**7 Dec 2022**

******************************************************************************* Third Call For Participation: Online Workshop Series "Proofs, Computation and Meaning" Online events: September 7, September 28 and December 7, 2022 Website: http://ls.informatik.uni-tuebingen.de/pcm-online/ ******************************************************************************* This online workshop series was originally planned as an in person meeting which was canceled due to the outbreak of the Coronavirus pandemic in early March 2020. The event was planned to bring researchers whose work focuses on the notion of formal proof from either a philosophical, computational or mathematical perspective. With the obvious limitations of an online format, we wish to keep this original motivation, which looks even more timely in a time in which interdisciplinary interactions are made more difficult by the pandemic. The goal is that of creating an opportunity for members of different communities to interact and exchange their views on proofs, their identity conditions, and the more convenient ways of representing them formally. ******************************************************************************* SCOPE: Around thirty years after the fall of Hilbert's program, the proofs-as-programs paradigm established the view that a proof should not be identified, as in Hilbert's metamathematics, with a string of symbols in some formal system. Rather, proofs should consist in computational or epistemic objects conveying evidence to mathematical propositions. The relationship between formal derivations and proofs should then be analogous to the one between words and their meanings. This view naturally gives rise to questions such as “which conditions should a formal arrangement of symbols satisfy to represent a proof?” or “when do two formal derivations represent the same proof?". These questions underlie past and current research in proof theory both in the theoretical computer science community (e.g. categorical logic, domain theory, linear logic) and in the philosophy community (e.g. proof-theoretic semantics). In spite of these common motivations and historical roots, it seems that today proof theorists in philosophy and in computer science are losing sight of each other. This workshop aims at contributing to a renaissance of the interaction between researchers with different backgrounds by establishing a constructive environment for exchanging views, problems and results. ******************************************************************************* ORGANIZATION: The workshop series includes three events, each focusing on one specific aspect of proofs and their representation. To foster interaction and discussion, each event will consists in short talks followed by a 15 minutes slot during which participants can engage in discussion or just take a short break. 1. Infinity and co-inductive proofs September 7, 10-13 am (CET) In Hilbert's program, the role of proof theory was that of assuring a solid finitistic foundations for the use of infinitary concepts in mathematics. By contrast, and somehow paradoxically, the development of the discipline led to the study of proof systems explicitly incorporating infinitary ideas such as impredicativity, co-induction and other constructions. Program: 10:00-10:30 Hidenori Kurokawa (Kanazawa University): "Takeuti's view of a proof-theoretic analysis of the concept of set" 10-30-10:45 Discussion/Break 10:45-11:15 Gilda Ferreira (Universidade Aberta, University of Lisbon): "The Russell-Prawitz embedding and the atomization of universal instantiation" 11-15-11:30 Discussion/Break 11:30-12:00 Laura Crosilla (University of Oslo): "Cantor's paradise?" 12:00-12:15 Discussion/Break 12:15-12:45 David Binder (Tübingen Univerisity): "Can functional programming be liberated from the natural deduction style? Programming in sequent calculus" 12:45-13:00 Discussion 2. On the syntax of proofs September 28, 4-7 pm (CET) Both in natural deduction and in sequent calculs, as well as in their associated type systems, the rules of the standard connectives have been generalized in various ways, thereby obtaining proof-theoretic characterizations of various families of connectives or more generally of data type constructors. Although the motivations for such generalizations are apparently very different (ranging from considerations about the inherent duality of the calculi, to the relation between syntax and semantics, to questions arising in the study of proof-search strategies), they often have a lot in common. Speakers: - Gabriel Scherer (INRIA Paris-Saclay) - Bahareh Afshari (University of Gothenburg) - Herman Geuvers (Nijmegen & Eindhoven University) - Iris van der Giessen (Utrecht University) - Matteo Acclavio (Università Roma Tre) 3. On the nature of proofs December 7, 4-6 pm (CET) The developments of logic, and of proof theory in particular, have lead us to look at proofs primarily through the lens of various formal systems, such as natural deduction, sequent calculus, tableaux, proof nets etc. Yet, is it possible to investigate the nature of proofs, their identity conditions, their relations with computation and with meaning in a direct way, i.e. independently of the choice of a particular formal system? Speakers: - Noam Zeilberger (INRIA Paris-Saclay) - Alberto Naibo (Paris 1 University) - Antonio Piccolomini d'Aragona (Aix-Marseille University) ******************************************************************************* CALL FOR PARTICIPATION: If you wish to attend, please send an e-mail to luca.tranchini@gmail.com or paolo.pistone@uniroma3.it. -- [LOGIC] mailing list http://www.dvmlg.de/mailingliste.html Archive: http://www.illc.uva.nl/LogicList/ provided by a collaboration of the DVMLG, the Maths Departments in Bonn and Hamburg, and the ILLC at the Universiteit van Amsterdam