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.
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Djelloul, K., Dao, TBH. (2006). Extension of First-Order Theories into Trees. In: Calmet, J., Ida, T., Wang, D. (eds) Artificial Intelligence and Symbolic Computation. AISC 2006. Lecture Notes in Computer Science(), vol 4120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11856290_7
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DOI: https://doi.org/10.1007/11856290_7
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