Metasystem transition schemes in computer science and mathematics

Abstract

We analyze metasystem transitions which may be observed, or are intentionally used, in computer science and mathematics. Various metasystem structures are present in their activities of executing, creating and manipulating formal linguistic models. The crucial role in automating the creation and manipulation of linguistic models is played by metacomputation, that is, computation over formal models. The manipulation of languages is one of the most essential problems of linguistic modeling. In this paper we analyze different schemes for transforming language definitions by metasystem transition and metacomputation, and present an example of ultra‐metasystem transition. We show that self‐application of metacomputation, a special case of metasystem transition, plays a central role in linguistic modeling. These techniques may also be utilized for reducing hierarchies of mathematical definitions and for manipulating mathematical texts effectively. Finally, we discuss a direct approach to theorem proving using a constructive representation of mathematical knowledge. We derive the basic requirements for metacomputation by a structural analysis of different model definitions using a single concept, namely formal linguistic modeling, and show that three operations must be performed effectively and efficiently by metacomputation: composition, inversion, and specialization of linguistic models.