Extension of first-order theories into trees

Authors:
Khalil Djelloul;Thi-Bich-Hanh Dao
Affiliations:
Faculty of Computer Science, DFG research project ”Glob-Con”, University of Ulm, Germany;Laboratoire d'Informatique Fondamentale d'Orléans, Orléans, France
Venue:
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
Year:
2006

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Abstract

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.