Modelling Equivalent Definitions of Concepts

We introduce the notions of syntactic synonymy and referential syn- onymy due to Moschovakis. Those notions are capable of accounting for fine- grained aspects of the meaning of linguistic expressions, by formalizing the Fregean distinction between sense and denotation. We integrate Moschovakis’s theory with the theory of concepts developed in the foundational ontology DOLCE, in order to enable a formal treatment of equivalence between concepts

Embedding Domain-Specific Modelling Languages in Maude Specifications

Extended version accepted in the Systems and Software Engineering Journal.International audienceWe propose an approach for embedding Domain-Specific Modelling Languages (\dsml) into Maude, based on representing models and metamodels as Maude specifications, and on representing operational semantics and model transformations as computable functions/relations between such specifications. This provides us, on the one hand, with abstract definitions of essential concepts of domain-specific modelling languages: model-to-metamodel conformance, operational semantics, and (operational-semantics-preserving) model transformations; and, on the other hand, with equivalent executable definitions for those concepts, which can be directly used in Maude for formal verification purpose

Model Creation and Equivalence Proofs of Cellular Automata and Artificial Neural Networks

Computational methods and mathematical models have invaded arguably every scientific discipline forming its own field of research called computational science. Mathematical models are the theoretical foundation of computational science. Since Newton's time, differential equations in mathematical models have been widely and successfully used to describe the macroscopic or global behaviour of systems. With spatially inhomogeneous, time-varying, local element-specific, and often non-linear interactions, the dynamics of complex systems is in contrast more efficiently described by local rules and thus in an algorithmic and local or microscopic manner. The theory of mathematical modelling taking into account these characteristics of complex systems has to be established still. We recently presented a so-called allagmatic method including a system metamodel to provide a framework for describing, modelling, simulating, and interpreting complex systems. Implementations of cellular automata and artificial neural networks were described and created with that method. Guidance from philosophy were helpful in these first studies focusing on programming and feasibility. A rigorous mathematical formalism, however, is still missing. This would not only more precisely describe and define the system metamodel, it would also further generalise it and with that extend its reach to formal treatment in applied mathematics and theoretical aspects of computational science as well as extend its applicability to other mathematical and computational models such as agent-based models. Here, a mathematical definition of the system metamodel is provided. Based on the presented formalism, model creation and equivalence of cellular automata and artificial neural networks are proved. It thus provides a formal approach for studying the creation of mathematical models as well as their structural and operational comparison.Comment: 13 pages, 1 tabl

Towards automated knowledge-based mapping between individual conceptualisations to empower personalisation of Geospatial Semantic Web

Geospatial domain is characterised by vagueness, especially in the semantic disambiguation of the concepts in the domain, which makes defining universally accepted geo- ontology an onerous task. This is compounded by the lack of appropriate methods and techniques where the individual semantic conceptualisations can be captured and compared to each other. With multiple user conceptualisations, efforts towards a reliable Geospatial Semantic Web, therefore, require personalisation where user diversity can be incorporated. The work presented in this paper is part of our ongoing research on applying commonsense reasoning to elicit and maintain models that represent users' conceptualisations. Such user models will enable taking into account the users' perspective of the real world and will empower personalisation algorithms for the Semantic Web. Intelligent information processing over the Semantic Web can be achieved if different conceptualisations can be integrated in a semantic environment and mismatches between different conceptualisations can be outlined. In this paper, a formal approach for detecting mismatches between a user's and an expert's conceptual model is outlined. The formalisation is used as the basis to develop algorithms to compare models defined in OWL. The algorithms are illustrated in a geographical domain using concepts from the SPACE ontology developed as part of the SWEET suite of ontologies for the Semantic Web by NASA, and are evaluated by comparing test cases of possible user misconceptions

Coping with lists in the ifcOWL ontology

Over the past few years, several suggestions have been made of how to convert an EXPRESS schema into an OWL ontology. The conversion from EXPRESS to OWL is of particular use to architectural design and construction industry, because one of the key data models in architectural design and construction industry, namely the Industry Foundation Classes (IFC) is represented using the EXPRESS information modelling language. In each of these conversion options, the way in which lists are converted (e.g. lists of coordinates, lists of spaces in a floor) is key to the structure and eventual strength of the resulting ontology. In this article, we outline and discuss the main decisions that can be made in converting LIST concepts in EXPRESS to equivalent OWL expressions. This allows one to identify which conversion option is appropriate to support proper and efficient information reuse in the domain of architecture and construction

Knowledge-based support in Non-Destructive Testing for health monitoring of aircraft structures

Maintenance manuals include general methods and procedures for industrial maintenance and they contain information about principles of maintenance methods. Particularly, Non-Destructive Testing (NDT) methods are important for the detection of aeronautical defects and they can be used for various kinds of material and in different environments. Conventional non-destructive evaluation inspections are done at periodic maintenance checks. Usually, the list of tools used in a maintenance program is simply located in the introduction of manuals, without any precision as regards to their characteristics, except for a short description of the manufacturer and tasks in which they are employed. Improving the identification concepts of the maintenance tools is needed to manage the set of equipments and establish a system of equivalence: it is necessary to have a consistent maintenance conceptualization, flexible enough to fit all current equipment, but also all those likely to be added/used in the future. Our contribution is related to the formal specification of the system of functional equivalences that can facilitate the maintenance activities with means to determine whether a tool can be substituted for another by observing their key parameters in the identified characteristics. Reasoning mechanisms of conceptual graphs constitute the baseline elements to measure the fit or unfit between an equipment model and a maintenance activity model. Graph operations are used for processing answers to a query and this graph-based approach to the search method is in-line with the logical view of information retrieval. The methodology described supports knowledge formalization and capitalization of experienced NDT practitioners. As a result, it enables the selection of a NDT technique and outlines its capabilities with acceptable alternatives

Towards Translating Graph Transformation Approaches by Model Transformations

Recently, many researchers are working on semantics preserving model transformation. In the field of graph transformation one can think of translating graph grammars written in one approach to a behaviourally equivalent graph grammar in another approach. In this paper we translate graph grammars developed with the GROOVE tool to AGG graph grammars by first investigating the set of core graph transformation concepts supported by both tools. Then, we define what it means for two graph grammars to be behaviourally equivalent, and for the regarded approaches we actually show how to handle different definitions of both - application conditions and graph structures. The translation itself is explained by means of intuitive examples

A Process Modelling Framework Based on Point Interval Temporal Logic with an Application to Modelling Patient Flows

This thesis considers an application of a temporal theory to describe and model the patient journey in the hospital accident and emergency (A&E) department. The aim is to introduce a generic but dynamic method applied to any setting, including healthcare. Constructing a consistent process model can be instrumental in streamlining healthcare issues. Current process modelling techniques used in healthcare such as flowcharts, unified modelling language activity diagram (UML AD), and business process modelling notation (BPMN) are intuitive and imprecise. They cannot fully capture the complexities of the types of activities and the full extent of temporal constraints to an extent where one could reason about the flows. Formal approaches such as Petri have also been reviewed to investigate their applicability to the healthcare domain to model processes. Additionally, to schedule patient flows, current modelling standards do not offer any formal mechanism, so healthcare relies on critical path method (CPM) and program evaluation review technique (PERT), that also have limitations, i.e. finish-start barrier. It is imperative to specify the temporal constraints between the start and/or end of a process, e.g., the beginning of a process A precedes the start (or end) of a process B. However, these approaches failed to provide us with a mechanism for handling these temporal situations. If provided, a formal representation can assist in effective knowledge representation and quality enhancement concerning a process. Also, it would help in uncovering complexities of a system and assist in modelling it in a consistent way which is not possible with the existing modelling techniques. The above issues are addressed in this thesis by proposing a framework that would provide a knowledge base to model patient flows for accurate representation based on point interval temporal logic (PITL) that treats point and interval as primitives. These objects would constitute the knowledge base for the formal description of a system. With the aid of the inference mechanism of the temporal theory presented here, exhaustive temporal constraints derived from the proposed axiomatic system’ components serves as a knowledge base. The proposed methodological framework would adopt a model-theoretic approach in which a theory is developed and considered as a model while the corresponding instance is considered as its application. Using this approach would assist in identifying core components of the system and their precise operation representing a real-life domain deemed suitable to the process modelling issues specified in this thesis. Thus, I have evaluated the modelling standards for their most-used terminologies and constructs to identify their key components. It will also assist in the generalisation of the critical terms (of process modelling standards) based on their ontology. A set of generalised terms proposed would serve as an enumeration of the theory and subsume the core modelling elements of the process modelling standards. The catalogue presents a knowledge base for the business and healthcare domains, and its components are formally defined (semantics). Furthermore, a resolution theorem-proof is used to show the structural features of the theory (model) to establish it is sound and complete. After establishing that the theory is sound and complete, the next step is to provide the instantiation of the theory. This is achieved by mapping the core components of the theory to their corresponding instances. Additionally, a formal graphical tool termed as point graph (PG) is used to visualise the cases of the proposed axiomatic system. PG facilitates in modelling, and scheduling patient flows and enables analysing existing models for possible inaccuracies and inconsistencies supported by a reasoning mechanism based on PITL. Following that, a transformation is developed to map the core modelling components of the standards into the extended PG (PG*) based on the semantics presented by the axiomatic system. A real-life case (from the King’s College hospital accident and emergency (A&E) department’s trauma patient pathway) is considered to validate the framework. It is divided into three patient flows to depict the journey of a patient with significant trauma, arriving at A&E, undergoing a procedure and subsequently discharged. Their staff relied upon the UML-AD and BPMN to model the patient flows. An evaluation of their representation is presented to show the shortfalls of the modelling standards to model patient flows. The last step is to model these patient flows using the developed approach, which is supported by enhanced reasoning and scheduling