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Monadic Second-Order Logic and Transitive Closure Logics Over Trees
Research on Language & Computation (2009)
  • Hans Joerg Tiede, Illinois Wesleyan University
  • Stephan Kepser
Abstract

Model theoretic syntax is concerned with studying the descriptive complexity of grammar formalisms for natural languages by defining their derivation trees in suitable logical formalisms. The central tool for model theoretic syntax has been monadic second-order logic (MSO). Much of the recent research in this area has been concerned with finding more expressive logics to capture the derivation trees of grammar formalisms that generate non-context-free languages. The motivation behind this search for more expressive logics is to describe formally certain mildly context-sensitive phenomena of natural languages. Several extensions to MSO have been proposed, most of which no longer define the derivation trees of grammar formalisms directly, while others introduce logically odd restrictions. We therefore propose to consider first-order transitive closure logic. In this logic, derivation trees can be defined in a direct way. Our main result is that transitive closure logic, even deterministic transitive closure logic, is more expressive in defining classes of tree languages than MSO. (Deterministic) transitive closure logics are capable of defining non-regular tree languages that are of interest to linguistics.

Keywords
  • Tree languages - Monadic second-order logic - Transitive closure logics - Cross-serial dependencies - Model theoretic syntax
Disciplines
Publication Date
2009
Citation Information
Hans Joerg Tiede and Stephan Kepser. "Monadic Second-Order Logic and Transitive Closure Logics Over Trees" Research on Language & Computation Vol. 7 Iss. 1 (2009)
Available at: http://works.bepress.com/htiede/11/