Modelling and solving temporal reasoning as propositional satisfiability

AbstractRepresenting and reasoning about time dependent information is a key research issue in many areas of computer science and artificial intelligence. One of the best known and widely used formalisms for representing interval-based qualitative temporal information is Allen's interval algebra (IA). The fundamental reasoning task in IA is to find a scenario that is consistent with the given information. This problem is in general NP-complete.In this paper, we investigate how an interval-based representation, or IA network, can be encoded into a propositional formula of Boolean variables and/or predicates in decidable theories. Our task is to discover whether satisfying such a formula can be more efficient than finding a consistent scenario for the original problem. There are two basic approaches to modelling an IA network: one represents the relations between intervals as variables and the other represents the end-points of each interval as variables. By combining these two approaches with three different Boolean satisfiability (SAT) encoding schemes, we produced six encoding schemes for converting IA to SAT. In addition, we also showed how IA networks can be formulated into satisfiability modulo theories (SMT) formulae based on the quantifier-free integer difference logic (QF-IDL). These encodings were empirically studied using randomly generated IA problems of sizes ranging from 20 to 100 nodes. A general conclusion we draw from these experimental results is that encoding IA into SAT produces better results than existing approaches. More specifically, we show that the new point-based 1-D support SAT encoding of IA produces consistently better results than the other alternatives considered. In comparison with the six different SAT encodings, the SMT encoding came fourth after the point-based and interval-based 1-D support schemes and the point-based direct scheme. Further, we observe that the phase transition region maps directly from the IA encoding to each SAT or SMT encoding, but, surprisingly, the location of the hard region varies according to the encoding scheme. Our results also show a fixed performance ranking order over the various encoding schemes

Finding Temporally Consistent Occlusion Boundaries in Videos using Geometric Context

We present an algorithm for finding temporally consistent occlusion boundaries in videos to support segmentation of dynamic scenes. We learn occlusion boundaries in a pairwise Markov random field (MRF) framework. We first estimate the probability of an spatio-temporal edge being an occlusion boundary by using appearance, flow, and geometric features. Next, we enforce occlusion boundary continuity in a MRF model by learning pairwise occlusion probabilities using a random forest. Then, we temporally smooth boundaries to remove temporal inconsistencies in occlusion boundary estimation. Our proposed framework provides an efficient approach for finding temporally consistent occlusion boundaries in video by utilizing causality, redundancy in videos, and semantic layout of the scene. We have developed a dataset with fully annotated ground-truth occlusion boundaries of over 30 videos ($5000 frames). This dataset is used to evaluate temporal occlusion boundaries and provides a much needed baseline for future studies. We perform experiments to demonstrate the role of scene layout, and temporal information for occlusion reasoning in dynamic scenes.Comment: Applications of Computer Vision (WACV), 2015 IEEE Winter Conference o

A Linked Data representation of the Nomenclature of Territorial Units for Statistics

The recent publication of public sector information (PSI) data sets has brought to the attention of the scientific community the redundant presence of location based context. At the same time it stresses the inadequacy of current Linked Data services for exploiting the semantics of such contextual dimensions for easing entity retrieval and browsing. In this paper describes our approach for supporting the publication of geographical subdivisions in Linked Data format for supporting the e-government and public sector in publishing their data sets. The topological knowledge published can be reused in order to enrich the geographical context of other data sets, in particular we propose an exploitation scenario using statistical data sets described with the SCOVO ontology. The topological knowledge is then exploited within a service that supports the navigation and retrieval of statistical geographical entities for the EU territory. Geographical entities, in the extent of this paper, are linked data resources that describe objects that have a geographical extension. The data and services presented in this paper allows the discovery of resources that contain or are contained by a given entity URI and their representation within map widgets. We present an approach for a geography based service that helps in querying qualitative spatial relations for the EU statistical geography (proper containment so far). We also provide a rationale for publishing geographical information in Linked Data format based on our experience, within the EnAKTing project, in publishing UK PSI data

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