We extend first-order logic with counting by a new operator that

allows it to formalise a limited form of recursion which can be

evaluated in logarithmic space. The resulting logic LREC has a

data complexity in LOGSPACE, and it defines LOGSPACE-complete

problems like deterministic reachability and Boolean formula

evaluation. We prove that LREC is strictly more expressive than

deterministic transitive closure logic with counting and

incomparable in expressive power with symmetric transitive closure

logic STC and transitive closure logic (with or without counting).

LREC is strictly contained in fixed-point logic with counting FPC.

We also study an extension LREC= of LREC that has nicer closure

properties and is more expressive than both LREC and STC, but is

still contained in FPC and has a data complexity in LOGSPACE.

Our main results are that LREC captures LOGSPACE on the class of

directed trees and that LREC= captures LOGSPACE on the class of

interval graphs.