Issues in the Eecient Use of a Relation Ontology for Conceptual Reasoning Issues in the Eecient Use of a Relation Ontology for Conceptual Reasoning

In this paper we extend the framework of combinatorial and conceptual worlds to allow arbitrary relations. Conceptual worlds of properties provide a framework for knowledge representation, reasoning, and in particular for conceptual belief revision. However, it is desirable to consider such worlds where relations are not restricted to properties. Firstly, we discuss foundations of the conceptual world framework such as the notion of a combinatorial world, mappings which allow us to build conceptual worlds out of combinatorial worlds, concepts and conceptual worlds. Then we present a sketch of a relation ontology and comment on its relationship to the framework. We also present initial steps for generalizing the framework to the case of unrestricted relations. Finally, we examine eeciency issues. We demonstrate that conceptual worlds are Boolean lattices and thus can be stored and retrieved eeciently. Moreover, proposed methods of computing entailment and accessibility relations on conceptual worlds prove an eecient use of the framework. Abstract In this paper we extend the framework of combinatorial and conceptual worlds to allow arbitrary relations. Conceptual worlds of properties provide a framework for knowledge representation, reasoning, and in particular for conceptual belief revision. However, it is desirable to consider such worlds where relations are not restricted to properties. Firstly, we discuss foundations of the conceptual world framework such as the notion of a combinatorial world, mappings which allow us to build conceptual worlds out of combinatorial worlds, concepts and conceptual worlds. Then we present a sketch of a relation ontology and comment on its relationship to the framework. We also present initial steps for generalizing the framework to the case of unrestricted relations. Finally, we examine eeciency issues. We demonstrate that conceptual worlds are Boolean lattices and thus can be stored and retrieved eeciently. Moreover, proposed methods of computing entailment and accessibility relations on conceptual worlds prove an eecient use of the framework.