MALOA

From Mathematical Logic To Applications

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 Obiettivo del progetto (Objective)

'Mathematical logic is a rapidly-developing subject with sophisticated techniques and many applications in algebra, geometry, number theory, analysis, and computer science. Even though the branches of logic share vital concepts and techniques, in recent years increased specialism has meant that most researchers are trained in just one branch of logic, and there is a need in Europe for researchers who have an overview of techniques from logic. To meet this need, this project will provide a broad training for early stage researchers across the main areas of mathematical logic and its many applications. 18 early-stage researchers (ESRs) will be trained for 36 months each, and a further 20 ESRs, undertaking doctoral studies elsewhere, will be appointed for 3--6 months each. Doctoral research projects for ESRs have been prepared in model theory, aspects of complexity theory (proof complexity, finite model theory), proof theory, computability theory, set theory, and real valued logics. Network-wide training will be provided through three 7-day training workshops, two 3-day and one 5-day research workshops, and a 5-day final conference. Some secondments of ESRs, and short ESR appointments, will be coordinated around a special semester in model theory in Lyon, and a later one in logical aspects of complexity theory in Prague. Complementary training is provided by the hosts, and through the training workshops. The network consists of 8 full partners, each a major logic group with strength in more than one branch of logic and experience in the training of early stage researchers, and each based in a major European university. The partners have been chosen to complement each other in strengths, and together to cover most branches of mathematical logic. In addition to the 8 full partners, training is provided by an academic Associated Partner (University of East Anglia) and two industrial Associated Partners (Onera and BT Group, each at Level 2).'

Introduzione (Teaser)

Growth in the many branches of mathematical logic reflects different schools of thought and various applications in algebra, analysis and geometry. An EU-funded training network targeted this fragmentation by providing young researchers with an overview of current knowledge and research directions.

Descrizione progetto (Article)

Since the earliest days of scientific thinking, logic has been the part of philosophy devoted to reasoning. Mathematical logic emerged from a need to formalise facts in the form of logical sentences and to reason systematically with this information to derive logical conclusions. Symbols and formulas resembling those of mathematics go beyond the reach of traditional logic.

The advent of computers led to real-world applications. Today, mathematical logic plays a central role in software engineering, programming, artificial intelligence, linguistics and theoretical computer science. Having outgrown its philosophical roots, mathematical logic also continuously interacts with other branches of mathematics.

'From mathematical logic to applications' (http://www1.maths.leeds.ac.uk/maloa/index.html (MALOA)) was a training network project reflecting a common research goal to unravel interactions between different branches of mathematical logic. A group of outstanding European mathematicians joined MALOA to provide 42 early-stage researchers (ESRs) with training in a broad range of concepts and state-of-the-art techniques.

MALOA participants represented eight of Europe's most active academic centres in model theory, complexity theory, proof theory and set theory. The training programme included the latest advances in mathematical logic with potential industrial applications. Young scientists left the network after successful completion of their training with a set of aptitudes that enables them to produce influential research.

Project efforts resulted in a long-lasting consortium for cutting-edge research, leading to accelerated discoveries even during its four-year lifespan. The recruited PhD students and postdoctoral fellows in MALOA have already contributed with new concepts to the model and proof theories.

Moreover, the training programme that addressed the fragmentation of mathematical logic also boosted the trainees' career opportunities. Besides providing support to PhD candidates through the completion of their theses, many MALOA ESRs attained permanent academic posts or employment in industry, thereby strengthening the European research base.