National Research Project (COFIN) in Mathematical Logic
Metodi logici per il trattamento dell'informazione
Antonio Di Nola
Università di Salerno
Università di Torino
Local researchers involved in the project:
BERARDI Stefano. Full Professor.
RONCHI DELLA ROCCA Simonetta. Full Professor.
PAOLINI Luca Luigi. Resercher
ROVERSI Luca. Associate Professor.
CARDONE Felice. Associate Professor.
The intense technological development in recent decades has brought our society to a point where the need to manage large amounts of information, variously structured, has become crucial. The need for rigorous and versatile models requires a coordinated study of the various ways in which information may take shape. This project responds to such a demand, by offering a collaboration of a large number of research groups, having a wide range of skills in mathematical logic. This discipline is in fact able to provide a formal and a well developed framework for the rigorous study of the dynamics of the information, allowing the development of models, the design of new methods, and of robust implementations for processing reliable information.
The project is designed to enable researchers with different skills to work together on concrete problems, in order to share methods and perspectives, creating a lasting network of in order to prevent the fragmentation in the discipline. We propose to combine algebraic methods, and topological, categorical and proof theoretical methods, to address the following topics of study.
Formal systems that enable the coexistence of vagueness and uncertainty.
New methods, versatile and efficient, for the formal verification of the software.
Interactive demonstrations, as well as their harmonization with the usual practice of mathematical proofs.
Computational logics in which the notion of resource consumed is implicit and incorporated into the system.
New paradigms of computations, that allow you to manage new forms of computing, such as competitor, probabilistic, quantum or computations based on continuations or learning.
Methods for the extraction of programs and other information from constructive proofs in mathematics.
These issues are of great importance for the coherent development of new computing paradigms, and for obtaining a finer understanding of the mathematical models involved. Significant new solutions are now accessible thanks to recent advances in these disciplines. Moreover, we believe that this combination of methods is of great importance, as it would lead to the establishment of a network of partnerships organic, interdisciplinary and long-lasting. We believe that this responds promptly to a growing need, widely perceived, to bring together this community of logic.
The participants in this project have a wealth of world-class collaborations, and some groups have already worked with profit in joint research projects. Moreover, the experience of the participants, demonstrated by their curriculum, the impact of their research and their prestigious international collaborations, ensure that the objectives can realistically be achieved. The interdisciplinary approach offered is genuinely original in that it springs from combining new methods and partnerships. In addition, the topics of cutting-edge research proposed is a further proof of the originality of the research. The innovative methods we are using guarantee originality of our approach to these issues.
We believe that this project will give a major boost to the excellence of research in Italy and in Europe, on strategic issues which have direct effects on technological paradigms that are driving growth, productivity, and progress. As a result, we expect that the creation of this network of partnerships is of decisive importance to create a major European project on logic, computing, and information.