First-Order Logic with Reachability Predicates on Infinite Systems

Stefan Schulz
This paper focuses on first-order logic (FO) extended by reachability predicates such that the expressiveness and hence decidability properties lie between FO and monadic second-order logic (MSO): in FO(R) one can demand that a node is reachably from another by some sequence of edges, whereas in FO(Reg) a regular set of allowed edge sequences can be given additionally. We study FO(Reg) logic in infinite grid-like structures which are important in verification. The decidability of logics...