Linguistics, Logic and Finite Trees

Logic Journal of the IGPL 2 (1):3-29 (1994)
Abstract
A modal logic is developed to deal with finite ordered binary trees a they are used in linguistics. A modal language is introduced with operators for the ‘mother of’, ‘first daughter of’ and ‘second daughter of’ relations together with their transitive reflexive closures. The relevant class of tree models is defined and three linguistic applications of this language are discussed: context free grammars, command relations, and trees decorated with feature structures. An axiomatic proof system is given for which completeness is shown with respect to the class of finite ordered binary trees. A number of decidability results follow
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DOI 10.1093/jigpal/2.1.3
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A First-Order Axiomatization of the Theory of Finite Trees.Rolf Backofen, James Rogers & K. Vijay-Shanker - 1995 - Journal of Logic, Language and Information 4 (1):5-39.
Fibred Semantics for Feature-Based Grammar Logic.Jochen Dörre, Esther König & Dov Gabbay - 1996 - Journal of Logic, Language and Information 5 (3-4):387-422.
Polyadic Dynamic Logics for Hpsg Parsing.Anders Søgaard & Martin Lange - 2009 - Journal of Logic, Language and Information 18 (2):159-198.

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