Proof-theoretic methods in algebra

Projektinformationen

PROALG

ID Finanzhilfevereinbarung: 256482

Abgeschlossenes Projekt

Startdatum 1 September 2010

Enddatum 31 August 2013

Finanziert unter

• Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)

Gesamtkosten € 75 000,00

EU-Beitrag € 75 000,00

Koordiniert durch

UNIVERSITAET BERN
Switzerland

Ziel

The goal of this project is to develop and exploit proof-theoretic methods for ordered algebraic structures. Traditionally, algebra and proof theory represent two distinct approaches within logic: the former concerned with semantic meaning and structures, the latter with syntactic and algorithmic aspects. In many intriguing cases, however, methods from one field have been essential to obtaining proofs in the other. In particular, proof-theoretic techniques have been used to establish important results for classes of algebras in the framework of residuated lattices. This includes both algebras for a wide range of non-classical logics investigated across mathematics, computer science, philosophy, and linguistics, and also important examples from algebra such as lattice-ordered groups. In recent years, researchers from many countries have begun to explore connections between these two fields more closely, providing algebraic interpretations of proof-theoretic methods, and vice versa. The time is now ripe to clarify and exploit these connections.

The concrete objectives of the project are: (A) to define uniform proof systems for classes of algebras and logic (such as e.g. lattice-ordered groups or cancellative residuated lattices) not covered by known frameworks, (B) to use proof systems to establish new decidability and complexity results, (C) to investigate relationships between the algebraic property of amalgamation and the logical property of interpolation and use proof systems to settle open problems, (D) to use proof systems to establish correspondences between algebraic properties and admissible rules. The main challenge and originality of the project will be to combine new insights and techniques from algebra and proof theory to tackle these goals.

Wissenschaftliches Gebiet

• humanities › languages and literature › linguistics
• natural sciences › mathematics › pure mathematics › discrete mathematics › mathematical logic
• natural sciences › mathematics › pure mathematics › algebra
• natural sciences › computer and information sciences
• humanities › philosophy, ethics and religion › philosophy

Programm/Programme

• FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)

Thema/Themen

• FP7-PEOPLE-2009-RG - Marie Curie Action: "Reintegration Grants"

Aufforderung zur Vorschlagseinreichung

FP7-PEOPLE-2009-RG
Andere Projekte für diesen Aufruf anzeigen

Finanzierungsplan

MC-IRG - International Re-integration Grants (IRG)

Koordinator

UNIVERSITAET BERN

Kontakt Verwaltung

Rachel Rossen (Prof.)

• EU-Beitrag: € 75 000,00
• Adresse: HOCHSCHULSTRASSE 6 ; 3012 Bern ; Schweiz
• Region: Schweiz/Suisse/Svizzera › Espace Mittelland › Bern / Berne
• Aktivitätstyp: Higher or Secondary Education Establishments
• Gesamtkosten: Keine Daten