A crash course in arrow logic

Abstract

This contribution gives a short introduction to arrow logic. We start by explaining the basic idea underlying arrow logic and the motivation for studying it (sections 1 and 2) We discuss some elementary duality theory between arrow logic and the algebraic theory of binary relations (section 3). In the sections 4 and 5 we give a brief survey of the theory that has been developed on the semantics (definability), axiomatics and decidability of various systems of arrow logic. We briefly describe some closely related formalisms and some extensions and reducts of arrow logic in section 6. We end with mentioning some promising research lines and open problems, in section 8.