September 8 – 13 , 2019, Dagstuhl Seminar 19371

Deduction Beyond Satisfiability


Carsten Fuhs (Birkbeck, University of London, GB)
Philipp Rümmer (Uppsala University, SE)
Renate Schmidt (University of Manchester, GB)
Cesare Tinelli (University of Iowa – Iowa City, US)

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Aims & Scope
List of Participants
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Dagstuhl Seminar Schedule [pdf]


This report contains the program and outcomes of Dagstuhl Seminar 19371 on "Deduction Beyond Satisfiability" held at Schloss Dagstuhl, Leibniz Center for Informatics, during September 10--15, 2017. It was the thirteenth in a series of Dagstuhl Deduction seminars held biennially since 1993.

Research in automated deduction has traditionally focused on solving decision problems, which are problems with a binary answer. Prominent examples include proving the unsatisfiability of a formula, proving that a formula follows logically from others, checking the consistency of an ontology, proving safety or termination properties of programs, and so on. However, automated deduction methods and tools are increasingly being used to address problems with more complex answers, for instance to generate programs from formal specifications, compute complexity bounds, or find optimal solutions to constraint satisfaction problems.

In some cases, the required extended functionality (e.g., to identify unsatisfiable cores) can be provided relatively easily from current deduction procedures. In other cases (e.g., for Craig interpolation, or to find optimal solutions of constraints), elaborate extensions of these procedures are needed. Sometimes, altogether different methods have to be devised (e.g., to count the number of models of a formula, compute the set of all consequences of an ontology, identify missing information in a knowledge base, transform and mine proofs, or analyze probabilistic systems). In all cases, the step from yes/no answers to such extended queries and complex output drastically widens the application domain of deductive machinery. This is proving to be a key enabler in a variety of areas such as formal methods (for software/hardware development) and knowledge representation and reasoning.

While promising progress has been made, many challenges remain. Extending automated deduction methods and tools to support these new functionalities is often intrinsically difficult, and challenging both in theory and implementation. The scarcity of interactions between the involved sub-communities represents another substantial impediment to further advances, which is unfortunate because these sub-communities often face similar problems and so could greatly benefit from the cross-fertilization of ideas and approaches. An additional challenge is the lack of common standards for interfacing tools supporting the extended queries. Developing common formalisms, possibly as extensions of current standard languages, could be as transformative to the field as the introduction of standards such as TPTP and SMT-LIB has been in the past.

This Dagstuhl seminar brought together researchers working on deduction methods and tools that go beyond satisfiability and other traditional decision problems; specialists that work on advanced techniques in deduction and automated reasoning such as model counting, quantifier elimination, interpolation, abduction, or optimization; and consumers of deduction technology who need answers to more complex queries than just yes/no questions.

The unifying theme of the seminar was how to harness and extend the power of automated deduction methods to solve a variety of non-decision problems with useful applications. Research questions addressed at the seminar were the following:

  • What kind of information should be passed to a "beyond satisfiability" deduction tool, and what information should be returned to the user? The goal should be to enhance the understanding of related concepts in different subfields and applications, and to converge towards common formalisms.
  • How can current ideas, results and systems in one sub-community of researchers and practitioners benefit the needs of other communities?
  • What are outstanding challenges in using and building deduction tools to attack logical problems with complex answers?
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  Creative Commons BY 3.0 Unported license
  Carsten Fuhs, Philipp Rümmer, Renate Schmidt, and Cesare Tinelli

Dagstuhl Seminar Series


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


  • Automated deduction
  • Abduction
  • Interpolation
  • Synthesis
  • Quantifier elimination


In the series Dagstuhl Reports each Dagstuhl Seminar and Dagstuhl Perspectives Workshop is documented. The seminar organizers, in cooperation with the collector, prepare a report that includes contributions from the participants' talks together with a summary of the seminar.


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Dagstuhl's Impact

Please inform us when a publication was published as a result from your seminar. These publications are listed in the category Dagstuhl's Impact and are presented on a special shelf on the ground floor of the library.


Furthermore, a comprehensive peer-reviewed collection of research papers can be published in the series Dagstuhl Follow-Ups.