Preface to the Special Issue on Automated Reasoning Systems

  • Armin Biere
  • Cesare Tinelli
  • Christoph WeidenbachEmail author

On March 8, 2018, Tobias Nipkow celebrated his sixtieth birthday. In anticipation of the occasion, after some discussion in early 2016 among all the editors of the Journal of Automated Reasoning except Tobias, it was decided to create two special issues to honor Tobias contributions to automated reasoning and their influence on the field.

The first issue, which has already appeared in Volume 61 under the title Introduction to Milestones in Interactive Theorem Proving, includes a synopsis on Tobias’s scientific life. In addition to his influence on interactive theorem proving, which was the focus of the first special issue, this special issue honors his influence on automated reasoning as well.

Interactive theorem proving, and in particular the Isabelle proof assistant co-developed by Tobias’s research group, have turned out to be a major success story for automatic reasoning itself. The need to improve automatic reasoning procedures to be used by interactive theorem provers to increase their own level of automation has led to an essential and vibrant new research direction in which Tobias and his close collaborators have played a crucial role so far. To honor that role this special issue is dedicated specifically to automated reasoning systems, as stated in its call for papers.

Call for papers for Special Issue on Automated Reasoning Systems of the Journal of Automated Reasoning

The past few decades have seen major developments and practical achievements in automated reasoning systems. For example, SAT solving has become an inherent part of the standard hardware production process; SMT solvers are now the backbone of most software verification techniques; first-order theorem provers have pushed the productivity of interactive theorem proving to a new level; computer algebra systems have solved difficult problems in mathematics and biology; knowledge representation systems have become indispensable for reasoning in the world wide web; automatic termination checkers routinely prove the termination of complex programs. This special issue is dedicated to automated reasoning systems in their full variety.

The preparation of this special issue involved the same rigorous reviewing and selection process that is applied to regular submission to this journal. In the end, five papers out of 21 submissions were selected for publication. Two papers, focus on formalizing aspects of automatic theorem proving procedures in an interactive theorem prover;
  • A Verified Implementation of Algebraic Numbers in Isabelle/HOL by

    Sebastiaan Joosten, René Thiemann and Akihisa Yamada,

  • Limited Second-Order Functionality in a First-Order Setting by

    Matt Kaufmann and J Strother Moore.

In one case, the goal is to generate code automatically for a correct-by-construction automatic reasoning procedure. In the other case, the higher-order formulation enables more powerful automatic reasoning later.
The remaining three papers discuss automatic reasoning systems:
  • OptiMathSAT: A Tool for Optimization Modulo Theories by

    Roberto Sebastiani and Patrick Trentin,

  • \({K}_{{S}}{P}\) A Resolution-Based Theorem Prover for \(K_n\): Architecture, Refinements, Strategies and Experiments by

    Cláudia Nalon, Ullrich Hustadt and Clare Dixon,

  • Scalable Fine-Grained Proofs for Formula Processing by

    Haniel Barbosa, Jasmin Christian Blanchette and Pascal Fontaine.

The first two provide results on the overall development of such systems for specific logics whereas the third paper addresses the problem of proof representation, pushing the integration of automatic and interactive theorem proving.



We thank all the authors who responded to our call for papers, and particularly the authors of the selected contributions for their excellent work. We are also grateful to the anonymous reviewers for their careful and constructive reviews. Finally, we would like to thank Tobias for pushing the performance of automated reasoning systems by posing challenges from interactive theorem proving.

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Johannes Kepler University LinzLinzAustria
  2. 2.Department of Computer ScienceThe University of IowaIowa CityUSA
  3. 3.Max Planck Institute for InformaticsSaarbrückenGermany

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