11-13 Jun 2015
Prague, Czech Republic
*** Call for papers and proposals for the round-table discussion *** Prague seminar on Non-Classical Mathematics Prague, 11-13. 6. 2015 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 see http://www.cs.cas.cz/ncm/). The goal of this seminar, along with presenting recent advances in particular areas (see the list of topics below), is to provide an opportunity for round-table discussions about the common aspects of various `non-classical' approaches, including similarities between results, proof methods, and methodological questions about the role of classical logic/mathematics in our work. Our goals is to have a compact, well-rounded working seminar with representation from as many different approaches to NCM as possible, and papers will be selected with this in mind. All are welcome to attend and participate at the discussions. Please let us know as soon as possible if you plan to attend and/or submit. Abstracts (up to one page) and the proposals for the round-table discussion (up to one page) should be sent via e-mail before March 15th 2015 to cintula@cs.cas.cz and zach.weber@otago.ac.nz. Related event: the conference LOGICA 2015 (http://logika.flu.cas.cz/en/logica/logica-2015) starts right after our seminar on 15th of June and has the deadline on 15th of February. We hope to see you in Prague in June. P. Cintula and Z. Weber (program and organizing committee) 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, 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.