September 10 – 15 , 2017, Dagstuhl Seminar 17371

Deduction Beyond First-Order Logic


Jasmin Christian Blanchette (VU University of Amsterdam, NL)
Carsten Fuhs (Birkbeck, University of London, GB)
Viorica Sofronie-Stokkermans (Universität Koblenz-Landau, DE)
Cesare Tinelli (University of Iowa – Iowa City, US)

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Dagstuhl Report, Volume 7, Issue 9 Dagstuhl Report
Aims & Scope
List of Participants
Dagstuhl Seminar Schedule [pdf]


Much research on automated deduction has traditionally focused on automated reasoning in first-order logic. First-order logic with equality is generally considered a sweet spot on the logic design continuum. Yet, from the point of view of several applications it can be too restrictive as a modeling and reasoning tool. In recent years, there has been a realization that while first-order reasoning is very useful to discharge the bulk of proof obligations, it must be tightly integrated with richer features to be useful in many applications. Practical problems often need a mixture of first-order proof search and some more advanced reasoning, for instance, about non-first-order-axiomatisable theories, higher-order formulas, or simply higher-level reasoning steps.

First-order logic cannot be used to finitely axiomatize many interesting theories, such as those including transitive closure operators, inductive predicates, datatypes, and standard arithmetic on integers or reals. Even provers that provide native support for some of these theories typically fail to prove trivial-looking problems because they lack general support for mathematical induction. Some applications need a richer set of constructs than those provided by first-order logic such as, for instance, the separating conjunction (*) and magic wand (-*) connectives of Separation Logic or the disjunctive well-foundedness predicates used in HSF, a popular approach to software model checking based on first-order Horn logic.

There are potential synergies between automatic first-order proving and verification methods developed in the context of richer logics. However, they have not received enough attention by the various deduction sub-communities so far. In general, there is a cultural gap between the various deduction communities that hinders cross-fertilization of ideas and progress.

This Dagstuhl Seminar brought together experts in automated reasoning in first-order logic and researchers working on deduction methods and tools that go beyond first-order logic. The latter included specialists on proof methods for induction, proof planning, and other higher-order or higher-level procedures; and consumers of deduction technology whose specification languages contain non-first-order features. The main goal of the seminar was to exchange ideas and explore ways to facilitate the transition from first-order to more expressive settings.

Research questions that were discussed and answered at the seminar included the following:

  • What higher-order features do applications need, and what features can be incorporated smoothly in existing first-order proof calculi and provers?
  • How can we best extend first-order reasoning techniques beyond first-order logic?
  • Can proof-assistant-style automation and first-order reasoning techniques be combined in a synergetic fashion?
  • What are good strategies for automatic induction and coinduction or invariant synthesis?
  • Is a higher layer of reasoning, in the spirit of proof planning, necessary to solve more difficult higher-order problems?
Summary text license
  Creative Commons BY 3.0 Unported license
  Jasmin Christian Blanchette, Carsten Fuhs, Viorica Sofronie-Stokkermans, and Cesare Tinelli

Dagstuhl Seminar Series


  • Artificial Intelligence / Robotics
  • Semantics / Formal Methods
  • Verification / Logic


  • Automated reasoning
  • Automated deduction
  • Decision procedures
  • Higher-order logic
  • Formal proof
  • Program verification


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