontology, limiting its use to ontologies with small signatures and building small models with less than 20 objects. To investigate how an ontology influences the size of its SAT translation and consequently the model finder’s performance, we develop a formalization of FOL ontologies with data. We theoretically identify parameters of an ontology that significantly contribute to the dramatic growth in size of the SAT problem. The search space of the SAT problem is exponential in the signature of the ontology (the number of predicates in the axiomatization and any additional predicates from skolemization) and the number of distinct objects in the model. Axiomatizations that contain many definitions lead to large number of SAT propositional clauses. This is from the conversion of biconditionals to clausal form. We therefore postulate that optional definitions are ideal sentences that can be eliminated from an ontology to boost model finder’s performance. We then formalize optional definition elimination (ODE) as an FOL ontology preprocessing step and test the simplification on a set of spatial benchmark problems to generate smaller SAT problems (with fewer clauses and variables) without changing the satisfiability and semantic meaning of the problem. We experimentally demonstrate that the reduction in SAT problem size also leads to improved model finding with state-of-the-art model finders, with speedups of 10-99%. Altogether, this dissertation improves spatial reasoning capabilities using FOL ontologies – in terms of a formal framework for integrated qualitative-geometric reasoning, and specific ontology preprocessing steps that can be built into automated reasoners to achieve better speedups in model finding times, and scalability with moderately-sized datasets