Classical versus Constructive: An Ecumenical Approach

ABSTRACT

Ecumenism can be understood as the pursuit of unity, a space where diverse thoughts, ideas, or perspectives coexist harmoniously. In logic, ecumenical systems broadly refer to proof systems that combine different logics. One captivating research direction over the past few decades has been the development of systems that merge classical and intuitionistic connectives, allowing them to coexist peacefully. In this talk, we will explore ecumenical systems, drawing inspiration from Prawitz's seminal work. We will begin by elucidating Prawitz's notion of ecumenism, then present several ecumenical proof systems and extend the discussion to include alethic modalities. We will examine translations, Glivenko theorems, and semantics, before concluding with reflections on ecumenism in mathematical proofs and refutations, as well as other approaches to combining classical and constructive behaviours in logical systems.

SHORT BIO:

Elaine Pimentel is a Professor of Logic and Computation in the Department of Computer Science at University College London (UCL), UK. She is also the UCL CS Schools Outreach Lead, Treasurer of ACM SIGLOG, Chair of the Latin American Committee of the Association for Symbolic Logic, and chair of the steering committees of TABLEAUX and LFMTP.

Elaine coordinates the research project ECUMENICAL, and her main research interests span several areas of Logic and Proof Theory, including the specification and verification of concurrent, computational, and logical systems, game semantics, ecumenical logics, and proof systems for automatic reasoning.

She is deeply committed to advancing diversity and inclusion in academia and beyond. Elaine leads the outreach project POTIMÁTICAS to encourage girls to pursue Mathematics and Computer Science. She also runs the platform Mathematics: feminine noun and co-founded the collective Brazilian Female Logicians, which has organized initiatives such as Logic and Representativeness. At UCL, she is an active member of the Athena SWAN group, working to connect her international experience with UCL’s ongoing equality and inclusion initiatives.

Webpage: http://sites.google.com/site/elainepimentel/
DBLP: https://dblp.org/pid/53/5809.html
ORCID: https://orcid.org/0000-0002-7113-0801

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