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Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Schloss Dagstuhl - Leibniz-Zentrum für Informatik

What is the computational content of proofs? This is one of the main topics in mathematical logic, especially proof theory, that is of relevance for computer science. The well-known foundational solutions aim at rebuilding mathematics constructively almost from scratch, and include Bishop-style constructive mathematics and Martin-Löf's intuitionistic type theory, the latter most recently in the form of the so-called homotopy or univalent type theory put forward by Voevodsky.

Schloss Dagstuhl - Leibniz-Zentrum für Informatik

The goal of this Dagstuhl Seminar is to provide an interdisciplinary forum to discuss the fundamental principles of fault management and diagnosis, bringing together international researchers from the fields of symbolic reasoning, machine learning, and control engineering. The seminar plans to identify an integrated framework to harmonize problems and algorithms from the different fields, as well as ideas for novel, integrated solutions; and to produce a comprehensive agenda for future research.

Neural Networks and Artificial Intelligence, Machine Learning,    Soft Computing, Evolutionary Computation, Metaheuristic Optimization, Fuzzy Logic

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Schloss Dagstuhl - Leibniz-Zentrum für Informatik

Proof theory is the study of formal proofs as mathematical objects in their own right. The subject has enjoyed continued attention among computer scientists in particular due to its significance for formalization, metalogic, and automation. In recent decades there has been a surge of interest on the representations of formal proofs themselves. The outcomes of these investigations have been remarkable, in particular extending the scope of structural proof theory to novel and richer settings. The point of this Dagstuhl Seminar is twofold. First and foremost, we want to bring together theorists and practitioners exploiting proof representations to identify new directions of application and, simultaneously, distill new theoretical directions from problems “in the wild”. At the same time, this seminar will expose the interface between the proof-normalization and proof-search traditions by probing proof representations from both directions.