##
###
Deduction Beyond Satisfiability (Dagstuhl Seminar 19371)

Carsten Fuhs, Philipp Rümmer, Renate Schmidt, Cesare Tinelli, Michael Wagner

2020
*
Dagstuhl Reports
*

Research in automated deduction is traditionally focused on the problem of determining the satisfiability of formulas or, more generally, on solving logical problems with yes/no answers. Thanks to recent advances that have dramatically increased the power of automated deduction tools, there is now a growing interest in extending deduction techniques to attack logical problems with more complex answers. These include both problems with a long history, such as quantifier elimination, which are
## more »

... being revisited in light of the new methods, as well as newer problems such as minimal unsatisfiable cores computation, model counting for propositional or first-order formulas, Boolean or SMT constraint optimization, generation of interpolants, abductive reasoning, and syntax-guided synthesis. Such problems arise in a variety of applications including the analysis of probabilistic systems (where properties like safety or liveness can be established only probabilistically), network verification (with relies on model counting), the computation of tight complexity bounds for programs, program synthesis, model checking (where interpolation or abductive reasoning can be used to achieve scale), and ontology-based information processing. The seminar brought together researchers and practitioners from many of the often disjoint subcommunities interested in the problems above. The unifying theme of the seminar was how to harness and extend the power of automated deduction methods to solve problems with more complex answers than binary ones. Seminar September 8-13, 2019 -http://www.dagstuhl.de/19371 License Creative Commons BY 3.0 Unported license © Carsten Fuhs, Philipp Rümmer, Renate Schmidt, and Cesare Tinelli 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:

doi:10.4230/dagrep.9.9.23
dblp:journals/dagstuhl-reports/FuhsRST19
fatcat:j6moci5zgvgjzgpsqblemwsrlm