PP-2008-44: Complete Axiomatizations of $MSO$, $FO(TC^1)$, $FO(LFP^1)$ on Finite Trees

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

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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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