Context Reasoning for Role-Based Models
When modeling a domain using concepts like rôles, phases, etc. it is important that all these so called meta-predicates have a formal definition and a well-defined semantics. To be able to express them in a suitable logic has several advantages. Stronger inferences can be drawn and inconsistencies can be found that would have stayed undetected otherwise. All the properties of these meta-predicates might be expressible in full first-order logic, but since reasoning in this logic is undecidable, automatic reasoning is not possible. Another family of knowledge representation formalisms are Description Logics (DLs) which are very expressive, but still provide decidable reasoning tasks.
Examining the properties of the meta-predicate rôle it becomes apparent that the notion of context is crucial for defining how a rôle behaves. DLs are well-suited to describe contexts as formal
objects with formal properties that are organized in relational structures. However, classical DLs lack expressive power to formalize furthermore that some individuals satisfy certain concepts and relate to other individuals depending on a specific context. Therefore, often two-dimensional DLs are employed. Based on approaches by Klarman et al., I investigated a family of two-dimensional Description Logics of contexts (CDLs) that stay decidable even in the presence of rigid roles, i.e. DL roles that are required to be interpreted the same in all contexts.
Another key property of rôles is their dynamic behaviour. One does not only change playing a rôle depending on the context, but also on a certain time. Until now that dynamic aspect of roles is neglected, but I will study combinations of DLs of context and temporal logics. Apart from choosing a suitable temporal logic, a main research question will be how different combinations affect the expressiveness and computational complexity. Prior work on temporal DLs by Baader et al. will serve as a starting point.
To my best knowledge, up to now there exists no DL reasoner that can handle DLs of context. So in order to use such systems, an appropriate calculus must be developed and implemented. There exist highly optimized DL reasoners, which are based on tableau or hypertableau calculus. Investigation and adaption of these calculi will result in a prototypical implementation of a CDL reasoner.