Model Theoretic Issues in Theoretical Computer Science, Part I: Relational Data Bases and Abstract Data Types

Abstract

The chapter deals with the problems in the foundations of computer science and three apparently different aspects of current computer science research: data base theory, algebraic specification of abstract data types, and algorithmic logic. The pure mathematician is content with knowledge, which contributes to the understanding of the internal problems of differential equations as such, and solving a particular one is seen by him/her as a challenge of his/her general understanding. The chapter discusses data base theory and specification of abstract data types, with various approaches to semantics of programming languages and demonstrates this in the case of data base theory. As it turns out, there are various intimate connections between finite model theory and data base theory, which have led people to think that either data base theory is just undergraduate logic or that the logicians try to sell it as such. But, the real problems in any applied science are neither defined by their mathematical difficulty nor by the methodologies used to solve them but rather by the questions they try to answer. Data base theory tries to answer the questions about design, design criteria, optimization and specification of data bases, and their queries. There are various approaches to this problem, but the most successful—at least in terms of fashion—is called “algebraic” and the technical parts of abstract model theory fit the needs of various branches of program semantics and program verification. The attention is on program correctness and programming logics and usage of the various logics to introduce a new type of semantics, which in contrast to operational or denotational semantics, maps programming languages into subsets of logics.