Extensions of first order logic
Extensions of first order logic
Descriptive Approach to Language - Theoretic Complexity
Descriptive Approach to Language - Theoretic Complexity
Monadic datalog and the expressive power of languages for web information extraction
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The Ehrenfeucht-Fraisse Games for Transitive Closure
TVER '92 Proceedings of the Second International Symposium on Logical Foundations of Computer Science
CSL '91 Proceedings of the 5th Workshop on Computer Science Logic
An "Ehrenfeucht-Fraïssé Game" for Fixpoint Logic and Stratified Fixpoint Logic
CSL '92 Selected Papers from the Workshop on Computer Science Logic
Querying Linguistic Treebanks with Monadic Second-Order Logic in Linear Time
Journal of Logic, Language and Information
Monadic Second-Order Logic and Transitive Closure Logics over Trees
Electronic Notes in Theoretical Computer Science (ENTCS)
XPath, transitive closure logic, and nested tree walking automata
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Axiomatizing the logical core of XPath 2.0
ICDT'07 Proceedings of the 11th international conference on Database Theory
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
An easy completeness proof for the modal µ-calculus on finite trees
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
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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.