A cookbook for temporal conceptual data modelling with description logic

We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. In the temporal dimension, they capture future and past temporal operators on concepts, flexible and rigid roles, the operators `always' and `some time' on roles, data assertions for particular moments of time and global concept inclusions. The logics are interpreted over the Cartesian products of object domains and the flow of time (Z,<), satisfying the constant domain assumption. We prove that the most expressive of our temporal description logics (which can capture lifespan cardinalities and either qualitative or quantitative evolution constraints) turn out to be undecidable. However, by omitting some of the temporal operators on concepts/roles or by restricting the form of concept inclusions we obtain logics whose complexity ranges between PSpace and NLogSpace. These positive results were obtained by reduction to various clausal fragments of propositional temporal logic, which opens a way to employ propositional or first-order temporal provers for reasoning about temporal data models

Tailoring temporal description logics for reasoning over temporal conceptual models

Temporal data models have been used to describe how data can evolve in the context of temporal databases. Both the Extended Entity-Relationship (EER) model and the Unified Modelling Language (UML) have been temporally extended to design temporal databases. To automatically check quality properties of conceptual schemas various encoding to Description Logics (DLs) have been proposed in the literature. On the other hand, reasoning on temporally extended DLs turn out to be too complex for effective reasoning ranging from 2ExpTime up to undecidable languages. We propose here to temporalize the ‘light-weight’ DL-Lite logics obtaining nice computational results while still being able to represent various constraints of temporal conceptual models. In particular, we consider temporal extensions of DL-Lite^N_bool, which was shown to be adequate for capturing non-temporal conceptual models without relationship inclusion, and its fragment DL-Lite^N_core with most primitive concept inclusions, which are nevertheless enough to represent almost all types of atemporal constraints (apart from covering)

Context Reasoning for Role-Based Models

In a modern world software systems are literally everywhere. These should cope with very complex scenarios including the ability of context-awareness and self-adaptability. The concept of roles provide the means to model such complex, context-dependent systems. In role-based systems, the relational and context-dependent properties of objects are transferred into the roles that the object plays in a certain context. However, even if the domain can be expressed in a well-structured and modular way, role-based models can still be hard to comprehend due to the sophisticated semantics of roles, contexts and different constraints. Hence, unintended implications or inconsistencies may be overlooked. A feasible logical formalism is required here. In this setting Description Logics (DLs) fit very well as a starting point for further considerations since as a decidable fragment of first-order logic they have both an underlying formal semantics and decidable reasoning problems. DLs are a well-understood family of knowledge representation formalisms which allow to represent application domains in a well-structured way by DL-concepts, i.e. unary predicates, and DL-roles, i.e. binary predicates. However, classical DLs lack expressive power to formalise contextual knowledge which is crucial for formalising role-based systems. We investigate a novel family of contextualised description logics that is capable of expressing contextual knowledge and preserves decidability even in the presence of rigid DL-roles, i.e. relational structures that are context-independent. For these contextualised description logics we thoroughly analyse the complexity of the consistency problem. Furthermore, we present a mapping algorithm that allows for an automated translation from a formal role-based model, namely a Compartment Role Object Model (CROM), into a contextualised DL ontology. We prove the semantical correctness and provide ideas how features extending CROM can be expressed in our contextualised DLs. As final step for a completely automated analysis of role-based models, we investigate a practical reasoning algorithm and implement the first reasoner that can process contextual ontologies

A Landscape of First-Order Linear Temporal Logics in Infinite-State Verification and Temporal Ontologies

We provide an overview of the main attempts to formalize and reason about the evolution over time of complex domains, through the lens of first-order temporal logics. Different communities have studied similar problems for decades, and some unification of concepts, problems and formalisms is a much needed but not simple task

Description Logics of Context with Rigid Roles Revisited

To represent and reason about contextualized knowledge often two-dimensional Description Logics (DLs) are employed, where one DL is used to describe contexts (or possible worlds) and the other DL is used to describe the objects, i.e. the relational structure of the specific contexts. Previous approaches for DLs of context that combined pairs of DLs resulted in undecidability in those cases where so-called rigid roles are admitted, i.e. if parts of the relational structure are the same in all contexts. In this paper, we present a novel combination of pairs of DLs and show that reasoning stays decidable even in the presence of rigid roles. We give complexity results for various combinations of DLs involving ALC, SHOQ, and EL

Temporalised Description Logics for Monitoring Partially Observable Events

Inevitably, it becomes more and more important to verify that the systems surrounding us have certain properties. This is indeed unavoidable for safety-critical systems such as power plants and intensive-care units. We refer to the term system in a broad sense: it may be man-made (e.g. a computer system) or natural (e.g. a patient in an intensive-care unit). Whereas in Model Checking it is assumed that one has complete knowledge about the functioning of the system, we consider an open-world scenario and assume that we can only observe the behaviour of the actual running system by sensors. Such an abstract sensor could sense e.g. the blood pressure of a patient or the air traffic observed by radar. Then the observed data are preprocessed appropriately and stored in a fact base. Based on the data available in the fact base, situation-awareness tools are supposed to help the user to detect certain situations that require intervention by an expert. Such situations could be that the heart-rate of a patient is rather high while the blood pressure is low, or that a collision of two aeroplanes is about to happen. Moreover, the information in the fact base can be used by monitors to verify that the system has certain properties. It is not realistic, however, to assume that the sensors always yield a complete description of the current state of the observed system. Thus, it makes sense to assume that information that is not present in the fact base is unknown rather than false. Moreover, very often one has some knowledge about the functioning of the system. This background knowledge can be used to draw conclusions about the possible future behaviour of the system. Employing description logics (DLs) is one way to deal with these requirements. In this thesis, we tackle the sketched problem in three different contexts: (i) runtime verification using a temporalised DL, (ii) temporalised query entailment, and (iii) verification in DL-based action formalisms