Verifying context-sensitive treebanks and heuristic parses in polynomial time

Proceedings of the 17th Nordic Conference of Computational Linguistics NODALIDA 2009. Editors: Kristiina Jokinen and Eckhard Bick. NEALT Proceedings Series, Vol. 4 (2009), 190-197. © 2009 The editors and contributors. Published by Northern European Association for Language Technology (NEALT) http://omilia.uio.no/nealt . Electronically published at Tartu University Library (Estonia) http://hdl.handle.net/10062/9206

Complete Axiomatizations of Fragments of Monadic Second-Order Logic on Finite Trees

We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present axiomatizations of the monadic second-order logic (MSO), monadic transitive closure logic (FO(TC1)) and monadic least fixed-point logic (FO(LFP1)) theories of this class of structures. These logics can express important properties such as reachability. Using model-theoretic techniques, we show by a uniform argument that these axiomatizations are complete, i.e., each formula that is valid on all finite trees is provable using our axioms. As a backdrop to our positive results, on arbitrary structures, the logics that we study are known to be non-recursively axiomatizable

Querying Linguistic Treebanks with Monadic Second-Order Logic in Linear Time

this paper we showed that linguistic treebanks can be queried with a very powerful query language, namely monadic second-order logic, in time linear in the size of the treebanks. We thus give an argument for that at least on a theoretical level the question of a choice of a query language for treebanks can be settled. We hardly expect the arise of a need of an even more powerful query language. And the fact that a large part of costly computations can be done in an offline preprocessing step to be performed only once lets us believe that the described approach is practically feasibl

Chapter 1 Querying Linguistic Treebanks with Monadic Second-Order Logic in Linear Time

In recent years large amounts of electronic texts have become available providing a new base for empirical studies in linguistics and offering a chance to linguists to compare their theories with large amounts of utterances from “the real world”. While tagging with morphosyntactic categories has become a standard for almost all corpora