Reachability and the power of local ordering
STACS '94 Selected papers of the eleventh symposium on Theoretical aspects of computer science
Descriptive Approach to Language - Theoretic Complexity
Descriptive Approach to Language - Theoretic Complexity
An operational and denotational approach to non-context-freeness
Theoretical Computer Science - Algebraic methods in language processing
The Expressive Power of Transitive Closue and 2-way Multihead Automata
CSL '91 Proceedings of the 5th Workshop on Computer Science Logic
Logics For Context-Free Languages
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
Journal of Computer and System Sciences
Complete Axiomatizations of MSO, FO(TC1) and FO(LFP1) on Finite Trees
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
Journal of Logic, Language and Information
Graph-transformation verification using monadic second-order logic
Proceedings of the 13th international ACM SIGPLAN symposium on Principles and practices of declarative programming
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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.