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

Towards Model Checking Executable UML Specifications in mCRL2

We describe a translation of a subset of executable UML (xUML) into the process algebraic specification language mCRL2. This subset includes class diagrams with class generalisations, and state machines with signal and change events. The choice of these xUML constructs is dictated by their use in the modelling of railway interlocking systems. The long-term goal is to verify safety properties of interlockings modelled in xUML using the mCRL2 and LTSmin toolsets. Initial verification of an interlocking toy example demonstrates that the safety properties of model instances depend crucially on the run-to-completion assumptions

Embedding object-oriented design in system engineering

The Unified Modeling Language (UML) is a collection of techniques intended to document design decisions about software. This contrasts with systems engineering approaches such as for exampleStatemate and the Yourdon Systems Method (YSM), in which the design of an entire system consisting of software and hardware can be documented. The difference between the system- and the software level is reflected in differences between execution semantics as well as in methodology. In this paper, I show how the UML can be used as a system-level design technique. I give a conceptual framework for engineering design that accommodates the system- as well as the software level and show how techniques from the UML and YSM can be classified within this framework, and how this allows a coherent use of these techniques in a system engineering approach. These ideas are illustrated by a case study in which software for a compact dynamic bus station is designed. Finally, I discuss the consequences of this approach for a semantics of UML constructs that would be appropriate for system-level design

Formal and efficient verification techniques for Real-Time UML models

The real-time UML profile TURTLE has a formal semantics expressed by translation into a timed process algebra: RT-LOTOS. RTL, the formal verification tool developed for RT-LOTOS, was first used to check TURTLE models against design errors. This paper opens new avenues for TURTLE model verification. It shows how recent work on translating RT-LOTOS specifications into Time Petri net model may be applied to TURTLE. RT-LOTOS to TPN translation patterns are presented. Their formal proof is the subject of another paper. These patterns have been implemented in a RT-LOTOS to TPN translator which has been interfaced with TINA, a Time Petri Net Analyzer which implements several reachability analysis procedures depending on the class of property to be verified. The paper illustrates the benefits of the TURTLE->RT-LOTOS->TPN transformation chain on an avionic case study

Automated Mapping of UML Activity Diagrams to Formal Specifications for Supporting Containment Checking

Business analysts and domain experts are often sketching the behaviors of a software system using high-level models that are technology- and platform-independent. The developers will refine and enrich these high-level models with technical details. As a consequence, the refined models can deviate from the original models over time, especially when the two kinds of models evolve independently. In this context, we focus on behavior models; that is, we aim to ensure that the refined, low-level behavior models conform to the corresponding high-level behavior models. Based on existing formal verification techniques, we propose containment checking as a means to assess whether the system's behaviors described by the low-level models satisfy what has been specified in the high-level counterparts. One of the major obstacles is how to lessen the burden of creating formal specifications of the behavior models as well as consistency constraints, which is a tedious and error-prone task when done manually. Our approach presented in this paper aims at alleviating the aforementioned challenges by considering the behavior models as verification inputs and devising automated mappings of behavior models onto formal properties and descriptions that can be directly used by model checkers. We discuss various challenges in our approach and show the applicability of our approach in illustrative scenarios.Comment: In Proceedings FESCA 2014, arXiv:1404.043