Reasoning on Knowledge in Symbolic Computing

Extended Abstract A novel framework, Formal, for specifying mathematical domains of computation and their inherently related type inference mechanisms as well as for transforming those speciications into knowledge bases is introduced. This framework Tja] aims at designing an environment for reasoning about knowledge in symbolic computing. It involves an algebraic speciication language, a method to transform speciications into knowledge bases and a hybrid knowledge representation system as well, cf. gure 1. The speciication language Formal-CT93] provides modular and well-structured spec-iications. It is well-suited to specify \mathematical objects" and, particularly, to specify the parametric and the inclusion polymorphisms in a uniied way. The underlying formalism is based upon the so-called homogeneous \ uniied algebras" allowing the treatment of sorts as values. Since algebraic speciications are the most appropriate formalism for embodying abstract algebras, e.g. group, ring, eld or module, and concrete algebras, e.g. polynomial rings, vector spaces or matrices, this speciication language can be regarded in the context of knowledge acquisition. There are many motivations and approaches to the executability of algebraic speciica-tions. Our approach is among the compilational ones. It consists in compiling a term to a representation in some model, e.g. the execution model is the semantics of the language of a hybrid knowledge representation. Such a language is of particular interest as an execution model since its data domain is the algebra of terms. In view of achieving the executability of speciications we have also developed the transformation method Formal-providing a capability for compiling a non-executable speciication into an executable one, i.e. into a knowledge base that can be processed by the inference machine of the hybrid knowledge representation system Mantra CTB91]. In Mantra four diierent knowledge representation formalisms are integrated: First-order logic, terminological languages, semantic networks and production systems. The role of Formal-consists in processing queries given by the user, e.g. to simplify a term or to deene the type of an expression. In this extended abstract we give an overview of Formal-, Mantra and Formal-. For the sake of clarity and of simplicity technical details are omitted.