LoLa: a modular ontology of logics, languages and translations

The Distributed Ontology Language (DOL), currently being standardised within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37/SC 3, aims at providing a unified framework for (i) ontologies formalised in heterogeneous logics, (ii) modular ontologies, (iii) links between ontologies, and (iv) annotation of ontologies.\ud \ud This paper focuses on the LoLa ontology, which formally describes DOL's vocabulary for logics, ontology languages (and their serialisations), as well as logic translations. Interestingly, to adequately formalise the logical relationships between these notions, LoLa itself needs to be axiomatised heterogeneously---a task for which we choose DOL. Namely, we use the logic RDF for ABox assertions, OWL for basic axiomatisations of various modules concerning logics, languages, and translations, FOL for capturing certain closure rules that are not expressible in OWL (For the sake of tool availability it is still helpful not to map everything to FOL.), and circumscription for minimising the extension of concepts describing default translations

Higher-order Representation and Reasoning for Automated Ontology Evolution

Abstract: The GALILEO system aims at realising automated ontology evolution. This is necessary to enable intelligent agents to manipulate their own knowledge autonomously and thus reason and communicate effectively in open, dynamic digital environments characterised by the heterogeneity of data and of representation languages. Our approach is based on patterns of diagnosis of faults detected across multiple ontologies. Such patterns allow to identify the type of repair required when conflicting ontologies yield erroneous inferences. We assume that each ontology is locally consistent, i.e. inconsistency arises only across ontologies when they are merged together. Local consistency avoids the derivation of uninteresting theorems, so the formula for diagnosis can essentially be seen as an open theorem over the ontologies. The system’s application domain is physics; we have adopted a modular formalisation of physics, structured by means of locales in Isabelle, to perform modular higher-order reasoning, and visualised by means of development graphs.

Institutionalising Ontology-Based Semantic Integration

We address what is still a scarcity of general mathematical foundations for ontology-based semantic integration underlying current knowledge engineering methodologies in decentralised and distributed environments. After recalling the first-order ontology-based approach to semantic integration and a formalisation of ontological commitment, we propose a general theory that uses a syntax-and interpretation-independent formulation of language, ontology, and ontological commitment in terms of institutions. We claim that our formalisation generalises the intuitive notion of ontology-based semantic integration while retaining its basic insight, and we apply it for eliciting and hence comparing various increasingly complex notions of semantic integration and ontological commitment based on differing understandings of semantics

Architectural Refinement in HETS

The main objective of this work is to bring a number of improvements to the Heterogeneous Tool Set HETS, both from a theoretical and an implementation point of view. In the first part of the thesis we present a number of recent extensions of the tool, among which declarative specifications of logics, generalized theoroidal comorphisms, heterogeneous colimits and integration of the logic of the term rewriting system Maude. In the second part we concentrate on the CASL architectural refinement language, that we equip with a notion of refinement tree and with calculi for checking correctness and consistency of refinements. Soundness and completeness of these calculi is also investigated. Finally, we present the integration of the VSE refinement method in HETS as an institution comorphism. Thus, the proof manangement component of HETS remains unmodified

Proof Support for Common Logic

We present an extension of the Heterogeneous Tool Set HETS that enables proof support for Common Logic. This is achieved via logic translations that relate Common Logic and some of its sublogics to already supported logics and automated theorem proving systems. We thus provide the first full theorem proving support for Common Logic, including the possibility of verifying meta-theoretical relationships between Common Logic theories