Extension of First-Order Theories into Trees

  • Khalil Djelloul
  • Thi-Bich-Hanh Dao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4120)


We present in this paper an automatic way to combine any first-order theory T with the theory of finite or infinite trees. First of all, we present a new class of theories that we call zero-infinite-decomposable and show that every decomposable theory T accepts a decision procedure in the form of six rewriting which for every first order proposition give either true or false in T. We present then the axiomatization T * of the extension of T into trees and show that if T is flexible then its extension into trees T * is zero-infinite-decomposable and thus complete. The flexible theories are theories having elegant properties which enable us to eliminate quantifiers in particular cases.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Khalil Djelloul
    • 1
  • Thi-Bich-Hanh Dao
    • 2
  1. 1.Faculty of Computer Science, DFG research project ”Glob-Con”University of UlmGermany
  2. 2.Laboratoire d’Informatique Fondamentale d’OrléansOrléansFrance

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