| The integration,representation,and reasoning of heterogeneous knowledge from multiple sources is one of the key research topics in artificial intelligence.Nonmonotonic multi-context systems(nMCS)proposed by Brewka and Eiter are an ideal framework for integrating heterogeneous knowledge from multiple sources,where heterogeneous knowledge is represented by distinct logics,the interaction between multiple knowledge sources is modeled via nonmonotonic bridge rules,and equilibrium characterizes acceptable belief states of such systems.However,the logical framework and bridge rules in nMCS are unsuitable for handling uncertain knowledge.This work proposes fuzzy multi-context systems(FMCS)based on nMCS to represent and reason heterogeneous uncertain knowledge from different sources,as well as investigates the inconsistency of FMCS and its resolution mechanisms.FMCS thus significantly enhances the expressive and processing capabilities of nMCS.The major work of this paper is summarized as follows:(1)We present an abstract logical framework for dealing with uncertain knowledge and introduce the notion of(strong)inconsistency in such a framework.To begin with,we propose a novel abstract logical framework to capture distinct types of logic,and further formalize the inconsistency of knowledge bases within this framework.Such inconsistency could occur in two cases: one is that knowledge bases lack acceptable fuzzy belief sets,and the other is that all of their acceptable fuzzy belief sets are inconsistent.Next,we define the notion of monotonicity based on Smyth ordering and Hoare ordering to divide monotonic abstract logic from nonmonotonic abstract logic.After that,we introduce notions of strong consistency and strong inconsistency for nonmonotonic abstract logic,as well as present a method based on strong inconsistency for quantifying the inconsistency of(finite)knowledge bases.This method can apply to both monotonic and nonmonotonic cases.Finally,we examine the complexity of(strong)consistency and strong inconsistency problems in abstract logic.(2)We propose fuzzy multi-context systems for representing and reasoning heterogeneous uncertain knowledge from various sources.logic serves as the theoretical foundation for fuzzy multi-context knowledge representation,fuzzy bridge rules interlink heterogeneous sources,and fuzzy equilibria are utilized to characterize the semantics of fuzzy multi-context systems.The syntactic and semantic framework for nonmonotonic fuzzy multi-context systems is then systematically constructed.Moreover,we investigate grounded fuzzy equilibrium semantics and well-founded fuzzy equilibrium semantics,as well as discuss the complexity of the existence of fuzzy equilibria of fuzzy multi-context systems.Finally,we show that fuzzy multi-context systems generalize nonmonotonic multi-context systems,possibilistic multi-context systems,and probabilistic multi-context systems.(3)We present methods based on diagnoses and explanations for handling the inconsistency of fuzzy multi-context systems.To start with,we formalize the inconsistency of fuzzy multi-context systems based on the inconsistency of knowledge bases,which includes two cases: global inconsistency and local inconsistency.Next,we provide a method based on consistent subsystems to measure the inconsistency of fuzzy multi-context systems.We then propose diagnoses based on fuzzy bridge rules to repair inconsistent fuzzy multi-context systems and investigate the necessary and sufficient conditions for the existence of diagnoses based on strong inconsistency.Meanwhile,we employ explanations based on fuzzy bridge rules to explain why fuzzy multi-context systems are inconsistent and explore the necessary and sufficient conditions for the existence of explanations.Moreover,we consider the relationship between diagnoses and explanations.Finally,we examine the complexity of whether a fuzzy multi-context system is consistent,and of diagnoses and explanations recognition.Particularly,our method for analyzing local inconsistency could apply to other multi-context systems such as nonmonotonic multi-context systems,possibilistic multi-context systems,and probabilistic multi-context systems.In summary,fuzzy multi-context systems provide a unified theoretical framework for the fusion of heterogeneous(uncertain)knowledge from distinct sources and thus offer a novel logic-based approach for knowledge fusion,reasoning,and inconsistency handling in intelligent systems. |
