A proof system for finite trees

Abstract

In this paper we introduce a description language for finite trees. Although we briefly note some of its intended applications, the main goal of the paper is to provide it with a sound and complete proof system. We do so using standard axioms from modal provability logic and modal logics of programs, and prove completeness by extending techniques due to Van Benthem and Meyer-Viol (1994) and Blackburn and Meyer-Viol (1994). We conclude with a proof of the EXPTIME-completeness of the satisfiability problem, and a discussion of issues related to complexity and theorem proving.