Non-Classical Mathematics

Here the schedule of the workshop

Workshop organized by

Libor Behounek and Petr Cintula

Institute of Computer Science,
Academy of Sciences of Czech Republic

The 20th century has witnessed several attempts to build (parts of) mathematics on grounds other than those provided by classical logic. The original intuitionist and constructivist renderings of set theory, arithmetic, analysis, etc. were later accompanied by those based on relevant, paraconsistent, contraction-free, modal, and other non-classical logical frameworks. The bunch of such theories can be called non-classical mathematics and formally understood as a study of (any part of) mathematics that is, or can in principle be, formalized in some logic other than classical logic. The scope of non-classical mathematics includes any mathematical discipline that can be formalized in a non-classical logic or in an alternative foundational theory over classical logic, and topics closely related to such non-classical or alternative theories. (For more information about Non-Classical Mathematics have a look here).

Particular topics of interest include (but are not limited to) the following:

• Intuitionistic, constructive, and predicative mathematics: Heyting arithmetic, intuitionistic set theory, topos-theoretical foundations of mathematics, constructive or predicative set and type theories, pointfree topology, etc.
• Substructural mathematics: relevant arithmetic, contraction-free naive set theories, axiomatic fuzzy set theories, fuzzy arithmetic, etc.
• Inconsistent mathematics: calculi of infinitesimals, inconsistent set theories, etc.
• Modal mathematics: arithmetic or set theory with epistemic, alethic, or other modalities, modal comprehension principles, modal treatments of vague objects, modal structuralism, etc.
• Non-monotonic mathematics: non-monotonic solutions to set-theoretical paradoxes, adaptive set theory, etc.
• Alternative classical mathematics: alternative set theories over classical logic, categorial foundations of mathematics, non-standard analysis, etc.
• Topics related to non-classical mathematics: metamathematics of non-classical or alternative mathematical theories, their relative interpretability, first- or higher-order non-classical logics, etc.

Call for papers

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

behounek@cs.cas.cz  or cintula@cs.cas.cz 

Keynote Speaker

Arnon Avron

Department of Computer Science,
University of Tel Aviv, Israel

Contributing Speakers

Frode Bjørdal, University of Oslo, Norway, A Sober Librationist Interpretation of ZF

Michal Holčapek, University of Ostrava, Czech Republic, Fuzzy Sets and Fuzzy Classes in Universes of Sets

Maarten McKubre-Jordens, University of Canterbury, New Zealand, Constructive Lessons for Paraconsistency

Chris Mortensen, University of Adelaide, Australia, Escher and the Theory of Impossibility

Hitoshi Omori, Kobe University, Japan and City University of New York, USA Remarks on Naive Set Theory Based on da Costa's Idea

Tomasz Polacik, University of Katowice, Poland, A Semantical Approach To Conservativity Of Classical First-Order Theories Over Intuitionistic Ones

Peter Verdee, University of Ghent, Belgium, Adding the Omega-Rule to Peano Arithmetic by Means of Adaptive Logic

Zach Weber, University of Otago, New Zealand, Fixed Point Theorems in Non-Classical Mathematics