Introduction

Abstract

The birth of any logical system inevitably gives rise to a number of issues pertaining to the system as e.g. the problem of its completeness, axiomatizability, decidability etc. The development of logic makes it possible to detect similarities among various methods of tackling these metalogical problems. It often turns out that a particular method, originally designed for a definite logic, has a much wider range of applicability and richer consequences than has been initially assumed. E.g. the techniques of relational semantics, invented by Kanger, Hintikka, Montague and Kripke, and initially applied to some simple deontic and modal systems, turned out to be a powerful tool in metalogical investigations. The significance of this tool goes far beyond modal logic, for relational methods proved to be useful in the semantic analysis of many other classes of logics. A similar remark concerns the scope of the so called algebraic approach in metalogic. This approach offers methods which can be uniformly applied to a wide variety of logical systems.

If for any language the term ‘consequence’ is established, then everything that is said concerning the logical connectives within this language is thereby determined.

Rudolf Carnap

The Logical Syntax of Language