Journal of Automated Reasoning

, Volume 57, Issue 2, pp 97–134

A Superposition Calculus for Abductive Reasoning


DOI: 10.1007/s10817-015-9344-2

Cite this article as:
Echenim, M. & Peltier, N. J Autom Reasoning (2016) 57: 97. doi:10.1007/s10817-015-9344-2


We present a modification of the Superposition Calculus that is meant to generate consequences of sets of first-order axioms. This approach is proven to be sound and deductive-complete in the presence of redundancy elimination rules, provided the considered consequences are built on a given finite set of ground terms, represented by constant symbols. In contrast to other approaches, most existing results about the termination of the Superposition calculus can be carried over to our procedure. This ensures in particular that the calculus is terminating for many theories of interest to the SMT community.


Equational first-order logic Abduction Superposition calculus  Deductive-completeness 

Mathematics Subject Classification

03B35 68T15 

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.University Grenoble AlpesGrenobleFrance
  2. 2.CNRS, LIGGrenobleFrance

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