Complete Axiomatizations of MSO, FO(TC1) and FO(LFP1) on Finite Trees

  • Amélie Gheerbrant
  • Balder ten Cate
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5407)


We propose axiomatizations of monadic second-order logic (MSO), monadic transitive closure logic (FO(TC1)) and monadic least fixpoint logic (FO(LFP1)) on finite node-labeled sibling-ordered trees. We show by a uniform argument, that our axiomatizations are complete, i.e., in each of our logics, every formula which is valid on the class of finite trees is provable using our axioms. We are interested in this class of structures because it allows to represent basic structures of computer science such as XML documents, linguistic parse trees and treebanks. The logics we consider are rich enough to express interesting properties such as reachability. On arbitrary structures, they are well known to be not recursively axiomatizable.


Trees Axiomatizations Fragments of MSO Henkin semantics Ehrenfeucht-Fraïssé games Feferman-Vaught theorems 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Amélie Gheerbrant
    • 1
  • Balder ten Cate
    • 2
  1. 1.ILLCUniversiteit van AmsterdamNetherlands
  2. 2.ISLAUniversiteit van AmsterdamNetherlands

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