Query Answering in Concept-Based Knowledge Representation Systems: Algorithms, Complexity, and Seman

The idea of developing knowledge representation systems based on a structured representation of knowledge was rst pursued with Semantic Networks and Frames. Later, concept languages (also called terminological languages, or description logics) have been introduced with the aim of providing a simple and well-established rst-order semantics to capture the meaning of the most popular features of the structured representations of knowledge. The basic inference tasks to be carried out on concept-based knowledge bases are Subsumption (\is one concept more general than the other one? ") and Instance Checking (\is an individual an instance of a concept? "). More complex query answering services, such as Retrieval (\ nd all the individuals that are instances of a concept"), can be reduced to a set of parallel Instance Checking tests, although the implementations may exploit suitable optimization strategies. In this thesis, we concentrate on Instance Checking, being understood that all the results on Instance Checking directly apply to more complex services. First, we analyze Instance Checking, providing algorithms for its solution and results for its intrinsic complexity in the various concept languages. The central question we address is whether Instance Checking can be easily reduced to Subsumption. To this aim, we present sound and complete methods for Instance Checking, and provide a complexity analysis of this problem, singling out languages for which Instance Checking is strictly harder than Subsumption, as well as languages for which Instance Checking can be solved by relying on Subsumption algorithms. This analysis highlights a new source of complexity in concept languages, which does not show up when checking Subsumption between concepts, and is due to the presence of individuals in the knowledge base. A practical implication of this fact is that any actual deduction procedure for reasoning in concept-based systems cannot be based solely on Subsumption, but has to embed some reasoning mechanisms that are not easily reducible to Subsumption. Such situation leads us to reconsider the semantics of knowledge bases and to address the various problems associated with it. Based on this, we consider 9 10 ABSTRACT concept constructors that allow to refer to individuals in the concept language. Constructors of that kind are generally used in concept-based systems (e.g., ONE-OF in classic) although the semantics employed for their treatment is a non-standard one. We perform a theoretical investigation on the use of those constructors with respect to the standard rst-order semantics, which shows various semantic issues and new sources of complexity. Further, we study the possibility of modifying the Instance Checking problem to the case in which the knowledge base and the concept representing the query are expressed in di erent languages. The aim of this is to gain expressivity of the query language without giving up the tractability of reasoning. Further, we introduce an epistemic operator that makes the query facilities to go beyond the rst-order setting of concept languages. Such an operator allows the user to express queries that address both aspects of the external world and aspects of the knowledge base state. We show that epistemic queries may have both a natural interpretation and good computational properties. We also show how the epistemic operator gives us the ability to formalize some procedural mechanism usually employed in actual systems, namely integrity constraints and trigger rules. We also discuss the complexity of reasoning with the most general form of statements about concepts (called free TBox), which allow us to express inclusions between general concepts, and terminological cycles as a particular case. Finally, we exploit all the results obtained in order to come up with an example of a concept-based system whose capabilities go beyond actual systems. Such system is meant to capture and precisely formalize the various features of early knowledge representation tools, embedding them in a concept-based framework that is still based on rst-order logic, but goes beyond it and overcomes some of the limitations of rst-order logic as a representational tool. Chapter