A formal framework for description logics with uncertainty
International Journal of Approximate Reasoning
Description logics (DLs) play an important role in the Semantic Web as the foundation of ontology language OWL DL. On the other hand, uncertainty is a form of deficiency or imperfection commonly found in real-world information/data. In this paper, we present a framework for knowledge bases with uncertainty expressed in the description logic ALC U , which is a propositionally complete representation language providing conjunction, disjunction, existential and universal quantifications, and full
... egation. The proposed framework is equipped with a constraint-based reasoning procedure that derives a collection of assertions as well as a set of linear/nonlinear constraints that encode the semantics of the uncertainty knowledge base. The interesting feature of our approach is that, by simply tuning the combination functions that generate the constraints, different notions of uncertainty can be modeled and reasoned with, using a single reasoning procedure. We establish soundness, completeness, and termination of the reasoning procedure. Detailed explanations and examples are included to describe the proposed completion rules. j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j a r realistic applications need the capability to handle uncertainty -from classification of genes in bioinformatics, schema matching in information integration, to matchmaking in Web services. The need to model and reason with uncertainty has been found in many different Semantic Web contexts. For example, in an online medical diagnosis system, one might want to find out to what degree a person, John, would have heart disease if the certainty that an obese person would have heart disease lies between 0.7 and 1, and John is obese with a degree between 0.8 and 1. Such knowledge cannot be expressed nor be reasoned with the standard DLs. In this paper, we propose a decidable constraint-based resolution approach to reason with uncertainty expressed in the DL ALC U . This language extends the standard DL ALC  with uncertainty, and is propositionally complete with conjunction, disjunction, existential and universal quantifications, and full negation. Constraint-based reasoning  solves reasoning problems by stating constraints about the problem and then finding solution satisfying all the constraints. There are several advantages in our constraint-based approach. For instance, constraints have well-defined and often intuitive semantics making them suitable to express complex uncertainty constraints. Also, constraints are declarative and hence easy to generate and use in other modules. Besides, there are many constraint solvers and algorithms to process them  . The constraint-based reasoning procedure proposed in this paper derives a set of assertions and constraints that encode the semantics of the ALC U knowledge base. These derived constraints are then solved using the constraint solver to perform the reasoning tasks. The interesting feature of this approach is that, by simply tuning the combination functions that generate the constraints, different notions of uncertainty can be modeled and reasoned with, using a single reasoning procedure. This paper is an extension of our previous work as follows. In , we presented a basic framework for representing the uncertainty knowledge as well as an initial attempt to study the inference rules. In , we presented a reasoning procedure for dealing with acyclic uncertainty knowledge bases. In this paper, we further extend  by presenting a reasoning procedure for dealing with general (both cyclic and acyclic) uncertainty knowledge bases. In addition, we establish soundness, completeness, and termination of the proposed reasoning procedure. The rest of this paper is organized as follows. Section 2 gives an overview of the DL ALC and other related work. Section 3 presents the DL ALC U , the proposed constraint-based tableau reasoning procedure, along with an illustrative example. We also establish the soundness, completeness, and termination of the ALC U reasoning procedure. Finally, concluding remarks and future directions are presented in Section 4.