Abstract Proof Theory

Here the schedule of the workshop

Workshop organized by

Luiz Carlos Pereira

PUC, Rio de Janeiro, Brazil

Peter Schroeder_Heister

University of Tübingen, Germany

At present we do not have Abstract Proof Theory as a branch of Mathematical Logic, in the same sense in which we do have Abstract Model Theory - there is nothing so far comparable e.g. to Lindström's theorem in proof theory. But, to borrow an expression used by Kreisel, although we do not have a science (a discipline), we do have a natural history (scattered results).

The changing scope of logic through its history also has important philosophical implications: is there such a thing as the essence of logic, permeating all these different developments? Or is the unity of logic as a discipline an illusion? What can the study of the changing scope of logic through its history tell us about the nature of logic as such? What do the different languages used for logical inquiry – regimented natural languages, diagrams, logical formalisms – mean for the practices and results obtained? 

Call for papers

We invite submissions that belong to this intended field. The following is a non-exclusive list of possible topics.

- Abstract deductive systems (generalized rules in natural deduction and in sequent calculi)
 - The nature and role of ordinal analysis
 - The identity problem (When are two proofs identical?)
 - Abstract normalization, strong normalization and confluence
 - Inversion principles
 - Reducibility predicates
 - Reducibility and definability
 - Translations and intepretations
 - The role of categorical logic

Abstracts for this workshop should be sent via e-mail before November 15 2012 to:

psh@informatik.uni-tuebingen.de

or

luiz@inf.puc-rio.br

 

 

 

 

 

 

 

 

 

Contributing Speakers

Maria da Paz Mederiros, Massimiliano Carrara and Vittorio Morato, Dpt of Philosophy, UFRN, Natal, Brazil, Dpt of Philosphy, University of Padua, Italy, Quantified Modal Logic: A Proof-Theoretic Approach

Ori Lahav, Dpt of Computer Science, Tel-Aviv, Israel, Semantic Investigation of Basic Sequent Systems

Silvia Ghilezan and Silvia Likavec, Faculty of Engineering, University of Novi Sad, Serbia and University of Turin, Italy, Reducibility Method and Resource Control

David Cerna, Technical University of Vienna, Austria, Towards Powerful and Decidable Formalizations Through Schematic Representation

Norbert Gratzl and Marta Sznadjer, Dpt of Philosophy, University of Munich, Germany, Generalized Identity of Proofs

Wagner de Campos Sanz, Dpt of Philosophy, Federal University of Goias, Brazil, The Constructivist Semantics of Problem

René Gasari, University of Lisboa, Portugal and University of Tübingen, Germany, Avoiding Axioms

Vivek Nigam and Elaine Pimentel, Dpt of Computer Science, Federal University of Paraiba, Brazil and Dpt of Mathematics, Federal University of Minais Gerais UFMG, Relating Focused Proofs with Different Polarity Assignments