Konferenzen  >  Mathematik  >  Computer-gestütztes Beweisen

California Institute of Technology (Caltech)

Neuronale Netze und Künstliche Intelligenz, Maschinelles Lernen,    Optimierungsrechnung, Entscheidungsunterstützung

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.

Neuronale Netze und Künstliche Intelligenz, Maschinelles Lernen,    Soft Computing, Evolutionäre Algorithmen, metaheuristische Optimierung, Fuzzylogik

This series of events began with the theme of foundations in the context of automated theorem proving: What are the chances and problems of the act of formalization in the context of mathematics? It is often said, that all of mathematics can be reduced to first-order logic and set theory. The derivation indicator view says that all proofs stand in some relation to a derivation, i.e. a mechanically checkable syntactical objects following fixed rules, that would not have any gaps. For a long time this was a mere hope. There may have been proofs of concepts from early logicists but derivation never played a big role in mathematical practice. The modern computer might change this. Interactive and automated theorem provers promise to make the construction of a justification without any gaps feasible for complex mathematics. Is this promise justified? Will the future of mathematical practice shift to more formal mathematics? Should it? We hope to illuminate such questions and focus especially on what these developments mean for the future of the curriculum of university students. After three years on the topic, we have realized that this context is too narrow to understand formalization and thus we have we added a yearly theme (although not all talks are necessarily aligned with it). This year we focus on historical perspectives: How were different formal systems implemented? How much choice was there? Is our current view an ironed out history, written by the winner of the debate?

VMCAI provides a forum for researchers from the communities of Verification, Model Checking, and Abstract Interpretation, facilitating interaction, cross-fertilization, and advancement of hybrid methods that combine these and related areas. VMCAI 2024 will be the 25th edition in the series.

Research Institute for Mathematical Sciences (RIMS)

Schloss Dagstuhl - Leibniz-Zentrum für Informatik

Probabilistic model checking is an area within the formal methods community that supports the analysis of a variety of queries on Markov chains (MCs), Markov decision processes (MDPs), and variations of these formalisms. Since MCs and MDPs are popular in a variety of research communities, probabilistic model checking research and algorithms have been applied by researchers in reliability engineering, robotics, safety in AI, computational biology, and others. We see two ingredients to this success story. First, the availability of the PRISM model checker, which has been developed over more than 20 years, has yielded a standard set of benchmarks, input language, and a de-facto standard to compare with. Second, a variety of modern tools have provided additional functionalities, and they de-facto adopted the PRISM interface. Consequently, users can easily run the tool that is most suited for their problem. However, the success and broad applicability of these model checkers yields tools and interfaces that are increasingly diverging, based on the domains they specialize on. In addition, for queries that have been developed more recently, there is no de-facto standard and thus, tools do not necessarily agree on the interface. In this workshop, we aim to converge on some of these interfaces, in order to align the tools and make sure that they keep providing value for researchers in a variety of communities.

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

CIRM – Centre International de Rencontres Mathématiques

Many proof assistants can be used to formalise mathematics. Two of the most commonly used today by “standard mathematicians” are Lean and Coq, and the conference will mainly focus on the first. Lean comes with a vast library of formalised mathematics, mathlib. The existence of such a library allows one to work on contemporary mathematics. The meeting’s main goal is to introduce mathematicians to Lean and to formalisation in general.

Hausdorff Research Institute for Mathematics (HIM)

The goal of this program is to bring together experts of Formal Mathematics, exploit their interactions, foster future collaborations, and interface them better with the mathematical mainstream. At the same time the goal is to provide a platform for junior researchers to enter Formal Mathematics. A central, unifying theme is to break down adoption barriers of formal methods in Mathematics.

Kurse und Veranstaltungen für Studenten der Mathematik,    Mathematische Logik, Grundlagen der Mathematik

Hausdorff Research Institute for Mathematics (HIM)

This workshop focusses on the man / machine interaction in Formal Mathematics. Presently, most formal proofs are practically unreadable by average mathematicians, as they appear like specialized computer code. Can this be improved by making proof languages "readable", or by automatic translation from formalizations into a natural language-like format?

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.

ICMS - International Centre for Mathematical Sciences

This workshop will unite zero-knowledge researchers in the UK and Europe and facilitate community building, especially among PhD students and early career researchers. The content that is presented will be published online as a lasting resource. The ultimate objective of the workshop is to have a significant long-term effect on research in zero-knowledge proofs and privacy-enhancing techniques by encouraging connections and creating resources for researchers.

The workshop will cover several topics within this field, including classical results, interactive oracle proofs, proof from symmetric primitives, group and pairing-based proof systems such as ZK-SNARKs, lattice-based proof systems, and real-world applications.

Schloss Dagstuhl - Leibniz-Zentrum für Informatik

The problem of deciding whether a propositional formula is satisfiable (SAT) is one of the most fundamental problems in computer science, both theoretically and practically. Due to its practical implications, intensive research has been performed on how to solve SAT problems in an automated fashion, and SAT solving is now a ubiquitous tool to solve many hard problems, both from industry and mathematics. SAT is also increasingly being applied in logics that are not decidable, particularly in the context of first-order theorem proving. Here, fast SAT solvers are used for reasoning sub-tasks and for guiding the theorem provers. The main aim of this Dagstuhl Seminar is to bring together researchers from different areas of activity on SAT and researchers that work in the field of first-order theorem proving so that they can communicate state-of-the-art advances and embark on a systematic interaction that will enhance the synergy between the different areas.