Modular construction of logic knowledge bases: an algebraic approach

Abstract Modularity, reusability, extension capabilities and transformations are among the main facilities that must be considered in knowledge engineering targeted to the development of knowledge bases in the large. Moreover, fast and efficient techniques for updating, querying and inferencing with knowledge bases are also important issues. It seems that current knowledge representation approaches, namely the logic and the structural approaches, do not cope with the essential aspects that must characterize a knowledge engineer workbench. Herein, an algebraic approach allowing the modular construction of knowledge bases is proposed. The main building blocks of knowledge bases are the semantic primitives defined by theory morphisms, mappings taking knowledge bases into knowledge bases, and an interpretation functor. The application of a semantic primitive is the value of the interpretation functor for the chosen interpretations of the argument knowledge bases of the theory morphisms involved. A knowledge base becomes a structured theory from which we can retrace the respective construction sequence. Incidentally, the approach allows the description of a new architecture for knowledge engineering supporting two alternative representations of knowledge bases: a data base representation and a theory representation. Fast, concurrent and dumb updating and querying of knowledge bases can be targeted to the data base representation, whereas intelligent accesses can be directed to the theory representation. The structure of the knowledge base makes possible the selection of the relevant fragment for the purposes at hand. The E-R modeling concepts are adopted for illustrating the approach. The structuring aspects are discussed upon an E-R example of a fragment of a stock management knowledge base.