PP-2008-44:
Gheerbrant, Amélie and ten Cate, Balder
(2008)
*Complete Axiomatizations of $MSO$, $FO(TC^1)$, $FO(LFP^1)$ on Finite Trees.*
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## Abstract

We propose axiomatizations of monadic second-order logic MSO, monadic

transitive closure logic (FO(TC^1)) and monadic least fixpoint logic

(FO(LFP^1)) 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.

Item Type: | Report |
---|---|

Report Nr: | PP-2008-44 |

Series Name: | Prepublication (PP) Series |

Year: | 2008 |

Uncontrolled Keywords: | Trees; Axiomatizations; Fragments of MSO; Ehrenfeucht-Fraisse games; Feferman Vaught Theorems |

Date Deposited: | 12 Oct 2016 14:37 |

Last Modified: | 12 Oct 2016 14:37 |

URI: | https://eprints.illc.uva.nl/id/eprint/318 |

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