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A Framework for the Flexible Integration of a Class of Decision Procedures into Theorem Provers

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Original languageEnglish
Title of host publicationAutomated Deduction — CADE-16
Subtitle of host publication16th International Conference on Automated Deduction Trento, Italy, July 7–10, 1999 Proceedings
PublisherSpringer-Verlag GmbH
ISBN (Electronic)978-3-540-48660-2
ISBN (Print)978-3-540-66222-8
Publication statusPublished - 1999

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Verlag
ISSN (Print)0302-9743


The role of decision procedures is often essential in theorem proving. Decision procedures can reduce the search space of heuristic components of a prover and increase its abilities. However, in some applications only a small number of conjectures fall within the scope of the available decision procedures. Some of these conjectures could in an informal sense fall ‘just outside’ that scope. In these situations a problem arises because lemmas have to be invoked or the decision procedure has to communicate with the heuristic component of a theorem prover. This problem is also related to the general problem of how to exibly integrate decision procedures into heuristic theorem provers. In this paper we address such problems and describe a framework for the exible integration of decision procedures into other proof methods. The proposed framework can be used in different theorem provers, for different theories and for different decision procedures. New decision procedures can be simply ‘plugged-in’ to the system. As an illustration, we describe an instantiation of this framework within the Clam proof-planning system, to which it is well suited. We report on some results using this implementation.

    Research areas

  • theorem proving, decision procedures, integrating decsion procedures, quantifier elimination

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