Inconsistency Management in Generalized Knowledge and Action Bases

The combination of static and dynamic aspects in modeling complex organizational domains is a challenging task that has led to study the combination of formalisms from knowledge representation, database theory, and process management [18,23,11]. Specifically, Knowledge and Action Bases (KABs) [3] have been put forward recently to provide a semantically rich representation of a domain. In KABs, static aspects are modeled using a Description Logic (DL) [1] knowledge base (KB), while actions are used to evolve its extensional part over time, possibly introducing fresh individuals. An important aspect that has received little attention so far in such systems is the management of inconsistency with respect to domain knowledge that may arise when the extensional information is evolved over time. In fact, inconsistency, both in KABs and in related approaches, is typically handled naively by just rejecting updates in actions when they would lead to inconsistency, see e.g., [16,4,9,2]. To overcome this limitation, KABs have been extended lately with mechanisms to handle inconsistency [12]. However, this has been done by defining ad-hoc execution semantics and corresponding ad-hoc verification techniques geared towards specific semantics for inconsistency management. It has also been left open whether adding inconsistency management to the rich setting of KABs, actually increases expressive power. This work attacks these issues by: (i) Proposing (standard) GKABs, which enrich KABs with a compact action language inspired by Golog [20] that can be conveniently used to specify processes at a high-level of abstraction. As in KABs, standard GKABs still manage inconsistency naively. (ii) Defining a parametric execution semantic for GKABs that is able to elegantly accomodate a plethora of inconsistency-aware semantics based on the well-known notion of repair [17,5,19,13]. (iii) Providing several reductions showing that verification of sophisticated first-order temporal properties over inconsistency-aware GKABs can be recast as a corresponding verification problem over standard GKABs. (iv) Showing that verification of standard and inconsistency-aware GKABs can be addressed using known techniques, developed for standard KABs.