Detection of First Order Axiomatic Theories

  • Guillaume Burel
  • Simon Cruanes
Conference paper

DOI: 10.1007/978-3-642-40885-4_16

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8152)
Cite this paper as:
Burel G., Cruanes S. (2013) Detection of First Order Axiomatic Theories. In: Fontaine P., Ringeissen C., Schmidt R.A. (eds) Frontiers of Combining Systems. FroCoS 2013. Lecture Notes in Computer Science, vol 8152. Springer, Berlin, Heidelberg

Abstract

Automated theorem provers for first-order logic with equality have become very powerful and useful, thanks to both advanced calculi — such as superposition and its refinements — and mature implementation techniques. Nevertheless, dealing with some axiomatic theories remains a challenge because it gives rise to a search space explosion. Most attempts to deal with this problem have focused on specific theories, like AC (associative commutative symbols) or ACU (AC with neutral element). Even detecting the presence of a theory in a problem is generally solved in an ad-hoc fashion. We present here a generic way of describing and recognizing axiomatic theories in clausal form first-order logic with equality. Subsequently, we show some use cases for it, including a redundancy criterion that can be applied to some equational theories, extending some work that has been done by Avenhaus, Hillenbrand and Löchner.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Guillaume Burel
    • 1
  • Simon Cruanes
    • 2
  1. 1.ÉNSIIE/CédricÉvry cedexFrance
  2. 2.École polytechnique and INRIAParisFrance

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